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Honors Review
Part I Kinematics
coordinate systems, the positive, negative values?
The slope of graphs
Vector vs. scalars
Define average, instantaneous velocity
Compare accuracy, precision, uncertainty.
convert hours to minutes, sec. Km to m or cm.
Know the basic metric prefixes
Define magnitude.
Add vectors.
What is the number of significant digits in the measurement 34.000 m? 34,000? 0.000340?
The slope of a curve
Natural accelerated motions
Units for gravity
negative acceleration could mean what?
definitions:
a. measurement
b. significant digits
c. scientific theory
d. scientific law
e. precision
f. physics
g. accuracy
h. Time dilation
Construct a velocity-time graph comparing two dogs running.
a.
b.
What is the SI unit of_________?
basic unit or a derived unit?
Find the units of measurement of X given an equation.
Differentiate between dependent variable and independent variable.
A boy starts from point A and moves 5 units toward the east, then turns South and moves7 units. What is the displacement
in the position of the boy, including precise direction?
The velocity-time graph of a car’s motion is given below. Plot the corresponding acceleration-time graph.
Problems
Any using the five formulas
The velocity-time graph of the motion of a particle is shown below. Calculate the total displacement of the particle.
A ball is thrown vertically upward with a speed. Calculate the time in which the ball will reach the ground.
Essay
Distinguish between accuracy and precision.
Distinguish between multiplication and addition of sig figs.
Part 2 Dynamics
Dynamics
Remember?
-Good times!!
True/False
Indicate whether the statement is true or false.
____
1. Inertia is a force.
____
2. The net force on an object is the resultant of the force vectors.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
3. ____Which of the following system of forces provides the block the highest net force?
a.
c.
11 N
71 N
b.
227 N
153 N
22.7 N
15.3 N
d.
405 N
403 N
____
4. When an object is in equilibrium, the net force is _____.
a. Zero
c. negative
b. Positive
d. changing
____
5. “ FA on B = -FB on A” is an expression of
a. Newton’s first law
b. Newton’s second law
c. Newton’s third law
d. Fig Newton’s law
6. Tension refers to
a. the force exerted by a string.
b. terminal velocity.
c. dynamic displacement.
d. free fall.
____
____
7. The normal force (FN) refers to
a. the parallel contact force exerted by a surface on another object.
b. the perpendicular contact force exerted by a surface on another object.
c. the perpendicular tension exerted by a surface on a rope.
d. the parallel acceleration of a body at terminal velocity.
____
8. A weight is hung from the ceiling of an elevator by a massless string. Under which circumstances will the
tension in the cord be the greatest?
a. The elevator rises with decreasing speed.
b. The elevator rises with increasing speed.
c. The elevator is at rest.
d. The elevator descends with increasing speed.
____
9. The relationship between force and acceleration is
a. direct linear.
c. direct quadratic.
b. inverse linear.
d. inverse quadratic.
____ 10. A 6.0-kg wooden block is pulled across a carpet with a force of F = 36 N. The block begins at rest and
accelerates to a velocity of 0.25 m/s in 0.50 s. What is the force of friction acting on the block?
a. 3.0 N
c. 36 N
b. 33 N
d. 39 N
____ 11. Which graph most accurately describes the relationship between the force of kinetic friction and the normal
force?
a.
c.
b.
d.
____ 12. You are pushing a rock along level ground and making the rock speed up. How does the size of the force you
exert on the rock compare with the size of the force the rock exerts on you? The force you exert
a. is larger than the force the rock exerts on you.
b. is the same size as the force the rock exerts on you.
c. is smaller than the force the rock exerts on you.
d. could be any of the above; it depends on other factors.
____ 13. How does the size of the friction force exerted by the ground on the rock in the previous problem compare
with the size of the force the rock exerts on you? The force of friction
a. is larger than the force the rock exerts on you.
b. is the same size as the force the rock exerts on you.
c. is smaller than the force the rock exerts on you.
d. could be any of the above; it depends on other factors.
____ 14. Two balls are thrown horizontally. Ball C is thrown with a force of 20 N, and ball D is thrown with a force of
40 N. Assuming all other factors are equal, ball D will fall toward the ground
a. faster than ball C.
b. more slowly than ball C.
c. at the same rate as ball C.
d. at a rate that cannot be compared with that of ball C using the information given.
Short Answer - Draw and lable all the real forces (FBD)
15. A tow truck uses a cable to pull a car onto the flat bed of the tow truck.
16. A piano is hoisted up into an apartment via a cable winch.
Problems
17. A car of mass 1330 kg is traveling at 28.0 m/s. The driver applies the brakes to bring the car to rest over a
distance of 79.0 m. Calculate the retarding force acting on the car.
18. Two men pull a 31-kg box with forces 9.7 N and 7.6 N in the directions shown below. Find the resultant
acceleration of the box and the direction in which the box moves.
9.7 N
7.6 N
19. An elevator is moving down with an acceleration of 3.36 m/s2. What would be the true weight __________ and
apparent weight (Normal force) ________on a 64.2 kg man in the elevator?
Show work.
20. Suppose the box in Problem 18 is on a table with mu ( μ) = 0.15 Find the Normal and the Friction forces.
21.A ball rolls across a table at a constant speed for 0.62 m. It then falls onto the floor. It takes the ball 0.35 s
to cover the 0.62 m. The path of the ball is shown in the drawing. The tabletop is 1.2 m above the floor.
Find t, the time the ball is in the air.
Find x, the distance that the ball travels horizontally after it leaves the tabletop.
22. An astronaut is preparing calculations for a flight to the Moon. The combined mass of the crew, all
equipment, fuel, and the rocket is 2.8106 kg on the launch pad.
a.The rocket’s engines produce a combined 35106 N of thrust. Is this enough to lift the rocket and its
payload?
What if the engines produced 30106 N of thrust?
Would 25106 N be enough?
b. What is the minimum force the rocket needs to exert in order to lift off the ground and accelerate upward?
c.To return to Earth, the crew must take off from the Moon, where gravity is one-sixth that of Earth. Since
most of the mass of the rocket is fuel, assume that three-fourths of the mass was lost in the journey to the
Moon. How much force does the rocket need to exert in order to lift off the surface of the Moon?
23. A sky diver with a mass of 85.0 kg jumps out of an airplane as part of a local air show.
a. Calculate the drag force on the sky diver when she reaches her terminal velocity.
b. Each cord connecting the sky diver and her parachute is rated to hold up to 105 N of tension. How many
cords must the parachute have in order to ensure safe operation when the sky diver opens the parachute after
she reaches terminal velocity?
c. Upon opening, the parachute pulls upward on the sky diver with a force of 950 N. What is the sky diver’s
acceleration with the open parachute? Neglect the mass of the parachute.
24. A Civil War reenactor is setting up a demonstration of targeting with a cannon. The cannon can fire a 4.5 kg
projectile with a total muzzle velocity of 125 m/s.
a.The target is placed 1.00103 m from the cannon. In order to hit the target (at the same height as the cannon)
in 15sec, what should be the cannon’s x velocity?
Original y velocity?
angle of elevation?
b.Given that the maximum range of a shot is achieved at an angle of 45°, what is the maximum range (x)of
the cannon?
What is the maximum height (y) reached by a projectile at this angle?
Two blocks are arranged as shown with your classic very low
friction pulley and light string deal. Find the acceleration of the two
blocks.
25.
3.15 kg
Then find the tension in the string.
3.05 kg
26.A wooden block of 20.0 kg rests on a horizontal wooden plank. The plank is lifted by one end until it forms
a 37° angle with the floor. Pretend there is no friction.
a. Draw a FBD diagram of the forces acting on this block as it is positioned.
b. Find the net Force down the plane.
c. Assume that the plank is 12 m long and that the block is at rest when it starts from the top of the plank.
What is the velocity of the block at the bottom when it slides all the way down this 37° incline?
Bonus: if μs = .25, at what minimum angle does the block start to slide?
Momentum and Collisions Review
Part A: Multiple-Multiple Choice
1. Which of the following statements are true about momentum?
a.
Momentum is a vector quantity.
b.
The standard unit on momentum is the Joule.
c.
An object with mass will have momentum.
d.
An object which is moving at a constant speed has momentum.
e.
An object can be traveling eastward and slowing down; its momentum is westward.
f.
The momentum of an object varies directly with the speed of the object.
g.
Two objects of different mass are moving at the same speed; the more massive object will
have the greatest momentum.
h.
A less massive object can never have more momentum than a more massive object.
i.
Two identical objects are moving in opposite directions at the same speed. The forward
moving object will have the greatest momentum.
j.
An object with a changing speed will have a changing momentum.
2. Which of the following are true about the relationship between momentum end energy?
a.
Momentum is a form of energy.
b.
If an object has momentum, then it must also have mechanical energy.
c.
If an object does not have momentum, then it definitely does not have mechanical energy
either.
3. Which of the following statements are true about impulse?
a.
Impulse is a force.
b.
Impulse is a vector quantity.
c.
An object which is traveling east would experience a westward directed impulse in a collision.
d.
The kg•m/s is equivalent to the units on impulse.
e.
An object which experiences a net impulse will definitely experience a momentum change.
f.
In a collision, the net impulse experienced by an object is equal to its momentum change.
g.
