Download Review Physics 201 Class Template

Physics 201 Class Template - Kinematics
Wednesday, September 23, 2015
7:42 PM
Review
Multiply the following two numbers without using a calculator. 2.0x105 and 2.5x106.
1. 4.0x106
2. 3.0x105
3. 5.0x1030
4. 4.5x1010
5. 5.0x1011
Using the dimensions given for the variables in the table, determine which of the following expressions
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Using the dimensions given for the variables in the table, determine which of the following expressions
could be correct.
The SI unit for energy is called a Joule and it has the same dimensions as a force times a change in
time. What is the fundamental dimensions of a Joule and what are the fundamental units of a Joule in
SI?
The surface of a lake has an area of 15.5 km2. What is the area of the lake in m2?
1. 1.55x107 m2
2. 3.10x105 m2
3. 1.55x104 m2
4. 15.5x103 m2
5. 30.1x102 m2
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Exercise for next class: Estimate the number of books in the Valley Library.
A woodworker has made four small airplanes and one large airplane. All airplanes are
exactly the same shape, and all are made from the same kind of wood. The larger plane is
twice as large in every dimension as one of the smaller planes. The planes are to be painted
and then shipped as gifts.
The amount of paint required to paint the planes is directly proportional to the surface area.
Will the amount of paint required for the single plane in Case A be _____ the total amount of
paint required for all four planes in Case B?.
1. greater than
2. equal to
3. less than
A woodworker has made four small airplanes and one large airplane. All airplanes are
exactly the same shape, and all are made from the same kind of wood. The larger plane is
twice as large in every dimension as one of the smaller planes. The planes are to be
painted and then shipped as gifts.
The shipping cost for the planes is proportional to the weight which is related directly to
the volume. Will the weight of the single plane in Case A be _____ the total weight of all
four planes in Case B?
1. greater than
2. less than
3. equal to
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3. equal to
Practice Problems
You have 1 Gallon of paint. Estimate the length, in meters, of each side of the largest square you
could paint. Note: 1 cubic foot is equal to 7.48 gallons and there are 3.28 ft per meter.
Create a model to estimate the distance, in Angstroms, between Carbon atoms in diamond.
Note: The molar mass of Carbon is 12.01 g/mol, the density of diamond is around 3.50 g/cm3,
and an Angstrom is equal to 1 x 10-10 m.
Kinematics
Consider the following statement about Winnie the Pooh's dream:
"There are three times as many heffalumps as woozles."
Some students were asked to write an equation to represent this statement, using h for the number of
heffalumps and w for the number of woozles. Which of the following are correct?
1.
2.
3.
4.
5.
3h/w
3h = w
3h + w
h = 3w
h/3 = w
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A small spherical object has a net charge q and generates an electric field E. If the charge on the
object quadruples and the object moves twice as far away, by what factor does the electric field
change?
The equation for the electric field strength as a function of the distance (r) away from a point charge
is equal to the equation below, where q is the charge and k is a constant.
1.
2.
3.
4.
5.
6.
1
2
4
9
0.5
0.25
A long straight wire carries a current I and generates a magnetic field B. If the current quadruples and
the wire moves twice as far away, by what factor does the magnetic field change?
The equation for the magnetic field strength as a function of the distance (r) away from an effectively
infinite wire is equal to the equation below, where I is the current and μo is a constant.
1.
2.
3.
4.
5.
6.
1
2
4
9
0.5
0.25
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Sketch a plot of the following equation: f(x)=1.5x+9.8x2
The velocity of a cheetah is found to be <15, -10> m/s. What is the speed and direction of the cheetah's
motion? Assume a standard x and y coordinate system.
1.
2.
3.
4.
5.
18 m/s, 33.7º from +x towards -y
9 m/s, 44.4º from +x towards -y
21 m/s, 12.0º from -x towards +y
13.5 m/s, 33.3º from -x towards –y
17.1 m/s, 58.7º from x towards y
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The change in position vector for an African Swallow you are studying is determined to be in a
direction 36.87º from +x towards +y. The x-component is 40 m. What is the magnitude of the
displacement in meters?
Start at the corner of a cube, of side length 1 m, and find the distance to the furthest point that still
resides on the cube.
Note: the magnitude of a vector in three dimensions is the square root of the summation of the square
of all three components of the vector.
Note: your answer should include units.
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Which of the following vector equations correctly describes the relationship among the vectors
shown in the figure?
1.
2.
3.
4.
5.
P+Q=R
P=Q+R
P+R=Q
P + Q + R =0
None of equations A - D is correct
You take off from La Guardia airport in a little airplane. First you fly NW for 5 miles. At the
George Washington bridge, you turn SSW for 10 miles. Above the Statue of Liberty, you turn S
toward the Verazzano Narrows bridge, 5 miles ahead. Over the bridge you turn ENE for a landing
at JFK airport, 10 miles ahead.
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toward the Verazzano Narrows bridge, 5 miles ahead. Over the bridge you turn ENE for a landing
at JFK airport, 10 miles ahead.
Suppose that instead of flying NW-SSW-S-ENE, you had followed the same "vectors" in a
different sequence: SSW-NW-ENE-S. Mark on the map where this path would have led you.
Three vectors, labeled P, Q, and R, are shown. The length of each vector is given in arbitrary
units.
