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Midterm Review Sheets Jan. 2010
Physics Mathematical
Math and Units
Metric units
Metric prefixes
Scientific notation
Significant figures
Graphing techniques
Dimensional analysis (units cancellation)
Problems
1.
2.
convert 50 km/hr to m/s
How many grams in 3.62 kg?
3. How many meters in 24.5 cm?
4. Multiply 2.54 x 10-6 by 6.95 x 1012
5. What is the slope of a straight line equal to?
Chapter 2
Motion 1-D
coordinates
displacement v/s distance
Velocity
Average
instantaneous
Change in d
change in t
Acceleration
Change in v
change in t
Constant velocity
Constant acceleration
Displacement time graphs
Graphs
v v/s t
a v/s t
Acceleration – positive and negative
Freefall
Initial velocity
Acceleration due to gravity
Object dropped
Object thrown up vertically
Object thrown down vertically
Effect of air resistance
Freefall Time independent of mass if no air resistance
Formulas
horizontal
Vf = vi +at
Vf2 = vi2 +2a(x)
Xf = xi +vit + 1/2 at2
Vaverage = (vf+vi)/2
vertical
Vf = vi +gt
Vf2 = vi2 +2gy
yf = yi +vit + 1/2 gt2
Labs
Graphical analysis of motion
Motion of a buggy
Motion of a bike
Measurement of g
Problems
1. A plane must reach a speed of 30 m/s for takeoff. How long a runway is needed if the plane can accelerate at 3.0
m/sec2
2. A world class sprinter can burst out of the blocks to a top speed of 11.5 m/s in the first 15 m of the race.
Calculate the sprinter’s acceleration.
How long does it take the sprinter to reach that top speed?
________
3. Calculate first, how long it took for King Kong to fall straight down from the Empire State Building (380 m high)
.
How fast was he going when he splattered on the streets of New York?
4. A car with good tires on a dry road can decelerate at 5.0 m/s 2 when braking. If a car is traveling at 25 m/s on
Route 80, how much time does it take for the car to stop?
5.A ball is thrown straight upward with a speed of 30 m/sec. What is the maximum height reached by the ball ?
a. 23 m
b. 46 m
c. 92 m
d. 138 m
6.A ball is thrown downward from the top of the building with an initial velocity of 25 m/s. It strikes the ground
after 2.0 s. How high is the building?
a. 20 m
b. 30 m
c. 50 m
d. 70 m
7.
When a ball is thrown upward what is its velocity at the maximum height ?
8.
Answer the following questions from graph #1
a. What was the average velocity of the object at t =3 sec ?______
b. What was the acceleration at t = 1 sec ?
______
c. How far did the object move from 0 to 4 sec ?
______
d. What was the velocity at t = 5 sec ?
______
Distance v Time
9. A jet was traveling at 1000 km/hr. What is its velocity in meters per second?
a. 1000 m/s
b. 250 m/s
c. 277 m/s
d. 27.0 m/s
13 m
-5m
4s
10. The correct definition of velocity is
a. Acceleration multiplied by time
b. displacement divided by time interval
c. change in acceleration divided by time interval
d. change in distance divided by time
11. The slope of a distance v/s time graph is equal to
a. time
b. displacement
c. acceleration
d. velocity
12. If a car is moving at a constant velocity the acceleration is
a. increasing
b. decreasing
c. zero
d. positive
13. A car that is slowing down at a constant rate has a __________ acceleration
a. positive
b. negative
c. zero
d. fluctuating
14. In a graph of velocity v/s time, if the slope of the line is equal to zero, then the velocity of the buggy is
a. zero
b. Increasing
c. decreasing
d. constant
15. What is the correct metric unit for acceleration
a. m/s2
b. m/s
c. m
d. 1/s
16. A Porsche 911 was speeding on Route 287 at a constant velocity of 50.0 m/s for 10.0 seconds. How much
distance did the car travel?
_______
17. A bicyclist in a Multiple Sclerosis bike-a-thon is traveling at 1.50 m/s, then speeds up to a velocity of 3.50 m/s
in a time interval of 5.00 s. Calculate the uniform acceleration of the bike.
_______
18. Fizzy the physics cat speeds up from 1.00 m/s to 5.00 m/s when being chased in a straight line by a dog. His
uniform acceleration is + 2.00 m/s2 . How far did Fizzy travel during this period?
________
19. An Olympic sprinter ran a 50.0 m race. How much time did the race take, starting from rest, if the sprinter had a
constant acceleration of 4.00 m/s2 from the starting line?
20 The initial velocity of a rocket ship was 250 m/s. How fast was it traveling after the rocket accelerated at 25 m/s 2
for 10.0 seconds?
_________
21. Calculate the displacement in meters for a football player who started at –5.0 meters in his own end zone and
moved forward till he was stopped at the 35 meter line.