A force of 100 N acting for 0.1 seconds would provide an equivalent impulse as a force of 5 N
acting for 2.0 seconds.
4. Which of the following statements are true about collisions?
a.
Two colliding objects will exert equal forces upon each other even if their mass is significantly
different.
b.
During a collision, an object always encounters an impulse and a change in momentum.
c.
During a collision, the impulse which an object experiences is equal to its velocity change.
d.
The velocity change of two respective objects involved in a collision will always be equal.
e.
While individual objects may change their velocity during a collision, the overall or total
velocity of the colliding objects is conserved.
f.
In a collision, the two colliding objects could have different acceleration values.
g.
In a collision between two objects of identical mass, the acceleration values could be
different.
h.
Total momentum is always conserved between any two objects involved in a collision.
i.
When a moving object collides with a stationary object of identical mass, the stationary
object encounters the greater collision force.
j.
When a moving object collides with a stationary object of identical mass, the stationary
object encounters the greater momentum change.
k.
A moving object collides with a stationary object; the stationary object has significantly less
mass. The stationary object encounters the greater collision force.
l.
A moving object collides with a stationary object; the stationary object has significantly less
mass. The stationary object encounters the greater momentum change.
5. Which of the following statements are true about elastic and inelastic collisions?
a.
Perfectly elastic and perfectly inelastic collisions are the two opposite extremes along a
continuum; where a particular collision lies along the continuum is dependent upon the amount
kinetic energy which is conserved by the two objects.
b.
Most collisions tend to be partially to completely elastic.
c.
Momentum is conserved in an elastic collision but not in an inelastic collision.
d.
The kinetic energy of an object remains constant during an elastic collision.
e.
Elastic collisions occur when the collision force is a non-contact force.
f.
Most collisions are not inelastic because the collision forces cause energy of motion to be
transformed into sound, light and thermal energy (to name a few).
g.
A ball is dropped from rest and collides with the ground. The higher that the ball rises upon
collision with the ground, the more elastic that the collision is.
9. Consider a karate expert. During a talent show, she executes a swift blow to a cement block and breaks it
with her bare hand. During the collision between her hand and the block, the ___.
a.
time of impact on both the block and the expert's hand is the same
b.
force on both the block and the expert's hand have the same magnitude
c.
impulse on both the block and the expert's hand have the same magnitude
d.
all of the above.
e.
none of the above.
10. It is NOT possible for a rocket to accelerate in outer space because ____. List all that apply.
a.
there is no air in space
b.
there is no friction in space
c.
there is no gravity in outer space
d.
... nonsense! Rockets do accelerate in outer space.
11. In order to catch a ball, a baseball player naturally moves his or her hand backward in the direction of the
ball's motion once the ball contacts the hand. This habit causes the force of impact on the players hand to be
reduced in size principally because ___.
a.
the resulting impact velocity is lessened
b.
the momentum change is decreased
c.
the time of impact is increased
d.
the time of impact is decreased
e.
none of these
12. Suppose that Paul D. Trigger fires a bullet from a gun. The speed of the bullet leaving the muzzle will be the
same as the speed of the recoiling gun ____.
a.
because momentum is conserved
b.
because velocity is conserved
c.
because both velocity and momentum are conserved
d.
only if the mass of the bullet equals the mass of the gun
e.
none of these
13. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which
undergoes the greater change is momentum?
a. the moth
b. your car
c. both the same
14. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which
undergoes the greater force?
a. the moth
b. your car
c. both the same
15. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which
undergoes the greater impulse?
a. the moth
b. your car
c. both the same
16. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which
undergoes the greater acceleration?
a. the moth
b. your car
c. both the same
17. Three boxes, X, Y, and Z, are at rest on a table as shown in the diagram at
the right. The weight of each box is indicated in the diagram. The net or
unbalanced force acting on box Y is _____.
a. 4 N down
b. 5 N down
c. 5 N up
d. 10 N up
e. zero
18. In a physics experiment, two equal-mass carts roll towards each other on a level, low-friction track. One cart
rolls rightward at 2 m/s and the other cart rolls leftward at 1 m/s. After the carts collide, they couple (attach
together) and roll together with a speed of _____________. Ignore resistive forces.
a. 0.5 m/s
b. 0.33 m/s
c. 0.67 m/s
d. 1.0 m/s
e. none of these
19. A physics cart rolls along a low-friction track with considerable momentum. If it rolls at the same speed but
has twice as much mass, its momentum is ____.
a. zero
b. four times as large
c. twice as large
d. unchanged
20. The firing of a bullet by a rifle causes the rifle to recoil backwards. The speed of the rifle's recoil is smaller
than the bullet's forward speed because the ___.
a. force against the rifle is relatively small
b. speed is mainly concentrated in the bullet
c. rifle has lots of mass
d. momentum of the rifle is unchanged
e. none of these
21. Two objects, A and B, have the same size and shape. Object A is twice as massive as B. The objects are
simultaneously dropped from a high window on a tall building. (Neglect the effect air resistance.) The objects will
reach the ground at the same time but object A will have a greater ___. Choose all that apply.
a. speed
b. acceleration
c. momentum
d. none of the above quantities will be greater
22. Cars are equipped with padded dashboards. In collisions, the padded dashboards would be safer than nonpadded ones because they ____. List all that apply.
a. increase the impact time
b. decrease an occupant's impulse
c. decrease the impact force
d. none of the above
23. A 4 kg object has a momentum of 12 kg•m/s. The object's speed is ___ m/s.
a. 3
b. 4
c. 12
d. 48
e. none of these.
24. A wad of chewed bubble gum is moving with 1 unit of momentum when it collides with a heavy box that is
initially at rest. The gum sticks to the box and both are set in motion with a combined momentum that is ___.
a. less than 1 unit
b. 1 unit
c. more than 1 unit
d. not enough information
25. A relatively large force acting for a relatively long amount of time on a relatively small mass will produce a
relatively ______. List all that apply.
a. small velocity change
b. large velocity change
c. small momentum change
d. small acceleration
26. Consider the concepts of work and energy (presuming you have already studied it) and those of impuse and
momentum. Force and time is related to momentum change in the same manner as force and displacement
pertains to ___________.
a. impulse
b. work
c. energy change
d. velocity
e. none of these.
27. A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. This impulse causes the
momentum change of the ball to be ____ kg•m/s.
a. -2.5
b. -10
c. -18
d. -45
e. none of these
28. A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. The impulse experienced
by the ball is ____ N•s.
a. -2.5
b. -10
c. -18
d. -45
e. none of these
29. A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. The impulse is
encountered by the ball for a time of ____ seconds.
a. 1.8
b. 2.5
c. 3.6
d. 10
e. none of these
30. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the
same velocity change of v, the force experienced by a mass of 2M in a time of (1/2)t is ____.
a. 2F
b. 4F
c. (1/2)*F
d. (1/4)*F
e. none of these
31. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the
same velocity change of v, the force experienced by a mass of 2M in a time of (1/4)t is ____.
a. 2F
b. 8F
c. (1/2)*F
d. (1/8)*F
e. none of these
32. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the
same velocity change of v, the force experienced by a mass of (1/2)M in a time of (1/2)t is ____.
a. 2F
b. 4F
c. (1/2)*F
d. (1/4)*F
e. none of these
33. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the
same velocity change of v, the force experienced by a mass of (1/2)M in a time of 4t is ____.
a. 2F
b. 8F
c. (1/2)*F
d. (1/8)*F
e. none of these
34. A 0.5-kg ball moving at 5 m/s strikes a wall and rebounds in the opposite direction with a speed of 2 m/s. If
the impulse occurs for a time duration of 0.01 s, then the average force (magnitude only) acting upon the ball is
____ Newtons.
a. 0.14
b. 150
c. 350
d. 500
e. none of these
35. If mass and collision time are equal, then impulses are greater on objects which rebound (or bounce).
a. TRUE
b. FALSE
36. Consider the head-on collision between a lady bug and the windshield of a high speed bus. Which of the
following statements are true? List all that apply.
a.
The magnitude of the force encountered by the bug is greater than that of the bus.
b.
The magnitude of the impulse encountered by the bug is greater than that of the bus.
c.
bus.
The magnitude of the momentum change encountered by the bug is greater than that of the
d.
The magnitude of the velocity change encountered by the bug is greater than that of the bus.
e.
The magnitude of the acceleration encountered by the bug is greater than that of the bus.
Part C: Diagramming and Analysis
For Questions #45-#49, determine the unknown velocity value. Assume that the collisions occur in an isolated
system.
45.
46.
47.
48.
49.
For Questions #50-#52, determine the total kinetic energy of the system before and after the collision and
identify the collision as being either perfectly elastic, partially inelastic/elastic or perfectly inelastic.
50.
Total System Kinetic Energy Before Collision:
Total System Kinetic Energy After Collision:
Perfectly Elastic, Partially Inelastic/Elastic or Perfectly Inelastic?
______________
______________
______________
51.
Total System Kinetic Energy Before Collision:
Total System Kinetic Energy After Collision:
Perfectly Elastic, Partially Inelastic/Elastic or Perfectly Inelastic?
______________
______________
______________
52.
Total System Kinetic Energy Before Collision:
Total System Kinetic Energy After Collision:
Perfectly Elastic, Partially Inelastic/Elastic or Perfectly Inelastic?