In each space provided above, construct a drawing of the indicated combinations of the
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In each space provided above, construct a drawing of the indicated combinations of the
vectors P, Q, and R, and then rank the magnitude of these resultant vectors.
Three wolves are pulling on the carcass of a dead animal but the net force on the animal is
zero. The first wolf pulls with a force of <2,1> N. The second pulls with a force magnitude
equal to 3.162 N in a direction 18.435 degrees from the positive y direction towards the
negative x direction. What must be the force of the third wolf?
1.
2.
3.
4.
5.
6.
7.
<1,4> N
<2,3> N
<-2,3> N
<-4,1> N
<-3,-4> N
<-1,-4> N
<1,-2> N
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For each situation below , combine the vectors as indicated and determine the direction of
the resultant vector. Then select the closest direction to the resultant from the direction
rosette.
Estimate the position vector to the location in the room defined as point A. Set the origin at the front, bottom, right
side of the room (as seen by the students). Consider left to right as the positive x direction, bottom to top as positive
y direction, and front to back as the positive z direction.
Answer in whole numbers of meters with the following format: <x,y,z> m. An example might look like: <4,1,7> m.
Estimate the position vector to the
location in the room defined as point B.
Using the class average for position vectors A and B, find the displacement vector from point A to B. Answer in
whole numbers of meters with the following format: <Δx,Δy,Δz>. An example might look like: <4,1,7> m.
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New Origin
Estimate the position vector to the locations in the room defined as point A and point B.
This time set the origin at the front, top, left side of the room (as seen by the students). Consider left to right as the
positive x direction, bottom to top as positive y direction, and front to back as the positive z direction.
Answer in whole numbers of meters with the following format: <x A,yA,zA> m, <xB,yB,zB> m. An example might look
like: <4,1,7> m, <-2,3,6> m.
Using the class average for position vectors
A and B from the new origin, find the
displacement vector from point A to B.
Answer in whole numbers of meters with the
following format: <Δx,Δy,Δz>. An example
might look like: <4,1,7> m.
Deserted on a deserted Island you spot a slightly exposed tin can under a tree. Upon opening it you find instructions
to a buried treasure. It reads: “Ten paces from this very tree in a direction twenty degrees south of west lies the first
location. Ten paces from this very tree in a direction sixty degrees north of east lies the second location. Walk from
this tree exactly the distance and direction you would walk from the first location to the second location and you will
find ye treasure. Yar” Sketch a physical representation of this situation on the grid provided. A physical
representation for this type of problem should include the two position vectors, the change in the position vector, and
the location of the treasure. Use the center of the grid as the tree location and scale appropriately to fit on the grid.
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What are the coordinates of treasure?
Sketch on the pictorial representation below the final position vector.
Note: the grid spacing is 1 m
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Sketch on the pictorial representation below the final position vector.
Upon waking from being hit in the head with a shovel you find yourself in the woods, next to a unfilled grave. You
start running from this nightmare in a direction 51.34 degree from the negative y direction towards the negative x
direction. Your acute direction senses surprise you but this is no time to contemplate a new super-power. You run
along that line for 6.403 miles until you run into a police officer located at a location <-2, -3> miles from the police
station. What are the coordinates of the grave you were presumably destined for?
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station. What are the coordinates of the grave you were presumably destined for?
1.
2.
3.
4.
5.
<1, 8> mi
<4, -5> mi
<-2, 3> mi
<-1, -1> mi
<3, 1> mi
Draw on the pictorial representation below the average velocity vector assuming it took 2 s to go from the initial to
final location.
Note: Assume the grid spacing is 1 m for position vectors and 1 m/s for velocity vectors.
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An object starts at the initial position indicated below. It travels with the average velocity represented below
for 3 s. Sketch on the plot below the final position of the object.
Assume the grid spacing is 1 m for position vectors and 1 m/s for velocity vectors.
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What is the final position vector of the object?
1.
2.
3.
4.
5.
6.
<-2, 12> m
-<10, 1> m
-<-10, -1> m
<4, -10> m
<10, -1> m
<10, 13> m
An object has a final position as indicated below. It traveled with the average velocity represented below for
4 s. Sketch on the plot below the initial position of the object.
Assume the grid spacing is 1 m for position vectors and 1 m/s for velocity vectors.
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If the time between the initial and the final velocity data points being acquired is 2 s, sketch on the vector
operation plot below the average acceleration vector.
Note: Assume the grid spacing is 1 m/s for velocity vectors and 1 m/s2 for acceleration vectors.
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What is the magnitude of the average acceleration
vector?
Sketch the average acceleration vector on the blank plot if 0.5 seconds pass between the initial and final
data points.
Note: Assume the grid spacing is 1 m for position vectors, 1 m/s for velocity vectors, and 1 m/s2 for
acceleration vectors.
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Practice Problem: The first stage of a trip has a displacement vector in the negative x direction. The
second stage has a displacement at an angle of 30.0º above the positive x axis. The final stage has a
displacement of magnitude 15 km and points in a direction 40.0º below the positive x axis. If after all
three stages you end up where you started, what was the magnitudes of the displacement of the first
two stages?