________
22. Calculate the final velocity of a plane that was taking off on a runway that was 500.0 m long and could
accelerate at a rate of 5.0 m/s2
________
23a. A RHS track runner named I.M. Quick, runs 3 complete laps around a 400 m circular track. The first lap she
runs at 4.0 m/s, the second lap at 5.3 m/s and the third lap at 3.0 m/s. What was the total time for this run. (Hint: do
not need equations with acceleration)
________
b. What was the average speed for the run?
________
c. What was the average velocity for the run?
________
Chapter 3
Vectors
Vectors
Magnitude
Direction
north, south, 210o , on the X-axis
Vector Components
Can resolve a vector into
X-component
Drop a perpendicular to X axis
Y component
Draw a parallel to X axis to intersect Y axis
Vector resultant - Vector resulting from adding or subtracting vectors
Adding Vectors
tail to tip method
parallelogram
Using X and Y components
Subtracting Vectors
V2- V1=V2 +(-V1)
Trigonometry SOH-CAH-TOA
Sin = Opposite / Hypotenuse
Cos = adjacent / hypotenuse
tan = opp/adj
Vector quantities
Velocity, Acceleration, Force
Motion 2-D
Projectile motion
Motion in two dimensions
Both X and Y components involved
X component of velocity is constant
X = vx T
Y component changes due to gravity (freefall)
Y = -1/2 gt2
Vy = -g T
Vy = -2g y
Projectile motion follows parabolic trajectories
Projectiles launched horizontally
Ball rolling off table
Projectiles launched at an angle
Cannon ball fired
Frames of reference
Velocity of two moving objects compared to each other
Formulas
Vf = vi +at
Vf2 = vi2 +2ax
Xf = xi +vit + 1/2 at2
Vaverage = (vf+vi)/2
Vf = vi +gt
Vf2 = vi2 +2gy
yf = yi +vit + 1/2 gt2
Labs
Projectile motion
Vector treasure hunt
Problems
1. A velocity vector must be described by
a. velocity and acceleration
b. force and distance
c. direction and magnitude
d. angle and resultant
2. The instant a ball rolls horizontally off a flat table the ball would have a
a. constant vertical velocity
b. initial vertical velocity of zero
c. initial horizontal velocity of zero
d. decreasing acceleration
3. A rocket fired into the air at an angle of 30o would have
a. constant horizontal velocity
b. constant vertical velocity
c. initial horizontal velocity of zero
d. initial vertical velocity of zero
4. The vertical velocity of a ball in projectile motion at the maximum height of trajectory is
a. maximum velocity
b. zero
c. 9.8 m/s
d. depends on initial velocity
5.The distance from the base of the cliff that a stone lands after horizontal launching from the top of the cliff is
dependent on
a. height of cliff and weight of stone
b. height of cliff and horizontal velocity of stone
c. initial vertical velocity and weight of stone
d. initial velocity and final velocity
6.The following vectors must be added in which order to achieve the correct resultant?
a. A, B, C ,D
b. A, C ,B, D
c. A, B, D, C
d. B, A, C, D
e. It does not matter
7. If you know the adjacent and opposite sides of a right triangle you would use which function to find the angle

a. Sin
b. cos-1
c. tan
d. tan-1
8. When a cannonball is launched upward at a 45o angle at 100 m/s when is the horizontal velocity zero?
a. At launch
b. Just before landing
c. At maximum height
d. never
9. Which of the following is a vector quantity?
a. mass of a car
b. color of a car
c. number of cars
d. velocity of a car backing up
10. When subtracting the following vectors A= 4 m East B= 6 m East
(A - B) the resultant is
a. 10 m East
b. 2 m East
c. -10 m East
d. –2 m East
11. Which of the following are Vectors (V) and which are Scalars (S)
____
the acceleration of a race car from the starting line
____
the number of people in the race car
____
the duration of the race
____
the displacement of the entire race
____
the amount of gas used in the race
12. A cross country skier travels 1200 meters east, then 600 meters north, then 200 meters west then 100 meters
south. What is his displacement from the starting point and what the angle from east (X axis)? Sketch a diagram
and solve algebraically.
______m
_____ angle
13. A mad good skateboarder rolls 25.0 m down a ramp at an angle of 20o with the horizontal. Determine the
horizontal and vertical components of his displacement.
X
Y
______ m
______ m
14. John is blocking an opposing football lineman at midfield. He pushes the opposing lineman downfield 4.0 m. At
the same time, his teamate Nick is pushing the opposing lineman 3.0 m to the right. Determine the actual
displacement of the opposing lineman and angle from midfield.
______m
____ angle
15. Calculate the time to landing and how far away a soccer ball would land from the base of the building, if it
rolls horizontally off the 15.0 meter high roof of Ridge H.S. at 9.50 m/sec initial velocity.
______ sec
______ m
16. The Phantom Physics Phly wants to have some fun by jumping from a first desk 2.0 meter high to a second desk
1.5 meters high. The desks are separated by 1.0 meter. The ant can travel at a constant horizontal velocity of 3.5 m/s
on the first desk.
a. Draw a diagram
b. What is Y in this problem
_____ m
c. How far is his landing spot from the base of the first desk?