______________
______________
______________
Part D: Qualitative Relationships Between Variables
53. An object with a mass M and a velocity v has a momentum of 32 kg•m/s. An object with a mass of ...
a.
... 2M and a velocity of 2v would have a momentum of ____ kg•m/s.
b.
... 2M and a velocity of 0.5v would have a momentum of ____ kg•m/s.
c.
... 0.5M and a velocity of 2v would have a momentum of ____ kg•m/s.
d.
... 0.5M and a velocity of 0.5v would have a momentum of ____ kg•m/s.
e.
... 4M and a velocity of v would have a momentum of ____ kg•m/s.
f.
... 4M and a velocity of 0.5v would have a momentum of ____ kg•m/s.
g.
... 0.5M and a velocity of 4v would have a momentum of ____ kg•m/s.
h.
... 3M and a velocity of 2v would have a momentum of ____ kg•m/s.
54. An object with a mass M and a velocity v undergoes a collision and encounters a force of F for a time of t.
The collision brings the object to a final rest position ...
a.
... If the object had a mass of 2M and a velocity of v, then it would need an impulse which is
____ F•t in order to be brought to rest. (Place a multiplying factor in the blank.)
b.
... If the same object encountered a force of 2F, then it would bring it to rest in a time of
____ t, The impulse would be _____ (twice the, one-half the, the same) size and the momentum
change would be _____ (twice the, one-half the, the same) size.
c.
... If the same object encountered a force of 10F, then it would bring it to rest in a time of
____ t, The impulse would be _____ (ten times the, one-tenth the, the same) size and the
momentum change would be _____ (ten times the, one-tenth the, the same) size.
d.
... If the same object encountered a force of 0.2F, then it would bring it to rest in a time of
____ t, The impulse would be _____ (five times the, one-fifth the, the same) size and the
momentum change would be _____ (five times the, one-fifth the, the same) size.
e.
... If the object had a mass of 2M and a velocity of v encountered a force of 4F, then it
would be brought to rest in a time of ____ t. The impulse would be _____ times the original impulse
(put a multiplier in the blank) and the momentum change would be _____ times the original impulse
(put a multiplier in the blank).
f.
... If the object had a mass of 2M and a velocity of 2v encountered a force of 4F, then it
would be brought to rest in a time of ____ t. The impulse would be _____ times the original impulse
(put a multiplier in the blank) and the momentum change would be _____ times the original impulse
(put a multiplier in the blank).
g.
... If the object had a mass of 0.5M and a velocity of 4v encountered a force of 2F, then it
would be brought to rest in a time of ____ t. The impulse would be _____ times the original impulse
(put a multiplier in the blank) and the momentum change would be _____ times the original impulse
(put a multiplier in the blank).
55. Two carts are placed next to each other on a low-friction track. The carts are equipped with a spring-loaded
mechanism which allows them to impart an impulse to each other. Cart A has a mass of M and Cart B has a
mass of M. The spring-loaded mechanism is engaged and then released. The impulse causes Cart A to be
propelled forward with a velocity of 40 cm/s.
a.
Cart B will be propelled backward with a velocity of ___ cm/s.
b.
cm/s.
... If Cart B had a mass of 2M then it would be propelled backwards with a velocity of ___
c.
cm/s.
... If Cart B had a mass of 0.5M then it would be propelled backwards with a velocity of ___
d.
... If Cart B has a mass of 2M then it would be propelled backwards with a momentum which
is ____ (two times the, one-half the, the same as the) original momentum.
e.
... If Cart B has a mass of 2M then it would encounter an impulse which is ____ (two times
the, one-half the, the same as the) original impulse.
56. A cart with a mass of M is moving along a low-friction track with a speed of 60 cm/s. A brick is gently
dropped from rest upon the cart. After the collision the cart and brick move together.
a.
... If the brick has a mass of 2M, then the post-collision speed of the two objects will be
____ cm/s.
b.
... If the brick has a mass of 3M, then the post-collision speed of the two objects will be
____ cm/s.
c.
... If the brick has a mass of 4M, then the post-collision speed of the two objects will be
____ cm/s.
d.
... If the brick has a mass of 5M, then the post-collision speed of the two objects will be
____ cm/s.
e.
... If the brick has a mass of 0.5M, then the post-collision speed of the two objects will be
____ cm/s.
f.
... If the brick has a mass of 0.25M, then the post-collision speed of the two objects will be
____ cm/s.
Part E: Problem-Solving
57. A 0.530-kg basketball hits a wall head-on with a forward speed of 18.0 m/s. It rebounds with a speed of
13.5 m/s. The contact time is 0.100 seconds. (a) determine the impulse with the wall, (b) determine the force of
the wall on the ball.
58. A 4.0-kg object has a forward momentum of 20. kg•m/s. A 60. N•s impulse acts upon it in the direction of
motion for 5.0 seconds. A resistive force of 6.0 N then impedes its motion for 8.0 seconds. Determine the final
velocity of the object.
59. A 3.0-kg object is moving forward with a speed of 6.0 m/s. The object then encounters a force of 2.5 N for
8.0 seconds in the direction of its motion. The object then collides head-on with a wall and heads in the opposite
direction with a speed of 5.0 m/s. Determine the impulse delivered by the wall to the object.
60. A 46-gram tennis ball is launched from a 1.35-kg homemade cannon. If the cannon recoils with a speed of
2.1 m/s, determine the muzzle speed of the tennis ball.
61. A 2.0-kg box is attached by a string to a 5.0-kg box. A compressed spring is placed between them. The two
boxes are initially at rest on a friction-free track. The string is cut and the spring applies an impulse to both
boxes, setting them in motion. The 2.0-kg box is propelled backwards and moves 1.2 meters to the end of the
track in 0.50 seconds. Determine the time it takes the 5.0-kg box to move 0.90 meters to the opposite end of
the track.
62. Two children are playing with a large snowball while on ice skates on a frozen pond. The 33-kg child tosses
the 5.0-kg snowball, imparting a horizontal speed of 5.0 m/s to it. The 33-kg child is 4.0 meters from a 28-kg
child and 8.0 meters from the edge of the pond (located behind him). Assuming negligible friction, how much
time elapses between when the 28-kg child gets hit by the snowball and when the 33-kg child reaches the edge
of the pond?
63. A 2.8-kg physics cart is moving forward with a speed of 45 cm/s. A 1.9-kg brick is dropped from rest and
lands on the cart. The cart and brick move together across the horizontal surface. Assume an isolated system.
a. Determine the post-collision speed of the cart and the brick.
b. Determine the momentum change of the cart.
c. Determine the momentum change of the brick.
d. Determine the net impulse upon the cart.
e. Determine the net impulse upon the system of cart and brick.
64. In a physics lab, a 0.500-kg cart moving at 36.4 cm/s collides inelastically with a second cart which is
initially at rest. The two carts move together with a speed of 21.8 cm/s after the collision. Determine the mass
of the second cart.
65. A 9230-kg truck collides head on with a 1250-kg parked car. The vehicles entangle together and slide a
linear distance of 10.6 meters before coming to rest. Assuming a uniform coefficient of friction of 0.820 between
the road surface and the vehicles, determine the pre-collision speed of the truck.
66. A classic physics demonstration involves firing a bullet into a block of wood suspended by strings from the
ceiling. The height to which the wood rises below its lowest position is mathematically related to the pre-collision
speed of the bullet. If a 9.7-gram bullet is fired into the center of a 1.1-kg block of wood and it rises upward a
distance of 33 cm, then what was the pre-collision speed of the bullet?
67. At an amusement park, twin brothers Tubby (m = 50 kg) and Chubby (m = 62 kg) occupy separate 36-kg
bumper cars. Tubby gets his car cruising at 3.6 m/s and collides head-on with Chubby who is moving the
opposite direction at 1.6 m/s. After the collision, Tubby bounces backwards at 0.5 m/s. Assuming an isolated
system, determine ...
a. ... Chubby's post-collision speed.
b. ... the percentage of original kinetic energy which is lost as the result of the collision.
69. A 1.72-kg block of soft wood is suspended by two strings from the ceiling. The wood is free to rotate in
pendulum-like fashion when a force is exerted upon it. A 8.50-g bullet is fired into the wood. The bullet enters
the wood at 431 m/s and exits the opposite side shortly thereafter. If the wood rises to a height of 13.8 cm,
then what is the exit speed of the bullet?
70. In a physics lab, the pitching speed of a student is determined by throwing a baseball into a box and
observing the box's motion after the catch. A measurement of the the distance the box slides across a rough
surface of known coefficient of friction will allow one to determine the pre-impact speed of the pitched ball. If a
0.256-kg ball hits a 3.46-kg box and the ball and box slide a distance of 2.89 meters across a surface with a
coefficient of friction of 0.419, then what is the pre-impact speed of the pitched ball?
71. Two ice skaters collide on the ice. A 39.6-kg skater moving South at 6.21 m/s collides with a 52.1-kg skater
moving East at 4.33 m/s. The two skaters entangle and move together across the ice. Determine the magnitude
and direction of their post-collision velocity.