A person initially at point P in the illustration stays there a moment and then moves along the axis
to Q and stays there a moment. She then runs quickly to R, stays there a moment, and then strolls
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to Q and stays there a moment. She then runs quickly to R, stays there a moment, and then strolls
slowly back to P. Which of the position versus time graphs below correctly represents this motion?
When is the speed maximum and the object moving in the negative direction?
The figure shows a plot of an object's velocity as a function of time. What is the value, in m/s2, of the
greatest magnitude acceleration the object undergoes.
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The graph shows position as a function of time for two trains running on parallel tracks.
Which of the following statements are true:
1. At time tB, both trains have the same
velocity.
2. Both trains speed up all the time.
3. Both trains have the same velocity at
some time before tB.
4. At some instant, both trains have the same
acceleration.
5. At time tB, both trains have the same
magnitude of displacement from t = 0.
The figure shows the velocities as a function of time of three different objects moving in a straight
line. All three graphs pass through points A and B. Order the magnitudes of the velocity at point B.
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Order the magnitudes of the distance
traveled between A and B.
Order the magnitude of the acceleration at point A.
Order the magnitude of the average acceleration between points A and B.
The position of two cars as a function of time is plotted in the figure. Which of the following
statements are false regarding this situation?
1. Car 1 has the greatest average velocity between points A and D.
2. Car 2 has the greatest average velocity between points A and D.
3. Car 2 has the same acceleration at point B as car 1 does at point E.
4. Car 2 has a greater acceleration than car 1 at point C.
5. Car 1 is momentarily at rest at point B.
6. Car 2 is momentarily at rest at point C.
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The velocity as a function of time for three different objects moving in a straight line are plotted to
the right. Which of the following statements about their motion are necessarily (must be) true?
1. At point A, the position of object 3 is the
same as object 1 or 2.
2. At point B, the position of object 2 is
greater than object 3.
3. Halfway between time tA and tB the
position of 3 is greater than 1 or 2.
4. Nothing can be determined about the
position of the objects from this plot.
Which of the following position as a function of time plots shows an object that has the direction
of velocity change during the motion plotted,
shows an object that is speeding
up during the entire time plotted,
shows an object that has an
acceleration with a constant
direction and magnitude?
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The graphs below show position versus time for six boats traveling along a straight, narrow
channel. The scales on both axes are the same for all of these graphs. In each graph, a point is
marked with a dot. Rank the magnitude of the velocity of the boat at the point indicated.
Two balls are released from rest and undergo free-fall. Ball A is released first, followed by ball B a
moment later. What happens to the distance between the balls while they are in free fall.
1. Increases
2. Decreases
3. Stays the same
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Steps to Solving Kinematics Problems with the Mathematical Representation
1. Conceptually grasp the question - mental visualization
2. Draw a physical representation (picture) - include x, v, and a vectors during the motion
3. Define known and unknown variables (5) for each object/stage/dimension (Δx, vi, vf, Δt, a)
4. Find at least the same number of unique equations as number of unknowns. Process of
elimination - at first avoid the unknown you’ve not been asked for. Algebraically solve for the
desired quantity.
4.1 If simple, desired unknown can be directly solved for
4.2 May have to solve for intermediate unknown to solve for desired unknown
4.3 May have to solve multiple equations and multiple unknowns
4.4 May have to refer to the geometry to create another equation
4.5 If multiple objects or constant acceleration stages or dimensions, there is a set of
kinematic equations for each. Something will connect them.
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Two runners are participating in a 5 km race. The first runner maintains a steady 5.5 kph pace
while the second maintains a steady 4 kph pace. How long will the first runner wait at the finish
line before the second runner arrives?
In each figure below, a car's velocity is shown before and after a short time interval. Rank the
magnitude of the change in velocity during the time interval.
Draw a vector to represent the acceleration
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Draw a vector to represent the acceleration
of the car on the spots marked by an X.
Constant Acceleration: A car traveling at 60.0 mph (26.82 m/s) suddenly slams on its brakes. If it slows at a
rate of 4.60 m/s2 , how far does it travel before it comes to a complete stop? Give your answer in meters, but
do not include them in your response.
Can an object be increasing in speed as it’s acceleration decreases?
1. Yes
2. No
Which of the following statements are false?
1.
2.
3.
4.
An object can be increasing in speed as it’s acceleration is decreasing.
An object can have zero velocity and nonzero acceleration at the same time.
An object can have a nonzero velocity and its acceleration be zero.
An object at rest can have a constant nonzero acceleration and stay stopped.
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T/F? If an object has an acceleration toward a point, then it must be getting closer and closer to
that point.
The following drawings represent strobe (flash) photographs of a ball moving in the direction of
the arrow. The circles represent the positions of the ball at succeeding instants of time. The time
interval between successive positions is the same in all cases. Assume all accelerations are
constant.
Rank the magnitude of the acceleration based on the drawings.
Answer
C<A<B=D
Which of the following statements are false?
1.
2.
3.
4.
An object can be increasing in speed as it's acceleration is decreasing.
An object can have zero velocity and nonzero acceleration at the same time.
An object can have nonzero velocity and its acceleration be zero.
An object at rest can have a constant nonzero acceleration and stay stopped.
Constant Acceleration Comparison: A sports car accelerates from zero to 30.0 mph (13.41 m/s) in 1.50 s. How
many seconds does it take for it to accelerate from zero to 60.0 mph, assuming its acceleration is constant?