_____ m
d. Will he land safely on the second desk?
Yes or No
17. A bowling ball rolls down a bowling alley and falls off the end a vertical distance of 0.95 m . It lands on the
ground a horizontal distance of 0.352 m from the edge.
How fast was the ball rolling?
______ m/s
18. A hiker walks 1500 meters east, then 500 meters north, then 200 meters south then 300 meters east. How far is
he from the starting point and what is the angle from east (x axis) he needs to follow to return to the start ?
19. A person who is 100 meters away from an oak tree wants to estimate the height of the tree. He takes a reading
with a transit and determines the angle of his view to the top of the tree from the ground measures 25 degrees. How
high is the tree?
20. Find the x and y components of a vector that has a magnitude of 25 m/s and a direction of southeast (halfway
between south and east)
21. Determine algebraically the distance and angle from x-axis for a plane that is traveling 150 m/s due west and a
cross wind of 25 m/s at 90 degree is blowing.
22. Determine the actual distance traveled and angle from x-axis for a boat that is moving across a river with a
current of 4 m/s due east. The boat maximum speed is at 10 m/s north.
23. Calculate the time to landing and how far away a lacrosse ball would land from the base of the building if it
rolls off the 13.5 meter high roof of Ridge H.S. at 16.6 m/sec initial velocity.
______ sec
______ m
24. Fido the physics dog is fired from a rocket launcher at a 36 o angle to the ground where he traveled 150 meters in
2 seconds (a doggone shame to lose old Fido!)
a. How long before Fido lands?
b. How far did Fido go?
c. If he is trying to land on a doggy bone at 125 meters, how close will he be?
d. What is his velocity in the y direction just before he lands?
_______ sec
______ m
______ m/sec
25. If you were one of Napoleon’s artillery men and you found that the cannonballs you fired were falling short of
the target, what could you do to improve your accuracy?
What effect if any, would real world air resistance have on variables in the calculations we made in projectile
motion? Be specific.
Chapter 4
Free body diagrams
Force vectors
Contact forces
Normal force (Fn)
Weight (Fg)
Frictional force (Ff)
Tension force (FT)
Applied force (pushing, pulling) Fp
Field forces
Gravity, magnetism
Newton’s Laws
1st
inertia
2nd
net external force = mass X acceleration
3rd
action-reaction
Net Force
Applied force - friction
Friction
Depends on surface contact
Usually in X direction opposing an Fp or Ft
Frictional Force
static
Fs
kinetic Fk
Coefficient of friction
varies from 0 to 1.0, the higher coefficient the “stickier” the material
us
uk
F = uN
Mass
Weight is force but is dependent on gravity
(on Earth multiply mass by 9.8)
Weight = mg = Fg
Inclined planes
Pulling or pushing force (Fp)
Use Trigonometry to
Solve for force in X direction (Fx =cos  Fp))
Solve for force in Y direction (Fy) = sin  Fp)
Use F = uN and F = ma to solve for acceleration
Pulleys
one block on table, one hanging down connected by string
Net Force = Fg - Ft
Solve for acceleration and tension
Same acceleration (different direction) and same tension throughout system
Atwood’s Machine
Relationship between mass and acceleration with two masses on a pulley
Labs
Newton’s 2nd Law,
Friction Lab
Problems
1. The acceleration produced by a constant net force on an object is
a. not related to the magnitude of the net force.
b. in the opposite direction as the net force.
c. inversely proportional to the mass of the object.
d. directly related to the normal force
2. What is the unit that is used for force?
a. Kg
b .Kg m/s
c. Newton
d. Joule
3. What is the weight of a 100.0 kg man?
a. 980 kg
b. 100 N
c 980 N
d. 100 kg
4. If the same 100.0 kg man were on the moon where the gravitational force is 1/6 of the earth’s, what is his
weight?
a. 980 kg
b. 16.3 N
c.
d.
600 N
163 N
5. A 3 N force and a 4 N force both act on an object at right angles to each other. What is the net force on the
object?
a. 7 N
b. 1 N.
c. 10 N
d. 5 N
6. A 25 N frictional force acts toward the right on an object and a 75 N applied force acts toward the left on the
same object. What is the net force on the object?
a. 25 N left
b. 30 N right
c. 50 N left
d. 50 N right
7. If the force on a 0.5 kg cart is doubled, what happens to the cart’s acceleration?
a. It is quadrupled
b. It is doubled
c. It is halved
d. It is quartered
8. A man with a mass of 50.0 kg sits on the floor. What is the normal force of the floor on the man?
a. 980 N
b. 490 N
c. 50 kg
d. 50 N
9. Which of the following is not a contact force?
a. normal force
b. tension force
c. pushing force
d. gravitational force
10. A bowling ball is given an initial push to start it rolling across a floor. The reason it continues to roll is
a. the pushing force is maintained
b. the weight changes as it moves
c. inertia
d. the floor push’s up on the ball
11. When a force is applied to move a crate sitting on the floor, the static friction is always_______ kinetic friction.
a. greater than
b. Smaller than
c. Equal to the
12, Which material would you predict would have the lowest coefficient of friction
b. wood
c. metal
d. rubber
e. teflon
13. How much acceleration does a 747 jumbo jet of 100,000 kg experience in departure when the thrust for its
engines is 200,000 N? Assume negligible friction
______
14. A 100.0 kg skydiver jumps out of a plane. What is his net force and acceleration when his parachute first opens
and the air resistance is equal to 300 N?