Answers for:Questions #1-5
Questions #6-36
Questions #37-56
Questions #57-72
June starts out hiking due south and travels 4.50 km. When she comes to a canyon running east to west, she
turns due east and travels 12.0 km before stopping for the night.
a.How far did she travel this first day? Draw the vectors of the distances walked.
b.The next day, June consults her map and sets out on a path 35.0° south of due east, hiking 7.75 km before
coming to a river flowing from north to south. She turns due south and follows the river for 11.0 km, and
again she stops for the night. How far did she travel this second day? Draw the vectors of the distances
walked.
c.After two days of hiking, how far is June from her original starting point?
A 5.0 kg mass ,
, and a 7.0 kg mass,
, are connected to a lightweight cord that passes over a frictionless pulley. The
pulley only changes the direction of the force exerted by the rope. The hanging masses are free to move.
What is the acceleration of
if gravity acts in the negative direction?
What is the tension in the cord?
As shown below, two blocks on an inclined plane are connected to each other by a light string, and the upper block also is
connected to a hanging ball by a light string passing over a frictionless pulley of negligible mass. The ball
hangs over the top edge of the inclined plane. The blocks move with a constant velocity down the inclined
plane.
Block 1 has a mass of m1 = 6.00 kg and block 2 has a mass of m2 = 3.00 kg. The inclined plane makes an
angle of  = 32.0° with the horizontal. The coefficient of kinetic friction between each block and the inclined
plane is 0.124.
a.
In the space below, draw and label a free-body diagram of all the forces acting on block 2.
b.
Determine the magnitude of the Normal force and the Force of kinetic friction acting on block 2.
c.
Determine the mass of the hanging ball, M, that enables blocks 1 and 2 to move with constant
velocity down the inclined plane.
Momentum and Collisions Review
Part A: Multiple-Multiple Choice
1. Which of the following statements are true about momentum?
k.
Momentum is a vector quantity.
l.
The standard unit on momentum is the Joule.
m.
An object with mass will have momentum.
n.
An object which is moving at a constant speed has momentum.
o.
An object can be traveling eastward and slowing down; its momentum is westward.
p.
The momentum of an object varies directly with the speed of the object.
q.
Two objects of different mass are moving at the same speed; the more massive object will
have the greatest momentum.
r.
A less massive object can never have more momentum than a more massive object.
s.
Two identical objects are moving in opposite directions at the same speed. The forward
moving object will have the greatest momentum.
t.
An object with a changing speed will have a changing momentum.
2. Which of the following are true about the relationship between momentum end energy?
d.
Momentum is a form of energy.
e.
If an object has momentum, then it must also have mechanical energy.
f.
If an object does not have momentum, then it definitely does not have mechanical energy
either.
3. Which of the following statements are true about impulse?
h.
Impulse is a force.
i.
Impulse is a vector quantity.
j.
An object which is traveling east would experience a westward directed impulse in a collision.
k.
The kg•m/s is equivalent to the units on impulse.
l.
An object which experiences a net impulse will definitely experience a momentum change.
m.
In a collision, the net impulse experienced by an object is equal to its momentum change.
n.
A force of 100 N acting for 0.1 seconds would provide an equivalent impulse as a force of 5 N
acting for 2.0 seconds.
4. Which of the following statements are true about collisions?
m.
Two colliding objects will exert equal forces upon each other even if their mass is significantly
different.
n.
During a collision, an object always encounters an impulse and a change in momentum.
o.
During a collision, the impulse which an object experiences is equal to its velocity change.
p.
The velocity change of two respective objects involved in a collision will always be equal.
q.
While individual objects may change their velocity during a collision, the overall or total
velocity of the colliding objects is conserved.
r.
In a collision, the two colliding objects could have different acceleration values.
s.
In a collision between two objects of identical mass, the acceleration values could be
different.
t.
Total momentum is always conserved between any two objects involved in a collision.
u.
When a moving object collides with a stationary object of identical mass, the stationary
object encounters the greater collision force.
v.
When a moving object collides with a stationary object of identical mass, the stationary
object encounters the greater momentum change.
w.
A moving object collides with a stationary object; the stationary object has significantly less
mass. The stationary object encounters the greater collision force.
x.
A moving object collides with a stationary object; the stationary object has significantly less
mass. The stationary object encounters the greater momentum change.
5. Which of the following statements are true about elastic and inelastic collisions?
h.
Perfectly elastic and perfectly inelastic collisions are the two opposite extremes along a
continuum; where a particular collision lies along the continuum is dependent upon the amount
kinetic energy which is conserved by the two objects.
i.
Most collisions tend to be partially to completely elastic.
j.
Momentum is conserved in an elastic collision but not in an inelastic collision.
k.
The kinetic energy of an object remains constant during an elastic collision.
l.
Elastic collisions occur when the collision force is a non-contact force.
m.
Most collisions are not inelastic because the collision forces cause energy of motion to be
transformed into sound, light and thermal energy (to name a few).
n.
A ball is dropped from rest and collides with the ground. The higher that the ball rises upon
collision with the ground, the more elastic that the collision is.
9. Consider a karate expert. During a talent show, she executes a swift blow to a cement block and breaks it
with her bare hand. During the collision between her hand and the block, the ___.
f.
time of impact on both the block and the expert's hand is the same
g.
force on both the block and the expert's hand have the same magnitude
h.
impulse on both the block and the expert's hand have the same magnitude
i.
all of the above.
j.
none of the above.
10. It is NOT possible for a rocket to accelerate in outer space because ____. List all that apply.
e.
there is no air in space
f.
there is no friction in space
g.
there is no gravity in outer space
h.
... nonsense! Rockets do accelerate in outer space.
11. In order to catch a ball, a baseball player naturally moves his or her hand backward in the direction of the
ball's motion once the ball contacts the hand. This habit causes the force of impact on the players hand to be
reduced in size principally because ___.
f.
the resulting impact velocity is lessened
g.
the momentum change is decreased
h.
the time of impact is increased
i.
the time of impact is decreased
j.
none of these
12. Suppose that Paul D. Trigger fires a bullet from a gun. The speed of the bullet leaving the muzzle will be the
same as the speed of the recoiling gun ____.
f.
because momentum is conserved
g.
because velocity is conserved
h.
because both velocity and momentum are conserved
i.
only if the mass of the bullet equals the mass of the gun
j.
none of these
13. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which
undergoes the greater change is momentum?
a. the moth
b. your car
c. both the same
14. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which
undergoes the greater force?
a. the moth
b. your car
c. both the same
15. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which
undergoes the greater impulse?
a. the moth
b. your car
c. both the same
16. Suppose that you're driving down the highway and a moth crashes into the windshield of your car. Which
undergoes the greater acceleration?
a. the moth
b. your car
c. both the same
17. Three boxes, X, Y, and Z, are at rest on a table as shown in the diagram at
the right. The weight of each box is indicated in the diagram. The net or
unbalanced force acting on box Y is _____.
a. 4 N down
b. 5 N down
c. 5 N up
d. 10 N up
e. zero
18. In a physics experiment, two equal-mass carts roll towards each other on a level, low-friction track. One cart
rolls rightward at 2 m/s and the other cart rolls leftward at 1 m/s. After the carts collide, they couple (attach
together) and roll together with a speed of _____________. Ignore resistive forces.
a. 0.5 m/s
b. 0.33 m/s
c. 0.67 m/s
d. 1.0 m/s
e. none of these
19. A physics cart rolls along a low-friction track with considerable momentum. If it rolls at the same speed but
has twice as much mass, its momentum is ____.
a. zero
b. four times as large
c. twice as large
d. unchanged
20. The firing of a bullet by a rifle causes the rifle to recoil backwards. The speed of the rifle's recoil is smaller
than the bullet's forward speed because the ___.
a. force against the rifle is relatively small
b. speed is mainly concentrated in the bullet
c. rifle has lots of mass
d. momentum of the rifle is unchanged
e. none of these
21. Two objects, A and B, have the same size and shape. Object A is twice as massive as B. The objects are
simultaneously dropped from a high window on a tall building. (Neglect the effect air resistance.) The objects will
reach the ground at the same time but object A will have a greater ___. Choose all that apply.
a. speed
b. acceleration
c. momentum
d. none of the above quantities will be greater
22. Cars are equipped with padded dashboards. In collisions, the padded dashboards would be safer than nonpadded ones because they ____. List all that apply.
a. increase the impact time
b. decrease an occupant's impulse
c. decrease the impact force
d. none of the above
23. A 4 kg object has a momentum of 12 kg•m/s. The object's speed is ___ m/s.
a. 3
b. 4
c. 12
d. 48
e. none of these.
24. A wad of chewed bubble gum is moving with 1 unit of momentum when it collides with a heavy box that is
initially at rest. The gum sticks to the box and both are set in motion with a combined momentum that is ___.
a. less than 1 unit
b. 1 unit
c. more than 1 unit
d. not enough information
25. A relatively large force acting for a relatively long amount of time on a relatively small mass will produce a
relatively ______. List all that apply.
a. small velocity change
b. large velocity change
c. small momentum change
d. small acceleration
26. Consider the concepts of work and energy (presuming you have already studied it) and those of impuse and
momentum. Force and time is related to momentum change in the same manner as force and displacement
pertains to ___________.
a. impulse
b. work
c. energy change
d. velocity
e. none of these.