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Constant Deceleration Example: Hammy the hamster is at full sprint when all of a sudden he spots a cat
in front of him. Within 0.10 s and 1 cm Hammy has uniformly reduced his speed to 0.50 cm/s, and is
about to turn around and run the other way. How fast was Hammy (a) originally running when he saw
the cat, and (b) what was his acceleration during this time?
Comparison Example: A person standing at the edge of a cliff throws one ball straight up and another ball
straight down at the same initial speed. Neglecting air resistance, which ball hits the ground below the cliff
with a greater speed?
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Two Stage Example: A construction worker’s hammer falls from rest off of the top of an apartment
building. A tenant notices it takes 0.20 s for the hammer to pass their 1.6-m-tall widow. How far above
the top of this window is the roof?
T/F? If an object has an acceleration toward a point, then it must be getting closer to that point?
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Which of the following statements are false?
1.
2.
3.
4.
An object can be increasing in speed as it’s acceleration is decreasing.
An object can have zero velocity and nonzero acceleration at the same time.
An object can have a nonzero velocity and its acceleration be zero.
An object at rest can have a constant nonzero acceleration and stay stopped.
Two balls are released from rest and undergo free-fall. Ball A is released first, followed by ball B a
moment later. Does the distance between the two balls stay the same?
Two balls are released from rest and undergo free-fall. Ball A is released first, followed by ball B a
time T0 later. The distance between the balls follows the following function of the change in time
(Δt).
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time T0 later. The distance between the balls follows the following function of the change in time
(Δt).
where g is the magnitude of the acceleration of gravity.
How does the distance change with respect to the change in time?
1.
2.
3.
4.
No dependence
Linearly
Quadratically
Cubically
A spaceship is traveling in the galactic northeast direction. The ship's thrusters then create a large
constant acceleration in the southern direction. Which of the following statements are necessarily
true regarding the time after the thrusters have fired.
1.
2.
3.
4.
5.
The ship will be moving in the southeast direction.
The ship will eventually be moving in the southern direction
The ship's displacement will be in the southern direction
The ship will eventually be moving with both southern and eastern components
The change in the ship's velocity will be in the southern direction.
A spaceship's controls fail for 5.00 s and during this time the thrusters on the ship give it an
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A spaceship's controls fail for 5.00 s and during this time the thrusters on the ship give it an
acceleration of 4.472 m/s2 in a direction 63.43 º from the positive x direction towards the positive y
direction. They know that after the incident the ship was traveling with a speed of 15.81 m/s in a
direction 18.43 º from the positive y direction towards the positive x direction. What are the final
velocity and the average acceleration in Cartesian coordinates?
The information they've lost is their initial velocity and the change in position they underwent. Find
those quantities.
A cart is rolling on a horizontal table when a ball is launched from the cart, vertically as seen with
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A cart is rolling on a horizontal table when a ball is launched from the cart, vertically as seen with
respect to the cart. Where does the ball land with respect to the cart?
1. In front of the cart.
2. Behind the cart.
3. On the cart.
Ball A is dropped at rest from a height h above the ground. At the same instant ball B is launched
horizontally from the same height. Which ball hits the floor first?
1. A
2. B
3. Both hit at the same time
A baseball is thrown from point S in right field to home plate. The dashed line in the diagram shows
the path of the ball. Use a coordinate system with up as the positive vertical direction and to the right
as the positive horizontal direction, with the origin at the point the ball was thrown from (point S)
(a) The horizontal acceleration versus time and the vertical acceleration versus time.
(b) The horizontal velocity versus time and the vertical velocity versus time.
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Cannonballs of different masses are shot from cannons at various angles above the horizontal. The
velocity of each cannonball as it leaves the cannon is given, along with the horizontal component of
that velocity, which is the same.
Rank the horizontal distance travelled
by the cannonballs. Explain your reasoning.
A baseball is hit with an initial speed of 36.0 m/s at an angle of 66.0º above the horizontal. At the
same moment a fielder 68.0 m away begins running away from where the ball was hit in the line of
the baseball’s flight, trying to catch it. How fast must the outfielder run to catch the ball at the same
height it was hit? How does this change if the runner is to catch the ball 1 m above where it was hit?
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Physics 201 Class Template - Mechanics
Wednesday, September 23, 2015
8:33 PM
Mechanics Page 38
A force is:
1.
2.
3.
4.
5.
6.
7.
equal to mass times acceleration.
an interaction between objects.
dependent on the mass of an object.
dependent on the acceleration of an object.
dependent on the velocity of an object.
only involving one object.
always making objects accelerate.
A ball rolls off a table at a pretty good speed and has not yet his the ground. What forces act on the ball?
A normal force, N
A tension force, T
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A ball rolls off a table at a pretty good speed and has not yet his the ground. What forces act on the ball?
A normal force, N
A tension force, T
A friction force, f
A weight, W
1.
2.
3.
4.
5.
6.
7.
8.
9.
Only W
Only N
Only T
Only f
No forces
N and W
N, W, and f
W and f
N and f
A baseball is thrown from right field to home plate (HP), traveling from right to left in the diagram.
A group of physics students watching the game create the following free-body diagrams for the
baseball at the top of its path (point T). Note that the forces are not drawn to scale.