_____N,
_____m/s2
15. A bag of sugar has a mass of 2.26 kg. What is its weight on the moon where g is 1.6m/s 2 ?
______N
What is its weight on Jupiter where g= 2.64 times that of Earth?
______N
16. A treasure chest is being fought over by two pirates (ARGHH!) as seen in the diagram on the board. The first
person is pushing to the right with an applied force of 250 N. The second person is pushing up with a force of 350
N.
a. What is the resulting force on the box?
______N
b. What is the direction of the box will move relative to the ground?
______o
17. Draw an FBD for a 5.0 kg box sliding down an inclined plane of 30 o with kinetic friction. Include all force
vectors and label them correctly.
18. What does Newton’s 3rd Law state? Give an example from a class demo.
19.Your car gets hit from the rear while moving at 25 mph. During the accident you receive a whiplash injury.
According to Newton’s Laws what causes this injury and what effect would a padded headrest have?
21a. Draw a free body diagram for pulling a 5 kg box horizontally on a flat wooden table including all forces.
b. Calculate the normal force.
______ N
c. If the frictional coefficient of the table/box is 0.15, calculate the minimum force needed to move the box to the
right.
______ N
22 a. Draw a free body diagram of a 40 N box being pulled up an inclined plane of 30
N
o
with a pulling force of 25
b. Set up new x and y axis on the 30o incline, label and include values (if known) for the weight vector (W) , the
normal vector (N) , pulling vector (P)
c. Calculate the x (horizontal component) and y (vertical component) of the weight
x = ______ N
y = ______
d. Calculate the Normal force between the plane and the box
______ N
23a. Describe Newton’s 1st Law?
b. Describe Newton’s 2nd Law?
c. Describe Newton’s 3rd Law ?
24. A force of 100 N on a mystery box gives an acceleration of 5 m/sec2. How much force would be needed to
accelerate this box to 15 m/sec2
________
25. What is the weight and mass of Ms. Musumeci on Mars where the force of gravity is 3.7 m/sec 2. Her mass on
Earth is 65 kg.
_______, _______
Chapter 5
Units
Mass - kilograms
Force – Newton’s
Work or energy – Joules
Power – watts or HP
Work
Physics work compared to muscle work
W = Fd
Angled work (need X-component of applied force)
W = F(cos0) d
Energy
Nonmechanical
Many different types
Mechanical
Kinetic
KE = 1/2 mv2
Potential
gravitational
PE = mgh
Elastic
PE = 1/2 kx2
F = kx
Conservation of energy
Can be transformed into different types but not lost/gained
KEi + PEi = KEf + PEf
Ex. Roller coaster
V = 2gh
Energy/ work relationship
Energy available to do work
Not 100 % efficient due to friction, heat, stretching, etc.
Power
Power = work per time
P = W/t
Power = force x velocity
P = Fv
Units
1 Watt = 1 J/s
1 HP = 746 watts
Labs
Weight room, stairs activity
Spring constant activity
Pendulum lab
Know how to Calculate
Work
PE and KE
Power
Velocity if energy is conserved
1. When calculating PE el the x is defined as
a. The stretched length of the spring
b. The unstretched length of the spring
c. The difference between the stretched and unstretched length of the spring
d. The difference between the compressed length and stretched length of the spring
2. A spring with a larger spring constant will have a _______ stretched distance when a 100 g mass is added than a
spring with a smaller spring constant.
a. larger
b. smaller
c. the same
d. variable
3. If energy is conserved in a frictionless pendulum that is swinging in a circular arc
a. The PE at the top of the swing equals the KE at the top of the swing
b. The KE at the bottom of the swing equals the PE at the top of the swing
c. The PE at the bottom of the swing equals the KE at the bottom of the swing
d. The KE at the bottom of the swing equals the KE at the top of the swing
4. Compare the kinetic energy of a collision between two cars. Car A has a mass that is twice that of car B
a. The KE of A is four times as much as B.
b. The KE of A is twice as much as much as B
c. The KE of A is the same amount as B.