27. A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. This impulse causes the
momentum change of the ball to be ____ kg•m/s.
a. -2.5
b. -10
c. -18
d. -45
e. none of these
28. A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. The impulse experienced
by the ball is ____ N•s.
a. -2.5
b. -10
c. -18
d. -45
e. none of these
29. A 5-N force is applied to a 3-kg ball to change its velocity from +9 m/s to +3 m/s. The impulse is
encountered by the ball for a time of ____ seconds.
a. 1.8
b. 2.5
c. 3.6
d. 10
e. none of these
30. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the
same velocity change of v, the force experienced by a mass of 2M in a time of (1/2)t is ____.
a. 2F
b. 4F
c. (1/2)*F
d. (1/4)*F
e. none of these
31. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the
same velocity change of v, the force experienced by a mass of 2M in a time of (1/4)t is ____.
a. 2F
b. 8F
c. (1/2)*F
d. (1/8)*F
e. none of these
32. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the
same velocity change of v, the force experienced by a mass of (1/2)M in a time of (1/2)t is ____.
a. 2F
b. 4F
c. (1/2)*F
d. (1/4)*F
e. none of these
33. When a mass M experiences a velocity change of v in a time of t, it experiences a force of F. Assuming the
same velocity change of v, the force experienced by a mass of (1/2)M in a time of 4t is ____.
a. 2F
b. 8F
c. (1/2)*F
d. (1/8)*F
e. none of these
34. A 0.5-kg ball moving at 5 m/s strikes a wall and rebounds in the opposite direction with a speed of 2 m/s. If
the impulse occurs for a time duration of 0.01 s, then the average force (magnitude only) acting upon the ball is
____ Newtons.
a. 0.14
b. 150
c. 350
d. 500
e. none of these
35. If mass and collision time are equal, then impulses are greater on objects which rebound (or bounce).
a. TRUE
b. FALSE
36. Consider the head-on collision between a lady bug and the windshield of a high speed bus. Which of the
following statements are true? List all that apply.
f.
The magnitude of the force encountered by the bug is greater than that of the bus.
g.
The magnitude of the impulse encountered by the bug is greater than that of the bus.
h.
bus.
The magnitude of the momentum change encountered by the bug is greater than that of the
i.
The magnitude of the velocity change encountered by the bug is greater than that of the bus.
j.
The magnitude of the acceleration encountered by the bug is greater than that of the bus.
Part C: Diagramming and Analysis
For Questions #45-#49, determine the unknown velocity value. Assume that the collisions occur in an isolated
system.
45.
46.
47.
48.
49.
For Questions #50-#52, determine the total kinetic energy of the system before and after the collision and
identify the collision as being either perfectly elastic, partially inelastic/elastic or perfectly inelastic.
50.
Total System Kinetic Energy Before Collision:
Total System Kinetic Energy After Collision:
Perfectly Elastic, Partially Inelastic/Elastic or Perfectly Inelastic?
______________
______________
______________
51.
Total System Kinetic Energy Before Collision:
Total System Kinetic Energy After Collision:
Perfectly Elastic, Partially Inelastic/Elastic or Perfectly Inelastic?
______________
______________
______________
52.
Total System Kinetic Energy Before Collision:
Total System Kinetic Energy After Collision:
Perfectly Elastic, Partially Inelastic/Elastic or Perfectly Inelastic?
______________
______________
______________
Part D: Qualitative Relationships Between Variables
53. An object with a mass M and a velocity v has a momentum of 32 kg•m/s. An object with a mass of ...
i.
... 2M and a velocity of 2v would have a momentum of ____ kg•m/s.
j.
... 2M and a velocity of 0.5v would have a momentum of ____ kg•m/s.
k.
... 0.5M and a velocity of 2v would have a momentum of ____ kg•m/s.
l.
... 0.5M and a velocity of 0.5v would have a momentum of ____ kg•m/s.
m.
... 4M and a velocity of v would have a momentum of ____ kg•m/s.
n.
... 4M and a velocity of 0.5v would have a momentum of ____ kg•m/s.
o.
... 0.5M and a velocity of 4v would have a momentum of ____ kg•m/s.
p.
... 3M and a velocity of 2v would have a momentum of ____ kg•m/s.
54. An object with a mass M and a velocity v undergoes a collision and encounters a force of F for a time of t.
The collision brings the object to a final rest position ...
h.
... If the object had a mass of 2M and a velocity of v, then it would need an impulse which is
____ F•t in order to be brought to rest. (Place a multiplying factor in the blank.)
i.
... If the same object encountered a force of 2F, then it would bring it to rest in a time of
____ t, The impulse would be _____ (twice the, one-half the, the same) size and the momentum
change would be _____ (twice the, one-half the, the same) size.
j.
... If the same object encountered a force of 10F, then it would bring it to rest in a time of
____ t, The impulse would be _____ (ten times the, one-tenth the, the same) size and the
momentum change would be _____ (ten times the, one-tenth the, the same) size.
k.
... If the same object encountered a force of 0.2F, then it would bring it to rest in a time of
____ t, The impulse would be _____ (five times the, one-fifth the, the same) size and the
momentum change would be _____ (five times the, one-fifth the, the same) size.
l.
... If the object had a mass of 2M and a velocity of v encountered a force of 4F, then it
would be brought to rest in a time of ____ t. The impulse would be _____ times the original impulse
(put a multiplier in the blank) and the momentum change would be _____ times the original impulse
(put a multiplier in the blank).
m.
... If the object had a mass of 2M and a velocity of 2v encountered a force of 4F, then it
would be brought to rest in a time of ____ t. The impulse would be _____ times the original impulse
(put a multiplier in the blank) and the momentum change would be _____ times the original impulse
(put a multiplier in the blank).
n.
... If the object had a mass of 0.5M and a velocity of 4v encountered a force of 2F, then it
would be brought to rest in a time of ____ t. The impulse would be _____ times the original impulse
(put a multiplier in the blank) and the momentum change would be _____ times the original impulse
(put a multiplier in the blank).
55. Two carts are placed next to each other on a low-friction track. The carts are equipped with a spring-loaded
mechanism which allows them to impart an impulse to each other. Cart A has a mass of M and Cart B has a
mass of M. The spring-loaded mechanism is engaged and then released. The impulse causes Cart A to be
propelled forward with a velocity of 40 cm/s.
f.
Cart B will be propelled backward with a velocity of ___ cm/s.
g.
cm/s.
... If Cart B had a mass of 2M then it would be propelled backwards with a velocity of ___
h.
cm/s.
... If Cart B had a mass of 0.5M then it would be propelled backwards with a velocity of ___
i.
... If Cart B has a mass of 2M then it would be propelled backwards with a momentum which
is ____ (two times the, one-half the, the same as the) original momentum.
j.
... If Cart B has a mass of 2M then it would encounter an impulse which is ____ (two times
the, one-half the, the same as the) original impulse.
56. A cart with a mass of M is moving along a low-friction track with a speed of 60 cm/s. A brick is gently
dropped from rest upon the cart. After the collision the cart and brick move together.
g.
... If the brick has a mass of 2M, then the post-collision speed of the two objects will be
____ cm/s.
h.
... If the brick has a mass of 3M, then the post-collision speed of the two objects will be
____ cm/s.
i.
... If the brick has a mass of 4M, then the post-collision speed of the two objects will be
____ cm/s.
j.
... If the brick has a mass of 5M, then the post-collision speed of the two objects will be
____ cm/s.
k.
... If the brick has a mass of 0.5M, then the post-collision speed of the two objects will be
____ cm/s.
l.
... If the brick has a mass of 0.25M, then the post-collision speed of the two objects will be
____ cm/s.
Part E: Problem-Solving
57. A 0.530-kg basketball hits a wall head-on with a forward speed of 18.0 m/s. It rebounds with a speed of
13.5 m/s. The contact time is 0.100 seconds. (a) determine the impulse with the wall, (b) determine the force of
the wall on the ball.
58. A 4.0-kg object has a forward momentum of 20. kg•m/s. A 60. N•s impulse acts upon it in the direction of
motion for 5.0 seconds. A resistive force of 6.0 N then impedes its motion for 8.0 seconds. Determine the final
velocity of the object.
59. A 3.0-kg object is moving forward with a speed of 6.0 m/s. The object then encounters a force of 2.5 N for
8.0 seconds in the direction of its motion. The object then collides head-on with a wall and heads in the opposite
direction with a speed of 5.0 m/s. Determine the impulse delivered by the wall to the object.
60. A 46-gram tennis ball is launched from a 1.35-kg homemade cannon. If the cannon recoils with a speed of
2.1 m/s, determine the muzzle speed of the tennis ball.
61. A 2.0-kg box is attached by a string to a 5.0-kg box. A compressed spring is placed between them. The two
boxes are initially at rest on a friction-free track. The string is cut and the spring applies an impulse to both
boxes, setting them in motion. The 2.0-kg box is propelled backwards and moves 1.2 meters to the end of the
track in 0.50 seconds. Determine the time it takes the 5.0-kg box to move 0.90 meters to the opposite end of
the track.
62. Two children are playing with a large snowball while on ice skates on a frozen pond. The 33-kg child tosses
the 5.0-kg snowball, imparting a horizontal speed of 5.0 m/s to it. The 33-kg child is 4.0 meters from a 28-kg
child and 8.0 meters from the edge of the pond (located behind him). Assuming negligible friction, how much
time elapses between when the 28-kg child gets hit by the snowball and when the 33-kg child reaches the edge
of the pond?