If they decide to ignore air friction, which
is the correct free-body diagram for the
baseball at point T?
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A person who weighs 600 N is standing on a scale in an elevator. The elevator is identical in all cases.
The velocity and acceleration of the elevators at the instant shown are given.
Rank the scale reading.
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A person throws a ball up in the air and then catches it again. Sketch the normal force of the hand on
the ball over time.
A box with wheels attached to bottom is on top of a horizontal scale. Attached to one side is a
horizontal rope with a spring scale to measure force (assume the scale and ropes are mass-less). On
the other side of the box is a rope that has no force being applied to it.
Sketch a FBD of the box.
A 10-kg-box with wheels attached to bottom is on top of a horizontal scale. Attached to one side is a
horizontal rope with a spring scale to measure force (assume the scale and ropes are mass-less). On the
other side of the box is a rope that now has a horizontal force equal to 150 N pulling on it.
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Sketch a FBD of the box, attempting to scale
each vector relative to each other.
A 10-kg-box with wheels attached to bottom is on top of a horizontal scale. Attached to one side is a
horizontal rope with a spring scale to measure force (assume the scale and ropes are mass-less). On
the other side of the box is a rope that now has a force equal to 150 N pulling on it in a direction 30
degrees up from the horizontal.
Sketch a FBD of the box, attempting to scale
each vector relative to each other.
What is the force the
spring scale measures?
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What is the force the
bottom scale measures?
A 10-kg-box with wheels attached to bottom is on top of a horizontal scale. Attached to one side is a
horizontal rope with a spring scale to measure force (assume the scale and ropes are mass-less). On
the other side of the box is a rope that now has a force equal to 150 N pulling on it in a direction up
from the horizontal.
What angle, in degrees, will the box begin to lift off the ground?
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A box on a frictionless horizontal surface is pulled at a constant rate by a rope that makes an angle up from the
horizontal. If the vertical component of the force is not large enough to lift the box off the table, what is the net force,
acceleration, velocity, position as a function of time?
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A box on a frictionless horizontal surface is pulled at a constant rate by a rope that makes an angle up from the
horizontal. If the vertical component of the force is large enough to lift the box off the table, what is the net force,
acceleration, velocity, position as a function of time?
A box on a horizontal surface (w/ friction) is pulled at a constant rate by a rope that makes an angle
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A box on a horizontal surface (w/ friction) is pulled at a constant rate by a rope that makes an angle
up from the horizontal for a while and then the rope breaks. If the vertical component of the force was
not large enough to lift the box off the table, how long will it take for the box to come to rest?
A box is sliding to the right on the floor of an elevator that is moving upwards and slowing down.
Sketch a FBD of the box during the time it slides to rest, being careful to scale the vectors relative to
each other.
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A box is sliding on the floor of an elevator that is moving upwards and slowing down. How does the
time it takes the box to come to rest compare to if the elevator was in equilibrium?
• more
• less
• same>
What is the direction of the friction on the block?
a.
b.
c.
d.
Towards the right
Downward
Upward
Not enough information
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What is the direction of the friction on the block from the hand?
a. Towards the right
b. Towards the left
c. Not enough information
What is the direction of the velocity of the block?
a. Towards the right
b. Towards the left
c. Not enough information
The half-kg-block on the hand undergoes an acceleration with a magnitude of 2
m/s2 and doesn't slip relative to the hand. What is the frictional force on the block?
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If wind imparts a 1/2 N force in the opposite direction of the block's acceleration,
what is the frictional force on the block?
If the coefficient of static friction between the block and the hand is 0.5, what is the
maximum acceleration, in m/s2, the block can attain without sliding relative to the hand?
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Starting from rest the hand increases the rate of its acceleration. Eventually the block begins
to slide relative to the hand.
Sketch a plot of the frictional force
on the block as a function of time.
Consider the object on an inclined plane shown below: Fkso is the
frictional force exerted on it by the plane, Fnso the normal force
exerted on it by the plane, and Fgeo the force of gravity exerted on it
by the Earth. Which of the following statements are true regarding
this situation?
a.
b.
c.
d.
Fkso = µ Fnso
Fkso = Fgeo sin θ
Fnso = Fgeo cos θ
The object is sliding up the incline
Mechanics Page 51
While starting to take off a rocket ship of mass m malfunctions horribly, leaving the antigravity
drive turned off and the throttle stuck with a constant thrust of magnitude F th. Making matters
worse, it’s on a hill angled θ with respect to the horizontal to a cliff of height h above ground.
Below the cliff the ground is angled downward α with respect to the horizontal. The coefficient of
static and kinetic friction between the rocket and the hill is µ s and µk respectively. A steady wind is
pushing downward on the ship with a magnitude F w force at an angle of φ with respect to the
vertical. What minimum magnitude thrust would be required for the ship to accelerate up the hill?
Mechanics Page 52
Two toy trucks travelling at different constant speeds are about to collide. The two identical
trucks are traveling in opposite directions, and truck A is carrying a heavy load.
During the collision, will the magnitude of the force exerted on truck A by truck B be _____ the
magnitude of the force exerted on truck B by truck A?
1. greater than
2. less than
3. equal to
Which pairs of forces in the free body diagram shown could be interaction force pairs?