d. The KE of A is one half as much as B
5. How much work is done on a barbell that has a weight of 5.0 N that is lifted 10.0 m?
a. 500 J
b. 50 J
c. 10 J
d. 1 J
6. Gravitational potential energy is due to its
a. velocity
b. height
c. shape
d. elasticity
7. A 10.0 N book is held 0.5 meters above the floor for 5.0 seconds. How much work is done on the book?
a. 0
b. 50 J
c. 20 J
d. 980 J
e. 200/3600 J
8. Freddy Phast is a 50.0 kg sprinter who is running with a velocity of 9.0 m/s. His kinetic energy is
a. 270 J
b. 2025 J
c. 4050 J
d. 4410 J
9. Which of the following describes work being done (based on the physics definition)
a. standing still at the bus stop
b. pushing against the wall in class but not moving it
c. walking at constant velocity across the room
d. lifting a chair off the floor in class
10. List the following as examples of kinetic energy (KE), potential energy (PE) or a nonmechanical form of energy
(N)
a. heating up water
_____
b. standing on the end of the 10 m diving board _____
c. throwing a baseball _____
d. lighting an electric light
_____
11. Match Units (put correct letter on line)
a. Force
______ m/s
b. Work
______N
c. Velocity
______ W
d. K
______m
e. displacement
______ J
f. power
______N/m
12. A sleepy physics student was pulled in his seat along the floor of the classroom by an irate teacher, using a force
of 100 N at an angle of 25o to the floor. The student is pulled a 15 meters distance. How much work was done on the
student?
______ J
13. A 80.0 kg person rides the looping coaster shown below.
(Assume there is no friction, energy is completely conserved)
Point A
h= 80 m
v= 0 m/s
Point B
h= 20 m
v= ? m/s
Point C
h= 0 m
v= ? m/s
a) What is the PE of the person at point A ?
_______ J
b) What is the KE of the person at point A ?
_______ J
c) What is the PE of the person at point C?
_______ J
d) What is the velocity of the person at point C?
_______ m/s
e) Why can't a real roller coaster ever reach its initial height after the first drop,? Doesn't this violate the Law of
Conservation of Energy? Explain.
f) What is the velocity of the person at point B?
_______ m/s
14. How much distance did a garage door spring stretch, if it has a spring constant of 2500. N/m and gained an
elastic potential energy of 5000. J when stretched?
_______ m
15. The indestructible Felix the Fisix cat whose mass is 3.0 kg, is napping on the refrigerator when she rolls over
and falls. She has a KE of 85.5 J just before striking the floor. How high is the refrigerator?
(assume no air friction and energy is completely conserved)
________m
16. A worker pushes a small crate with a horizontal force of 345 N a distance of 24.0 m across the floor. If the
frictional force from the floor is 100 N, what is the net work done?
________J
17. A baseball with a mass of 0.15 kg is thrown straight up from the ground with an initial velocity of 12.0 m/s.
Assuming the total energy is completely conserved, calculate
a)
the initial kinetic energy
______J
b)
the potential energy at maximum height
______J
18. A helicopter is dropping supplies to stranded hikers. The velocity of the copter with the 120 kg load of supplies
is moving at 25.0 m/s. The helicopter’s altitude from the ground is 550 m. How fast would the package be traveling
just before it hit the ground? Assume there is no air resistance and energy is completely conserved.
19.
A baseball with a mass of 0.5 kg is thrown straight up from the ground with an initial velocity of 10 m/s..
Assume energy is conserved. Calculate
a)
the initial KE
b)
the PE at maximum height
c)
the maximum height above the ground
20. A sleepy physics student is pulled by his ear along the floor of the classroom by an irate teacher using a force of
100 N at an angle of 25o to the floor. If the student were pulled all the way to the door, which is 15 meters away,
How much work was done on the student?
______ J
21. A pendulum is set up in lab with a bob that has a mass of 1 kg. The maximum height of the bob is 15 cm.
Calculate the potential energy at the maximum height.
______ J
What velocity is it traveling at the bottom of the swing?
_____ m/s
22. Calculate the Power that is required by a 1250 kg car to go up a 100 m high hill when the trip takes 15 seconds.
_____ W
23. My hefty VW bug won’t start again! What is the amount of work need to push my1000 kg car 300 meters on a
flat road. Assume the coefficient of friction of the road is 0.25
_____ J
24. A truck weighs twice as much as a car and is moving at twice the speed of the car. How would you describe the
kinetic energy of the two vehicles ?
a. The truck has twice as much KE
b. The truck has four times as much KE
c. The truck has eight times the KE
d. The truck has about the same KE
25. A force of 20 N is used to push a 5 kg weight across the floor for 3 meters. The weight starts from rest and
there is no friction.
a) what is the final kinetic energy
_______ J
b) what is the final velocity
_______ m/s
26. Find the work associated with pulling a box using a rope at an angle of 30o with an angled force of 980 N. The
box is moved horizontally a distance of 10 meters.
27. Calculate the PE of a 0.5 kg ball dropped from a height of 100 m.
28. Calculate the KE of a 100 gram bullet fired at a velocity of 150 m/s.
29. Calculate the power in watts and HP of a person who lifts a 100 kg mass a distance of 0.5 m in 2.0 s.
Chapter 6
Momentum
P=mv
Units kg m/s
Impulse
Ft
Ft=mv
Collisions
Be careful with sign of velocity
Right = +
Left = Elastic
(m1v1)i + (m2v2 )i = (m1v1)f + (m2v2)f
Inelastic
(m1v1)i + (m2v2 )i = (m1 +m2)vf
Recoil
Same equation as elastic but bounce off in opposite directions
Conservation of momentum (in a perfect world without friction, heat loss, stretching, etc.)