63. A 2.8-kg physics cart is moving forward with a speed of 45 cm/s. A 1.9-kg brick is dropped from rest and
lands on the cart. The cart and brick move together across the horizontal surface. Assume an isolated system.
a. Determine the post-collision speed of the cart and the brick.
b. Determine the momentum change of the cart.
c. Determine the momentum change of the brick.
d. Determine the net impulse upon the cart.
e. Determine the net impulse upon the system of cart and brick.
64. In a physics lab, a 0.500-kg cart moving at 36.4 cm/s collides inelastically with a second cart which is
initially at rest. The two carts move together with a speed of 21.8 cm/s after the collision. Determine the mass
of the second cart.
65. A 9230-kg truck collides head on with a 1250-kg parked car. The vehicles entangle together and slide a
linear distance of 10.6 meters before coming to rest. Assuming a uniform coefficient of friction of 0.820 between
the road surface and the vehicles, determine the pre-collision speed of the truck.
66. A classic physics demonstration involves firing a bullet into a block of wood suspended by strings from the
ceiling. The height to which the wood rises below its lowest position is mathematically related to the pre-collision
speed of the bullet. If a 9.7-gram bullet is fired into the center of a 1.1-kg block of wood and it rises upward a
distance of 33 cm, then what was the pre-collision speed of the bullet?
67. At an amusement park, twin brothers Tubby (m = 50 kg) and Chubby (m = 62 kg) occupy separate 36-kg
bumper cars. Tubby gets his car cruising at 3.6 m/s and collides head-on with Chubby who is moving the
opposite direction at 1.6 m/s. After the collision, Tubby bounces backwards at 0.5 m/s. Assuming an isolated
system, determine ...
a. ... Chubby's post-collision speed.
b. ... the percentage of original kinetic energy which is lost as the result of the collision.
69. A 1.72-kg block of soft wood is suspended by two strings from the ceiling. The wood is free to rotate in
pendulum-like fashion when a force is exerted upon it. A 8.50-g bullet is fired into the wood. The bullet enters
the wood at 431 m/s and exits the opposite side shortly thereafter. If the wood rises to a height of 13.8 cm,
then what is the exit speed of the bullet?
70. In a physics lab, the pitching speed of a student is determined by throwing a baseball into a box and
observing the box's motion after the catch. A measurement of the the distance the box slides across a rough
surface of known coefficient of friction will allow one to determine the pre-impact speed of the pitched ball. If a
0.256-kg ball hits a 3.46-kg box and the ball and box slide a distance of 2.89 meters across a surface with a
coefficient of friction of 0.419, then what is the pre-impact speed of the pitched ball?
71. Two ice skaters collide on the ice. A 39.6-kg skater moving South at 6.21 m/s collides with a 52.1-kg skater
moving East at 4.33 m/s. The two skaters entangle and move together across the ice. Determine the magnitude
and direction of their post-collision velocity.
Answers for:Questions #1-5
Questions #6-36
Questions #37-56
Questions #57-72
Work and Energy Review
Part A: Forced Choice Questions
1. Which of the following statements are true about work? Include all that apply.
a.
Work is a form of energy.
b.
A Watt is the standard metric unit of work.
c.
Units of work would be equivalent to a Newton times a meter.
d.
A kg•m2/s2 would be a unit of work.
e.
Work is a time-based quantity; it is dependent upon how fast a force displaces an object.
f.
Superman applies a force on a truck to prevent it from moving down a hill. This is an
example of work being done.
g.
An upward force is applied to a bucket as it is carried 20 m across the yard. This is an
example of work being done.
h.
A force is applied by a chain to a roller coaster car to carry it up the hill of the first drop of
the Shockwave ride. This is an example of work being done.
i.
The force of friction acts upon a softball player as she makes a headfirst dive into third base.
This is an example of work being done.
j.
An eraser is tied to a string; a person holds the string and applies a tension force as the
eraser is moved in a circle at constant speed. This is an example of work being done.
k.
A force acts upon an object to push the object along a surface at constant speed. By itself,
this force must NOT be doing any work upon the object.
l.
A force acts upon an object at a 90-degree angle to the direction that it is moving. This force
is doing negative work upon the object.
m.
An individual force does NOT do positive work upon an object if the object is moving at
constant speed.
n.
work.
An object is moving to the right. A force acts leftward upon it. This force is doing negative
o.
A non-conservative force is doing work on an object; it is the only force doing work.
Therefore, the object will either gain or lose mechanical energy.
2. Which of the following statements are true about power? Include all that apply.
a.
Power is a time-based quantity.
b.
Power refers to how fast work is done upon an object.
c.
Powerful people or powerful machines are simply people or machines which always do a lot
of work.
d.
A force is exerted on an object to move it at a constant speed. The power delivered by this
force is the magnitude of the force multiplied by the speed of the object.
e.
The standard metric unit of power is the Watt.
f.
If person A and person B do the same job but person B does it faster, then person A does
more work but person B has more power.
g.
The Newton•meter is a unit of power.
h.
Watt.
A 60-kg boy runs up a 2.0 meter staircase in 1.5 seconds. His power is approximately 80
i.
A 300-Newton force is applied to a skier to drag her up a ski hill at a constant speed of 1.5
m/s. The power delivered by the toe rope is 450 Watts.
3. Consider the following physical situations. For each case, determine the angle between the indicated force (in
boldface type) and the displacement ("theta" in the work equation).
a. 0 degrees
b. 180 degrees
c. 90 degrees
d. 30 degrees
e. 60 degrees
a.
A rightward applied force is used to displace a television set to the right.
b.
The force of friction acts upon a rightward-moving car to bring it to a stop.
c.
A waiter uses an applied force to balance the weight of a tray of plates as he carries the
tray across the room.
d.
The force of air resistance acts upon a vertically-falling skydiver.
e.
The force of friction acts upon a baseball player as he slides into third base.
f.
An applied force is used by a freshman to lift a World Civilization book to the top shelf of
his locker.
g.
A bucket of water is tied to a string and tension supplies the centripetal force to keep it
moving in a circle at constant speed.
h.
right.
An applied force acting at 30-degrees to the horizontal is used to displace an object to the
i.
A group of football players use an applied force to push a sled across the grass.
j.
The tension in the elevator cable causes the elevator to rise at a constant speed.
k.
In a physics lab, an applied force is exerted parallel to a plane inclined at 30-degrees in
order to displace a cart up the incline.
l.
An applied force is exerted upwards and rightwards at an angle of 30-degrees to the
vertical in order to displace an object to the right.
m.
A child rests on the seat of a swing which is supported by the tension in its cables; he
swings from the highest position to its lowest position.
4. Consider the following physical situations. Identify whether the indicated force (in boldface type) does
positive work, negative work or no work.
a. Positive Work
b. Negative Work
c. No Work
Description of Physical Situation
a. A cable is attached to a bucket and the force of tension is used to pull the
+, -, or no Work
_______________
bucket out of a well.
b. Rusty Nales uses a hammer to exert an applied force upon a stubborn nail to
_______________
drive it into the wall.
c. Near the end of the Shockwave ride, a braking system exerts an applied
_______________
force upon the coaster car to bring it to a stop.
d. The force of friction acts upon a baseball player as he slides into third base.
e. A busy spider hangs motionless from a silk thread, supported by the tension
_______________
_______________
in the thread.
f. In baseball, the catcher exerts an abrupt applied force upon the ball to stop it
_______________
in the catcher's mitt.
g. In a physics lab, an applied force is exerted parallel to a plane inclined at 30-
_______________
degrees in order to displace a cart up the incline.
h. A pendulum bob swings from its highest position to its lowest position under
the influence of the force of gravity.
_______________
5. Which of the following statements are true about conservative and non-conservative forces? Include all that
apply.
a.
A force is regarded as a conservative force if it does work but does not remove mechanical
energy from a system of objects.
b.
A force is regarded as a non-conservative force if it does not add mechanical energy to a
system of objects.
c.
The force of gravity and elastic (spring) force are both examples of a conservative forces.
d.
Applied forces, air resistance, friction forces, and tension are common examples of nonconservative forces.
e.
Physicists envy biologists' ability to instill order on the world of animal species through their
taxonomic system. So physicists have made a habit of identifying forces as conservative and nonconservative forces in order to instill order on the world of forces.
f.
If a non-conservative force acts upon an object, then the object will either gain or lose
mechanical energy.
g.
If the only forces which do work upon an object are conservative forces, then the object will
conserve its mechanical energy.
h.
If the sum of an object's KE and PE is remaining constant, then non-conservative forces are
NOT doing work.
i.
If work is NOT done on an object by a non-conservative force, then the object will experience
a transformation of energy from kinetic to potential energy (or vice versa).
j.
An object starts from an elevated position with 50 J of potential energy and begins its fall
towards the ground. If non-conservative forces can be assumed to NOT do work, then at some point
during the fall the object will have 20 J of potential energy and 30 J of kinetic energy.
6. Which of the following statements are true about kinetic energy? Include all that apply.
a.
Kinetic energy is the form of mechanical energy which depends upon the position of an
object.
b.
If an object is at rest, then it does not have any kinetic energy.
c.
If an object is on the ground, then it does not have any kinetic energy.
d.
The kinetic energy of an object is dependent upon the weight and the speed of an object.
e.
Faster moving objects always have a greater kinetic energy.
f.