Mechanics Page 53
1.
2.
3.
4.
5.
6.
A and D
A and E
B and E
C and F
F and G
None of these
A 10 kg box is atop a 5 kg box and both are in an elevator. If the elevator starts from rest and
accelerates upwards to a speed of 2.0 m/s in 1.5 s, what was the magnitude of the acceleration of
the top block in m/s2?
Match the FBD below with the appropriate system, top box,
bottom box, or the top plus bottom box system.
What is the magnitude of the normal force from the bottom
box on the top box?
What is the magnitude of the normal force from
the elevator on the bottom box?
Mechanics Page 54
The diagram shows two blocks (on a frictionless horizontal surface) with two external forces
acting, one on each block as shown.
Compared to the net force on the smaller block, the net force on the larger block is _____
1.
2.
3.
4.
5.
6.
7.
equal in magnitude & opposite in direction.
equal in magnitude & in the same direction.
larger in magnitude & opposite in direction.
larger in magnitude & in the same direction.
smaller in magnitude & opposite in direction.
smaller in magnitude & in the same direction.
zero, since both net forces vanish & have no direction.
Mechanics Page 55
Two boxes of equal mass M, are placed one on top of each other as shown in the figure. In
case 1 an applied force acts on box B while A is fixed to a wall by a rope. In case 2 an applied
force acts on box A while box B is fixed to the wall by a rope. All surfaces have friction with the
same coefficients.
In which case will the force to break static friction be greater?
What is the ratio of the applied force (case 1 over case 2) required to break static friction?
Mechanics Page 56
A box is on a horizontal frictionless table and is attached via a string and pulley to a another mass
M that is hanging off the end of the table.
The tension in the cable is ___________
1. greater than Mg
2. less than Mg
3. equal to Mg
Mechanics Page 57
Rank the following situations, greatest to least, based on the tension in the string. Assume the
hanging mass in each case is the same, friction is negligible, and the pulley and the rope are
massless.
Which of the following are constraints on mass 1 and mass 2?
1.
2.
3.
4.
|a1|= |a2|
|a1|= 2 |a2|
|v1|= |v2|
|v1|= 2 |v2|
Mechanics Page 58
The figure shows the use of a pulley to obtain mechanical advantage when lifting an object.
Mechanical advantage is defined as the ratio of the force required to do a task without the use of a
device divided by the force required with the device. What is the mechanical advantage of the pulley
system shown in the figure.
Mechanics Page 59
The box of mass m is suspended above the floor of an elevator with the aid of some mass-less, frictionless pulleys. The elevator is moving in the upward direction and slowing down.
Which of the of the following are true regarding the tension in the cable?
1.
2.
3.
4.
5.
6.
7.
greater than mg
equal to mg
greater than mg/2 and less than mg
equal to mg/2
greater than mg/4 and less than mg/2
equal to mg/4
less than mg/4
Mechanics Page 60
A square block (m1) sits atop a triangular wedge (m2) that sits on the horizontal bed of a truck (m 3). One of
the angles of the wedge is θ, as shown in the figure. There is no friction between the wedge and the block
but there is friction (µs) between the truck and the wedge. When the truck accelerates as much as it can
(amax) and not have the wedge + block system slide relative to the truck, it is noticed that the block does
not slide relative to the wedge. (a) For this max acceleration situation draw a free-body diagram for the
square, wedge, and truck separately. (b) Identify all Newton’s third law force pairs. (c) When analyzing
these objects what coordinate system orientation would best be suited? Explain. (d) Create a set of
Newton’s 2nd law equations for each mass using the variables given, and g, the acceleration of gravity.
Identify any quantities that are zero. (you do not have to solve for anything) (e) Identify any constraints
these objects may have with respect to each other.
Mechanics Page 61
A box is on a horizontal frictionless table and is attached via a string and pulley to a another mass
M that is hanging off the end of the table.
The tension in the cable is ___________
1. greater than Mg
2. less than Mg
3. equal to Mg
Mechanics Page 62
Rank the following situations, greatest to least, based on the tension in the string. Assume the
hanging mass in each case is the same, friction is negligible, and the pulley and the rope are
massless.
Which of the following are constraints on mass 1 and mass 2?
1.
2.
3.
4.
|a1|= |a2|
|a1|= 2 |a2|
|v1|= |v2|
|v1|= 2 |v2|
Mechanics Page 63
The figure shows the use of a pulley to obtain mechanical advantage when lifting an object.
Mechanical advantage is defined as the ratio of the force required to do a task without the use of a
device divided by the force required with the device. What is the mechanical advantage of the pulley
system shown in the figure.
Mechanics Page 64
The box of mass m is suspended above the floor of an elevator with the aid of some mass -less, frictionless pulleys. The elevator is moving in the upward direction and slowing down.
Which of the of the following are true regarding the tension in the cable?
1.
2.
3.
4.
5.
6.
7.
greater than mg
equal to mg
greater than mg/2 and less than mg
equal to mg/2
greater than mg/4 and less than mg/2
equal to mg/4
less than mg/4
If an object moves in uniform circular motion what can be said?
1. The velocity is constant
2. The speed is constant
Mechanics Page 65
3. The acceleration is constant
4. The net force is constant
5. The magnitude of the displacement is constant
What is the speed of a point on the tip of a 3-cm-long second hand of a clock?