Elastic – conserved
Inelastic - conserved
Kinetic energy
KE = 1/2 mv2
Elastic
KE Conserved
1/2m1v12 + 1/2m2v22 = 1/2m1v12 + 1/2m2v22
Initial
Final
Inelastic
KE Not conserved, some “loss “of energy
Newton’s Laws and momentum
1st law – Inertia
2ndlaw – force in collisions
F = ma
3rd law – equal and opposite forces due to collisions
conservation of energy
Demo’s
Bowling balls, super balls, Astroblaster
Labs
Conservation of momentum, egg drop
Problems
1. List the following as an elastic collision (E) or an inelastic collision (IN) or Neither (N)
______Bullet fired lodges in wood
______Cue ball striking the other balls in billiards
______ football player running down the field
______ football player getting tackled by a defensive player
______ a super ball is dropped to the ground and returns to its original height
2. A 5.0 kg bowling ball is rolled down the alley at 10.0 m/s. The ball stops after collision with the pins in 0.20 sec,
how much force did the ball exert? Assume perfectly elastic collision.
a. 0 N
b. 10 N
c. 50 N
d. 250 N
3. You collide with a brick wall in your car (Ouch!), which is traveling at 25 m/s. What factors would change the
force to the passengers ?
a. mass of the car
b. velocity of the car
c. collision time
d. a, b, c
4. A student walks to Dr. Flo’s Physics class at 3.0 m/s. At a traffic jam in the 500 wing, he slows to 0.5 m/s. Now
since he is late, he runs down the hall at 7.0 m/s. When did he have the least momentum?
a. walking
b.
c.
d.
slowing for the door
running at 7.0 m/s
the momentum is constant, so they are all the same
5. If a force is exerted on an object which statement is true?
a. a large force produces a large change in the object’s momentum
b. a large force produces a large change in the object’s momentum only if the force is applied over a very
short time interval
c. a small force applied over a long time interval can produce a large change in the object’s momentum
d. a small force produces a large change in the object’s momentum
6. A billiard ball collides with another billiard ball moving toward it and they bounce off each other in a perfectly
elastic collision. The masses and velocities are the same. After the collision, which is true of the first ball?
a. Same direction, same velocity
b. Same direction one-half of the initial velocity
c. Opposite direction, different velocity
d. Opposite direction, same velocity
7. The egg thrown into the sheet in the class demo did not break. What specifically was the reason from a
momentum point of view?
a. the velocity was increased during the collision
b. the mass was decreased during the collision
c. the collision time was decreased during the collision
d. the collision time was increased during the collision
8. If a head-on collision takes place between two equal mass clay balls m1 moving right at v1 and m2 moving left at
v2 with the result they stick together, what would the correct sign be for v f?
a. positive
b. negative
c. depends on velocity of m1 and m2
d. sign is not important with velocity
9. A 1500 kg car doubles its velocity upon entering a highway. How much did its kinetic energy change. (Hint:
remember the KE formula)
a. 2 X
b. 4X
c. 8 X
d. KE does not change
10. The trip to Grandma’s house in a 500.0 kg mass of a car is increased when the trunk is filled with 500.0 kg of
holiday presents.(Wow!) How much did the momentum change if the car travels at the same velocity?
a. no change
b. 1.5 x more
c. 2x more
d. 3x more
11. If the same 1000 kg car travels at half the velocity, what happens to the car’s momentum?
a. 2 x
b. 1.5 x
c. 1/2 x
d. 3x
12. In a perfectly elastic collision between two billiard balls on a pool table, what is true of kinetic energy?
a) KE is gained
b) KE is lost
c) KE is conserved
d) PE is conserved
13. A 25.0 kg cannon ball is fired from a cannon at 250 m/s What is the momentum of the cannonball?
______
14. A 70.0 kg RHS hockey player is moving at 4.0 m/s and holds a 75 kg opposing player who initially is not
moving. How fast does the pair then move together down the ice?
______
15. A 2.0 kg block slides to the right at 8.0 m/s on a frictionless surface. It collides with a 8.0 kg block at rest. After
the collision the 2.0 kg block bounces to the left at 3.0 m/s.What is the velocity of the 8.0 kg block?
______
16. In lab, two magnetic carts have collided. Cart #1 had a mass of 0.490 kg going right with a velocity of 2.5 m/s.
Cart #2 had a mass of 0.525 kg going left with a velocity of 1.5 m/s. After the collision, cart #1 traveled left at 1.8
m/s.
a. How fast was the cart #2 traveling in the opposite direction
______ m/s
b.
What was the initial kinetic energy of the carts? Was this a perfect elastic collision?