More massive objects always have a greater kinetic energy.
g.
Kinetic energy is a scalar quantity.
h.
An object has a kinetic energy of 40 J. If its mass were twice as much, then its kinetic energy
would be 80 J.
i.
An object has a kinetic energy of 40 J. If its speed were twice as much, then its kinetic
energy would be 80 J.
j.
Object A has a mass of 1 kg and a speed of 2 m/s. Object B has a mass of 2 kg and a speed
of 1 m/s. Objects A and B have the same kinetic energy.
k.
An object can never have a negative kinetic energy.
l.
A falling object always gains kinetic energy as it falls.
m.
A 1-kg object is accelerated from rest to a speed of 2.0 m/s. This object gains 4.0 Joules of
kinetic energy.
n.
If work is done on an object by a non-conservative force, then the object will either gain or
lose kinetic energy.
7. Which of the following statements are true about potential energy? Include all that apply.
a.
Moving objects cannot have potential energy.
b.
Potential energy is the energy stored in an object due to its position.
c.
Both gravitational and elastic potential energy are dependent upon the mass of an object.
d.
The gravitational potential energy of an object is dependent upon the mass of the object.
e.
If the mass of an elevated object is doubled, then its gravitational potential energy will be
doubled as well.
f.
Gravitational potential energy is lost as objects free-fall to the ground.
g.
The higher that an object is, the more potential energy which it will have.
h.
The unit of measurement for potential energy is the Joule.
i.
A 1-kg mass at a height of 1 meter has a potential energy of 1 Joule.
j.
A 1-kg object falls from a height of 10 m to a height of 6 m. The final potential energy of the
object is approximately 40 J.
k.
If work is done on an object by a non-conservative force, then the object will either gain or
lose potential energy.
8. Which of the following statements are true about mechanical energy? Include all that apply.
a.
The total amount of mechanical energy of an object is the sum of its potential energy and the
kinetic energy.
b.
Heat is a form of mechanical energy.
c.
The mechanical energy of an object is always conserved.
d.
When non-conservative forces do work, energy is transformed from kinetic to potential (or
vice versa), but the total mechanical energy is conserved.
e.
A bowling ball is mounted from a ceiling by way of a strong cable. It is drawn back and
released, allowed to swing as a pendulum. As it swings from its highest position to its lowest position,
the total mechanical energy is mostly conserved.
f.
When a friction force does work on an object , the total mechanical energy of that object is
changed.
g.
The total mechanical energy of an object remains constant if the only forces doing work on
the object are conservative forces.
h.
If an object gains mechanical energy, then one can be certain that a non-conservative force
is doing work.
9. Rank these four objects in increasing order of kinetic energy, beginning with the smallest.
Object B
Object C
Object D
m = 5.0 kg
m = 10.0 kg
m = 1.0 kg
m = 5.0 kg
v = 4.0 m/s
v = 2.0 m/s
v = 5.0 m/s
v = 2.0 m/s
h = 2.0 m
h = 3.00 m
h = 5.0 m
h = 4.0 m
Object A
10. Rank these four objects in increasing order of potential energy, beginning with the smallest.
Object B
Object C
Object D
m = 5.0 kg
m = 10.0 kg
m = 1.0 kg
m = 5.0 kg
v = 4.0 m/s
v = 2.0 m/s
v = 5.0 m/s
v = 2.0 m/s
h = 2.0 m
h = 3.00 m
h = 5.0 m
h = 4.0 m
Object A
NOTE: The next 15 questions approximate the value of g as 10 m/s/s.
11. A 1200 kg car and a 2400 kg car are lifted to the same height at a constant speed in a auto service station.
Lifting the more massive car requires ____ work.
a. less
b. the same
d. four times as much
e. more than 4 times as much
c. twice as much
12. An arrow is drawn back so that 50 Joules of potential energy is stored in the stretched bow and string. When
released, the arrow will have a kinetic energy of ____ Joules.
a. 50
b. more than 50
c. less than 50
13. A child lifts a box up from the floor. The child then carries the box with constant speed to the other side of
the room and puts the box down. How much work does he do on the box while walking across the floor at
constant speed?
a. zero J
b. more than zero J
c. more information needed to determine
14. A 1000-kg car is moving at 40.0 km/hr when the driver slams on the brakes and skids to a stop (with locked
brakes) over a distance of 20.0 meters. How far will the car skid with locked brakes if it is traveling at 120.
km/hr?
a. 20.0 m
b. 60.0 m
c. 90.0 m
d. 120. m
e. 180. m
15. A platform diver weighs 500 N. She steps off a diving board that is elevated to a height of 10 meters above
the water. The diver will possess ___ Joules of kinetic energy when she hits the water.
a. 10
b. 500
c. 510
d. 5000
e. more than 5000 .
16. A ball is projected into the air with 100 J of kinetic energy. The kinetic energy is transformed into
gravitational potential energy on the path towards the peak of its trajectory. When the ball returns to its original
height, its kinetic energy is ____ Joules. Do consider the effects of air resistance
a. less than 100
b. 100
c. more than 100
d. not enough information given
17. During a construction project, a 2500 N object is lifted high above the ground. It is released and falls 10.0
meters and drives a post 0.100 m into the ground. The average impact force on the object is ____ Newtons.
a. 2500
b. 25000
c. 250,000
d. 2,500,000
18. A 10-Newton object moves to the left at 1 m/s. Its kinetic energy is approximately ____ Joules.
a. 0.5
b. 1
c. 10
d. more than 10
19. Luke Autbeloe stands on the edge of a roof throws a ball downward. It strikes the ground with 100 J of
kinetic energy. Luke now throws another identical ball upward with the same initial speed, and this too falls to
the ground. Neglecting air resistance, the second ball hits the ground with a kinetic energy of ____ J.
a. less than 100
b. 100
c. 200
d. more than 200
e. none of these
20. An object at rest may have __________.
a. speed
b. velocity
c. acceleration
d. energy
e. all of these
21. A 50-kg platform diver hits the water below with a kinetic energy of 5000 Joules. The height (relative to the
water) from which the diver dove was approximately ____ meters.
a. 5
b. 10
c. 50
d. 100
22. A job is done slowly, and an identical job is done quickly. Both jobs require the same amount of ____, but
different amounts of ____. Pick the two words which fill in the blanks in their respective order.
a. energy, work
b. power, work
c. work, energy
d. work, power
e. power, energy
f. force, work
g. power, force
h. none of these
23. Which requires more work: lifting a 50.0 kg crate a vertical distance of 2.0 meters or lifting a 25.0 kg crate a
vertical distance of 4.0 meters?
a. lifting the 50 kg sack
b. lifting the 25 kg sack
c. both require the same amount of work
24. A 50.0 kg crate is lifted to a height of 2.0 meters in the same time as a 25.0 kg crate is lifted to a height of
4 meters. The rate at which energy is used (i.e., power) in raising the 50.0 kg crate is ____ as the rate at which
energy is used to lift the 25.0 kg crate.
a. twice as much
b. half as much
c. the same
25. Using 1000. J of work, a small object is lifted from the ground floor to the third floor of a tall building in 20.0
seconds. What power was required in this task?
a. 20 W
b. 50 W
c. 100 W
d. 1000 W
e. 20000 W
Part B: Straightforward Computational Problems
26. Approximate the work required lift a 2.5-kg object to a height of 6.0 meters. PSYW
27. A student applies a force to a cart to pull it up an inclined plane at constant speed during a physics lab. A
force of 20.8 N is applied parallel to the incline to lift a 3.00-kg loaded cart to a height of 0.450 m along an
incline which is 0.636-m long. Determine the work done upon the cart and the subsequent potential energy
change of the cart. PSYW
28. Eddy, whose mass is 65-kg, climbs up the 1.6-meter high stairs in 1.2 s. Approximate Eddy's power rating.
PSYW
29. A 51.7-kg hiker ascends a 43.2-meter high hill at a constant speed of 1.20 m/s. If it takes 384 s to climb the
hill, then determine ... . PSYW
a.
kinetic energy change of the hiker.
b.
the potential energy change of the hiker.
c.
the work done upon the hiker.
d.
the power delivered by the hiker.
30. An 878-kg car skids to a stop across a horizontal surface over a distance of 45.2 m. The average force acting
upon the car is 7160 N. Determine ... . PSYW
a.
the work done upon the car.
b.
the initial kinetic energy of the car.
c.
the acceleration of the car.
d.
the initial velocity of the car.
31. A 510-kg roller coaster car starts at a height of 32.0 m. Assuming negligible energy losses to friction and air
resistance, determine the PE, KE, and speed of the car at the various locations (A, B, C, D, and E) along the
track.
Location
Start
A
B
C
D
E
F
Height (m)
32.0
28.0
11.0
20.0
5.0
15.0
0
PE (J)
________
________
________
________
________
________
________
KE (J)
________
________
________
________
________
________
________
velocity (m/s)
0
________
________
________
________
________
________
32. A 65.8-kg skier accelerates down an icy hill from an original height of 521 meters. Use the work-energy
theorem to determine the speed at the bottom of the hill if...
a. ... no energy is lost or gained due to friction, air resistance and other non-conservative forces. PSYW
b. ... 1.40*105 J of energy are lost due to external forces. PSYW
33. Use the work-energy theorem to determine the force required to stop a 988-kg car moving at a speed of
21.2 m/s if there is a distance of 45.7 m in which to stop it. PSYW
Part C: Work-Energy Bar Charts, Analysis, and Conceptual Reasoning
34. Consider the following physical situations. Identify the forces which do work upon the indicated object (in
boldface type) and categorize them as conservative or non-conservative forces. Then indicate whether the
total mechanical energy of the object changes; it it changes, then indicate whether the change is a positive or
negative change. Finally, indicate whether the potential energy and the kinetic energy changes; if PE or KE
changes, then indicate whether the change is a positive or negative change.