1.
2.
3.
4.
5.
1.57 m/s
1.57 x 10-3 m/s
6.28 x 10-4 m/s
3.14 x 10-5 m/s
3.14 x 10-3 m/s
A car travels around a circular corner of radius r at constant speed. The corner is not banked. Which force
is responsible for keeping the car on the road?
1.
2.
3.
4.
5.
Normal
Centripetal
Friction
Gravity
Force of acceleration
Mechanics Page 66
A ball is rolling on a horizontal table on the inside of a hula-hoop of radius r. At what speed must the ball
be moving so that the normal force from the hoop is equal to the normal force from the floor?
Mechanics Page 67
Assume the ball is rolling counter-clock wise and is located at the
dot on the figure when the loop is removed. Sketch the trajectory
of the ball after the removal of the loop.
The ball and loop are now placed vertically. A rocket makes sure the ball is always moving at a constant
speed. At what point(s) is there only one force in the radial direction?
Draw the free body diagram for point C.
What should the axis for the
FBD at point C be labeled?
Mechanics Page 68
A rollercoaster goes through a loop-the-loop of radius r. At the top of the loop (point A), what is the
direction of the acceleration?
At point A, what must the speed be
to feel momentarily weightless?
A car is rolling over the top of a hill at speed v. At this instant,
1.
2.
3.
4.
n>w
n<w
n=w
We can’t tell about n without knowing v.
Mechanics Page 69
A car travels around a frictionless banked circular corner of radius r at constant speed. Which force
has a radial component?
1.
2.
3.
4.
5.
Normal
Centripetal
Friction
Gravity
Force of acceleration
Mechanics Page 70
The figure shows a binary star system. The mass of star 2 is twice the mass of star 1. Compared to F 21, the
magnitude of the force F12 is
a. one quarter as large.
b. half as large.
c. the same magnitude.
d. twice as large.
e. four times as large.
A planet, a distance r away from its local star, has a gravitational force F G applied to it. If it was to be located
distance 3r away, what gravitational force would be applied to it.
a. FG/2
b. 3FG/2
c. FG/4
d. FG/3
e. FG/9
A planet, a distance r away from its local star, has a gravitational force F G applied to it. If it was to be located
distance 3r/2 away, what gravitational force would be applied to it.
a. FG/2
b. 3FG/2
Mechanics Page 71
b. 3FG/2
c. 2FG/3
d. 4FG/9
e. 3FG/9
Two massive stars are separated by some distance. In which region could a planet be in equilibrium?
Star 1 is four times as massive as star 2. Where along the line that connects two massive stars could a
planet be in equilibrium?
Star 1 is four times as massive as star 2 and the two are separated by a distance d. If a planet is placed at
the equilibrium point, how far is it from star 1?
a.
b.
c.
d.
e.
x=d/2
x=d/4
x=d/3
x=2d/3
x=4d/3
Mechanics Page 72
A planet has 4 times the mass of the earth, but the acceleration due to gravity on the planet’s surface is the
same as on the earth’s surface. The planet’s radius is
a. Re/4
b. Re/2
c. Re
d. 2Re
e. 4Re
Mechanics Page 73
A satellite orbits the earth with constant speed at a height above the surface equal to the earth’s
radius divided by two. The magnitude of the satellite’s acceleration is
a. (4/9)*gon earth
b. ¼*gon earth
c. (4/3)* gon earth
d. (3/2)*gon earth
e. 2gon earth
Mechanics Page 74
Physics 201 Class Template - Momentum
Wednesday, September 23, 2015
8:46 PM
Two carts moving on a track are shown, along with their masses and velocities.
Consider the system consisting of the two carts. What is the total momentum of the system?
The diagram depicts two pucks on a frictionless table. Puck II is four times as massive as puck I. Starting
from rest, the pucks are pushed across the table by two equal forces. The forces act on both of them for
6.0 s.
Rank the final momentum of the two pucks.
The diagram depicts two pucks on table (with friction). Puck II is four times as massive as puck I.
Starting from rest, the pucks are pushed across the table by two equal forces. The forces act on both
of them for 6.0 s.
Rank the final momentum of the two pucks.
Momentum Page 75
The diagram depicts two pucks on a frictionless table. Puck II is four times as massive as puck I.
Starting from rest, the pucks are pushed across the table by two equal forces. The forces are active
all the way to the finish line.
Which puck will have the greater momentum upon reaching the finish line?
1.
2.
3.
4.
Puck I
Puck II
Both will have the same.
There is not enough
information to decide.
Three basketball players are shooting hoops and bouncing each shot off the backboard.
What is the direction of the change in momentum vector, from before the ball hits the backboard to
after, for player one's shot. (Ignore gravity)
Momentum Page 76
Assuming positive x-direction is to the right, the cart’s change of momentum is
A 10 g rubber ball and a 10 g clay ball are thrown at a wall with equal speeds. The rubber
ball bounces, the clay ball sticks. Which ball exerts a larger impulse on the wall?
1.
2.
3.
4.
They exert equal impulses because they have equal momenta.
The clay ball exerts a larger impulse because it sticks.
Neither exerts an impulse on the wall because the wall doesn't move.