17. Planet X, located 100 light years from Earth, exploded into several pieces. The two pieces had masses of 1.25 x
109 kg and 7.75 x 1012 kg. The smaller piece of planet X went flying in the opposite direction at a velocity of 2.5 x
108 m/s. What was the velocity of the larger piece?
______ m/s
18. Two snowball’s with masses of 0.2 kg and 0.6 kg, collide and combine to form a single snowball. The 0.6 kg
snowball is at rest, while the 0.2 kg snowball is moving at 15.0 m/s to the right.
a. Calculate the final velocity of the combined snowball
______ m/s
b. Calculate the KE before and after the collision
______ J
19A. Using physics terms, how does an air bag in a car work?
B. How does Newton’s Cradle work ? Be specific
20. Calculate the momentum of a moving car if it has a mass of 1000 kg and a velocity of 100 km/hr.
21. Calculate the force that the car in #1 experiences when it crashes into a wall, where it takes 0.1 s for the collision
to take place.
22. If the velocity of the car increases, what happens to the force in the collision?
23. How can you decrease the force involved in the collision?
24. A 4.0 kg bowling ball moving right at 2.0 m/s collides with a 3.5 kg bowling ball moving left at 3.0 m/s. If the
collision is perfectly elastic and the 4.0 kg ball moves to the left at 1.5 m/s after the collision, what is the velocity of
the 3.5 kg ball? (draw a labeled picture and be careful of signs!)
25. A 150 gram bullet moving at 200 m/s became lodged in a 2.5 kg piece of wood that was initially part of a barn.
After the bullet struck, the piece of wood with the imbedded bullet broke away. At what velocity was it traveling?
26a. A marble with a mass of 0.020 kg was shot to the right at 3.5 m/s and collided with a 0.015 kg marble, which
was at rest. If the heavier marble bounced off to the left at 1.0 m/s, how fast and in what direction did the lighter
marble travel?
Chapter 7
Circular motion
Frequency
Revolutions per second, rpm
Period
Time for one revolution
Linear velocity
Circumference of circle traveled per time
V = 2 pi r/T
Velocity depends on radius
Angular velocity
Change in angle or radians per time
 / time
Velocity does not depend on radius
Radians
360o = 2 radians
Centripetal acceleration
Ac = v2/r
Centripetal force
Directed toward center
Fc = mv2/r
Actual force compared to “centrifugal force”
Gravitation
Universal law of gravity
F = G m1m2
D2
Masses must be in kg and distance in m
G = universal gravitation constant
6.679 x 10-11 Nm2
kg2
Inverse square Law
1/d2
when distance is doubled, force is one fourth less
when distance is halved, force is four times more
Problems
1. The linear velocity of an object in uniform circular motion is equal to the
a. Arc length divided by the period
b. Angular displacement divided by time
c. Circumference of the circle divided by the period
d. Time divided by Distance
2. If the second hand on the clock moves from 12:00 noon to 6:00 PM what was its angular displacement (how
many radians did it travel)
a. 2 radians
b .360o
cradians
d. 90o
3. If Bart Simpson were being spun in a circle by a rope by Homer and he let go of the rope, which direction would
Bart go flying?
a. perpendicular to the rotation
b. tangent to the rotation
c. toward the center of the circle
d. can’t predict direction
4. The wheel is rotating around its axis 100 times per second.
What is the period for the rotation?
a. 100 s
b. 0.01 s
c. 6000 s
d. .06 sec
5. A bicycle tire is rotating about the axle with a period of 0.5 seconds. What is the frequency the wheel rotating?
a. 0.50 rps
b. 10.0 rps
c. 2.0 rps
d. 30.0 rpm
6. If the velocity is increased for a ball being swung by a string in circular motion, the centripetal force is
a. decreased
b. increased
c. unchanged
d. cannot determine
7. A figure skater jumps and spins with an angular displacement of 6 radians. How many complete revolutions
does she make?
a. 1
b.
c.
d.
2
3
6
8. If the distance between the moon and earth were doubled by some supernatural force, what would happen to the
gravitational force between them?
a. it would be increased by 2X
b. it would be increased by 4X
c. it would be decreased by 1/2X
d. it would be decreased by 1/4X
9. Matching Units
1. Frequency
2. Period
3. Angular velocity
4. Centripetal force
5. Linear velocity
6. centripetal acceleration
7. Universal gravitation constant
_____ s
_____Hz
_____m/s
_____rad/s
_____N
_____Nm2/kg2
_____m/s2
10. A wheel with a radius of 0.50 m made 5 complete revolutions in 2.5 seconds.
How many radians is this?
______
Calculate the angular velocity.
______
11. A tachometer showed that an engine was rotating at 200 Hz.
What is its frequency in rev/s
______
Calculate its period in sec.
______
12.
A 100.0 kg person is standing on the Tilt-a-Whirl ride a distance 5.0 m from
the center. The ride makes one revolution every 20.0 seconds.
a) What is the frequency in Hertz and rpm?