Description of Physical
Situation
Identity of Forces
Which Do Work:
Conserv.
a. A force is applied to move a
Change in TME Change in PE Change in KE
Non-
Yes
Conserv.
(+ or -)
_________ _________
_____
No
Yes
(+ or -)
_____
No
Yes
No
(+ or -)
_____ _____ _____ _____
physics cart from the floor to the
top of an inclined plane at a
constant speed.
b. A physics student scurries up a
_________ _________
_____
_____
_____ _____ _____ _____
_________ _________
_____
_____
_____ _____ _____ _____
_________ _________
_____
_____
_____ _____ _____ _____
_________ _________
_____
_____
_____ _____ _____ _____
_________ _________
_____
_____
_____ _____ _____ _____
_________ _________
_____
_____
_____ _____ _____ _____
_________ _________
_____
_____
_____ _____ _____ _____
_________ _________
_____
_____
_____ _____ _____ _____
flight of stairs at constant speed.
c. In a moment of unsupervised
phun, a physics student hoists
herself onto a staircase banister and
accelerates down the banister.
Ignore all friction forces.
d. A ball is dropped from rest from
on the top of a hill and falls to the
ground below. Ignore air resistance.
e. A ball leaves top of a hill with a
large horizontal velocity. It falls to
the ground below. Ignore air
resistance.
f. A Hot Wheels car is at rest at an
elevated position along an inclined
plane; it is released and rolls to a
position along the ground. Ignore air
resistance.
g. A Hot Wheels car is in motion at
the bottom of a hill when it hits a
computer diskette box and skids to a
stop.
h. A pendulum bob swings from its
highest position to its lowest
position.
i. A physics cart is released from
rest at an elevated position along an
inclined plane; it is released and
rolls to a position along the incline
approximately 5 cm from the
bottom.
35. The diagrams below depict a physical situation. Analyze each situation and construct work-energy bar
charts.
Work-Energy Bar Chart
Description of Physical Situation
a. A Hot Wheels car starts from rest on top
of an inclined plane and rolls down the
incline through a loop and along a
horizontal surface. Ignore the effect of
friction and air resistance on the car.
b. A Hot Wheels car starts from rest on
top of an inclined plane and rolls down
the incline through a loop and along a
horizontal surface. Friction and air
resistance have a significant effect on the
car.
c. A pendulum bob is mounted on
top of a lab pole and drawn back
to a string which it tied between
two other poles. The pendulum
bob is released from rest. Upon reaching the vertical, the string hits a
barrier and a new pivot point is established as the bob continues in
motion along an upward trajectory. Ignore the effect of air resistance.
d. A track is constructed by stretching a
grooved and pliable material between two
lab poles. A metal ball starts from rest at
point A and rolls along the groove to point
B. Friction and air resistance have an
effect upon the ball's motion.
e. A dart is placed in a dart
gun and the springs are
compressed. The trigger is
pulled and the dart is projected
towards a wall. The dart
collides with the wall and
sticks to it. Ignore the effect of friction and air resistance.
f. Ben Laborin applies a
force to push a crate from
the bottom of an inclined
plane to the top at a
constant speed.
36. Several physical situations are described below. For each situation, simplify the work-energy equation by
canceling any zero terms and any energy terms (whether KE or PE) which are unchanging. Explain each term
which gets canceled. The first problem is done as an example.
Description of Physical Situation
a. A ball starts from rest on top of a tall
pillar and falls to the ground below.
Assume the effect of air resistance is
negligible.
Simplification of Work-Energy Equation
KEi + PEi + Wnc = KEf + PEf
b. A ball starts from rest at
an elevated position along an
KEi + PEi + Wnc = KEf + PEf
inclined plane and rolls to the
ground below. Assume that
the effect of friction and air
resistance is negligible.
c. A ball starts from rest at
an elevated position along an
KEi + PEi + Wnc = KEf + PEf
inclined plane and rolls to the
ground below. Consider the
effect of friction and air
resistance.
d. A track is constructed by stretching
a grooved and pliable material
KEi + PEi + Wnc = KEf + PEf
between two lab poles. A metal ball
starts from rest at point A and rolls to
point B. Friction and air resistance
have an effect upon the ball's motion.
e. A pendulum bob is
mounted on top of a lab pole
KEi + PEi + Wnc = KEf + PEf
and drawn back to a string
which it tied between two
other poles. The pendulum
bob is released from rest. Upon reaching the vertical, the string
hits a barrier and a new pivot point is established as the bob
continues in motion along an upward trajectory. Ignore the effect
of air resistance.
f. A Hot Wheels car starts from rest
on top of an inclined plane and rolls
down the incline through a loop and
along a horizontal surface. Friction
and air resistance have a significant
effect on the car.
KEi + PEi + Wnc = KEf + PEf
g. An unattended hot dog wagon starts
from rest and rolls down a hill and up a
KEi + PEi + Wnc = KEf + PEf
second hill. Ignore the effect of friction
and air resistance.
h. A roller coaster car is already
in motion on the top of the first
KEi + PEi + Wnc = KEf + PEf
drop and rolls along the track
over a couple of hills. Ignore the
effect of friction and air resistance.
i. A cross-country
skier is in motion on
KEi + PEi + Wnc = KEf + PEf
top of a small hill.
He skis down the hill
into the valley and
up a second smaller hill. He uses his poles to propel himself
during the entire motion. Ignore the effect of friction and air
resistance.
Part D: Complex Analysis and Problem-Solving
37. A 21.3-kg child positions himself on an inner-tube which is suspended by a 7.28-m long rope attached to a
strong tree limb. The child and tube is drawn back until it makes a 17.4-degree angle with the vertical. The child
is released and allowed to swing to and from. Assuming negligible friction, determine the child's speed at his
lowest point in the trajectory. PSYW
38. A baseball player catches a 163-gram baseball which is moving horizontally at a speed of 39.8 m/s.
Determine the force which she must apply to the baseball if her mitt recoils a horizontal distance of 25.1 cm.
PSYW
39. A 62.9-kg downhill skier is moving with a speed of 12.9 m/s as he starts his descent from a level plateau at
123-m height to the ground below. The slope has an angle of 14.1 degrees and a coefficient of friction of 0.121.
The skier coasts the entire descent without using his poles; upon reaching the bottom he continues to coast to a
stop; the coefficient of friction along the level surface is 0.623. How far will he coast along the level area at the
bottom of the slope? PSYW
40. A 29.1-kg sledder is traveling along a level area with a speed of 8.96 m/s when she approaches a gentle
incline which makes an angle of 12.5 degrees with the horizontal. If the coefficient of friction between the sled
and the incline is 0.109, then what will be her speed at the bottom of the inclined plane, located 8.21 m above
the top of the incline. PSYW
41. A 221-gram ball is thrown at an angle of 17.9 degrees and a speed of 36.7 m/s from the top of a 39.8-m
high cliff. Determine the impact speed of the ball when it strikes the ground. Assume negligible air resistance.
PSYW
42. Claire deAisles has just completed her shopping at the grocery food store. She accidentally bumps her 42.5kg cart, setting it in motion from rest down a hill inclined at 14.9 degrees. Upon descending a distance of 9.27
meters along the inclined plane, the cart hits a tree stump (which was placed in the parking lot for the sole
purpose of this problem). A 0.295-kg can of tomato soup is immediately hurled from the moving cart and heads
towards Will N. Tasue's brand new Lexus. Upon striking the Lexus, the tomato soup can creates a dent with a
depth of 3.16 cm. Noah Formula, who is watching the entire incident and fixing to do some physics, attempts to
calculate the average force which the Lexus applies to the soup can. Assume negligible air resistance and friction
forces and help Noah out. PSYW
43. Pete Zaria applies a 11.9-Newton force to a 1.49-kg mug of root beer in order to accelerate it from rest over
a distance of 1.42-m. Once released, how far will the mug slide along the counter top if the coefficient of friction
is 0.728? PSYW
44. Suzie Lovtaski has a mass of 49.7 kg. She is at rest on top of a hill with a height of 92.6 m and an incline
angle of 19.2 degrees. She coasts down the hill to the bottom and eventually comes to a stop; she never uses
her poles to apply a force. The coefficient of friction is 0.0873 along the hill and 0.527 along the horizontal
surface at the bottom. What total distance will Suzie coast (include both incline and level surface)? PSYW
45. Mia Kneezhirt jumps from a second story dorm room (h = 7.91 m) to the ground below. Upon contact with
the ground, she allows her 62.4-kg body to come to an abrupt stop as her center of gravity is displaced
downwards a distance of 89.2 cm. Calculate the average upward force exerted by the ground upon Mia's fragile
body. PSYW
Navigate to Answers for:
Questions #1-#10
Questions #11-#25
Questions #26-#36
Questions #37-#45