______
b) What is the period of this circular motion?
______
c) What distance does the person travel in one revolution?
______
d) What is the linear speed of the person?
______
e) What is the centripetal force the person experiences?
______
13. A lead weight is placed on a rim of a wheel with a radius of 40.0 cm, when it is balanced at Firestone. The
weight has a mass of 80.0 grams. The machine determines that the wheel is rotates at 240.0 rpm.
Include Units
e.
Calculate the frequency of the weight on the wheel
______
f.
Calculate the period of the weight on the wheel
______
g.
Calculate the linear velocity of the
weight on the wheel
______
h.
Calculate the centripetal acceleration of the weight on the wheel
i.
______
Calculate the centripetal force of the weight on the wheel
______
14. An asteroid with a mass of 1.50 x 10 3 kg was being attracted to the earth
(mass = 6 x 1024 kg) by its gravitational field. If the distance between the objects was 2.5 x 10 8 m, what is the force
attracting them?
15. You are a operating race track and are having trouble with too many accidents in the sharp turns of the course.
Using physics terms, what are some of the things that might be done to improve the safety on the track?
16. A quarter at 10 cm and a dime at 20 cm from the center are rotating on a turntable. Which one is going faster?
Explain your reasons
17. In the centripetal force lab, we loaded washers onto the paper clip and spun the rubber stopper in a fixed radius
circle. Use the following information to calculate the centripetal force acting on the stopper.
Stopper mass = 15 grams
16 washers weighing about 5 grams each were used
The radius of the circle was about 20 cm
The time it took for 30 revolutions was 9.5 s.
_______ N
18.A wheel is rotating at 250.0 Hz
What is its frequency in revolutions per second?
______
What is the period?
19. Two coins are placed on a spinning turntable with a radius of 12 cm. The quarter is at a radius of 12 cm while
the dime is at 3 cm radius. An observer determines that the turntable rotates at 78 rpm
a. Calculate the period of dime
______
b. Calculate the frequency
of dime
______
c. Calculate the linear velocity of dime
_____
d. Calculate the centripetal acceleration of dime
______
20. A ball is rotated on a string in a vertical circle with a radius of 85 cm and a speed of 4.15 m/s and its mass is 300
grams.
a. Draw a free body diagram showing and labeling all the forces at both top and bottom
b. Calculate the tension of the string at the top of the circle
c. Calculate the tension of the string at the bottom of the circle
Chapter 8 Rotational dynamics
Torque
T = F d sin
Units = Nm
Dependent on angle and distance from axis of rotation
Ex. Opening door by handle or hinges
Translational equilibrium
Sum of down forces = sum of forces up
Add total masses including stick
Rotational equilibrium
Sum of torque cw = Sum of torque ccw
Fulcrum, weights at positions
Left side of meter stick = 0 cm
F1d1+F2d2 + F3d3 = (total force) x (fulcrum position)
Be sure to include the stick mass, balanced at the center (50 cm)with no masses on it
Moment of inertia = I
Resistance to rotation or “Rotational inertia”
units kg m2
I = mr2 hoop
I = 1/2 mr2 cylinder
Angular momentum = L
Units kg m2/s
Similar to linear momentum (P = mv ) but in rotational motion
Angular momentum = moment of inertia X angular velocity
L = 
Conservation of angular momentum, similar to conservation of linear momentum
Simple Machines
IMA = Di/Do, geometric ratio
AMA = Fo/Fi
ratio of forces
Efficiency = AMA
IMA
Pulleys
IMA = Number of strands supporting weight
AMA = ratio of forces
Efficiency – if more pulleys, then more friction which decreases AMA
Labs
Rotational equilibrium lab
Calculate position of a mass
Calculate position of fulcrum
Pulley
Calculate unknown mass
lab
Calculate distance, force
Calculate AMA, IMA, efficiency
Problems
1. Calculate torque when a door is opened with a force of 100 N. A force is applied at an angle of 45 o and 50
cm from the axis of rotation.
Would it be easier to open the door at a larger or smaller angle?
How does the distance from the hinges affect the force needed to open?
2. Calculate the moment of inertia for a hoop v/s a cylinder both with a radius of. 0.2 m and a mass of 0.5 kg. If both
were rolled down a ramp, which one will finish first and why?
3. Calculate the angular momentum of an ice skater with has an angular velocity () of 5.0 rad/sec and a moment of
inertia of 10 kg m2 Why does the ice skater moves faster when she pulls her arms toward the center and slows when
she moves them out?
4. Solve the following rotational equilibrium
Set-up #1
Place 500g @ 1 cm
Place 100g @ 99 cm
Where should you place the fulcrum for rotational equilibrium?
The stick has a mass of 200 grams and is centered at 50 cm w/o weights
FBD
Translational Equilibrium Equation
Rotational Equilibrium Equation
5. List the correct metric units for
a. Torque  
b. Moment of inertia
c. Angular momentum
d. Angular velocity
e. Mass
m
f.
force
F

I
L
ω
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