The rubber ball exerts a larger impulse because it bounces.
Momentum Page 77
Three basketball players are shooting hoops and bouncing each shot off the backboard.
Sketch the change in momentum vector for player two assuming the speed is the same
before and after hitting the backboard. (Ignore gravity)
Three basketball players are shooting hoops and bouncing each shot off the backboard.
Sketch the change in momentum vector for player 3 assuming the speed is reduced during
the bounce. (Ignore gravity)
Momentum Page 78
The two particles are both moving to the right. Particle 1 catches up with particle 2 and collides with it.
The particles stick together and continue on with velocity vf. Which of these statements is true?
a.
b.
c.
d.
e.
vf = v2
vf is less than v2
vf is greater than v2, but less than v1
vf = v1
vf is greater than v1
An object is in free-fall near the surface of Earth. Which one of the following statements is true?
a. The object is in equilibrium.
b. The momentum of the object is conserved.
c. The object is isolated.
d. The impulse acting on the object is zero.
e. The change in momentum of the object is zero.
f. The change in the momentum during the 1st second is the same as during the 2nd second.
Momentum Page 79
Block A slides to the right with a speed v when it collides with block B traveling with the same speed in the opposite
direction. After the collision block A's velocity has decreased by a factor of 3. If Block A is three times as massive as
block B, how many times faster is block B moving than block A? Solve with either the vector representation or the
mathematical representation.
A mine car (mass = 440 kg) rolls at a speed of 0.50 m/s on a horizontal track, as the drawing shows. A 150 -kg chunk of
coal has a speed of 0.80 m/s sliding downward at an angle 25 o from the horizontal when it leaves the chute and lands in
Momentum Page 80
coal has a speed of 0.80 m/s sliding downward at an angle 25 o from the horizontal when it leaves the chute and lands in
the coal car.
Sketch the net momentum of the coal + car system, before
the coal lands in the cart, using the head-to-tail method of
addition. There should be three vectors on your diagram.
Sketch the net momentum of the coal + car
system, after the coal lands in the cart, using
the head-to-tail method of addition. There
should be three vectors on your diagram.
The net momentum of the coal + cart system
appears to be down and the to the right before the
coal lands in the cart and towards the right after.
Which of the following statements about the coal +
cart system can account for this phenomena.
a. The momentum is conserved
b. The system is isolated
c. The momentum is not conserved
d. The system is not isolated
e. The system is not large enough to justify
conservation of momentum
Determine the velocity of the car/coal system after the coal has come to rest in the car.
Momentum Page 81
A spaceship of mass 2.0x106 kg is cruising at a speed of 5.0x106 m/s when the antimatter reactor fails, blowing up the
ship in three pieces. One section, having a mass of 5.0x105 kg, is blown straight backward in the negative x-direction
with a speed of 2.0x106 m/s. A second piece, with mass 8.0x105 kg, continues forward at an angle of 30° upward with
respect to the original trajectory at 1.0x106 m/s. If the original spaceship was traveling in the +x direction, sketch a
vector representing the direction of the third piece.
A spaceship of mass 2.0x106 kg is cruising at a speed of 5.0x10 6 m/s when the antimatter reactor fails, blowing up the ship in three
pieces. One section, having a mass of 5.0x10 5 kg, is blown straight backward with a speed of 2.0x10 6 m/s. A second piece, with mass
Momentum Page 82
pieces. One section, having a mass of 5.0x10 5 kg, is blown straight backward with a speed of 2.0x10 6 m/s. A second piece, with mass
8.0x105 kg, continues forward at an angle of 30° upward with respect to the original trajectory at 1.0x10 6 m/s. What is the magnitude
and direction of the velocity of the third piece after the explosion? (Answer: 1.471x10 7 m/s, 2.22° below original trajectory)
A sports car weighing 500 kg and traveling at 27 m/s fails to stop at an intersection and crashes into a 1600 kg delivery tru ck traveling
at 20 m/s in a direction at right angles to it. The wreckage becomes locked and travels 18 m before coming to rest. Find the coefficient
of kinetic friction between the road and the car + truck system during the sliding -to-rest stage. (Answer: 0.77)
Momentum Page 83
How many stages should this problem be broken into?
The first stage of this problem should be dealt with using conservation of momentum. Which one of the following reasons most
justifies that approach.
a. The energy of the collision is conserved.
b. No external forces act on the two during the collision.
c. No net external force act on the two during the collision.
d. The collision is assumed to be done so quickly that the impulse from friction can be neglected during the collision.
e. The two become locked together.
During the sliding to rest stage, identify all the types of physics that could be used to analyze the physics.
a. Kinematics
b. Mechanics (specifically forces)
c. Impulse
d. Conservation of Momentum
e. Work and Energy
Momentum Page 84
Physics 201 Class Template - Work and Energy
Wednesday, September 23, 2015
8:57 PM
Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. Just before hitting
the ground, the heavier marble has
a. as much kinetic energy as the lighter one.
b. twice as much kinetic energy as the lighter one.
c. half as much kinetic energy as the lighter one.
d. four times as much kinetic energy as the lighter one.
e. impossible to determine
Work and Energy Page 85
A particle moving along the x-axis experiences the force shown in the graph. If the particle has 2.0 J of kinetic energy
as it passes x = 0 m, what is its kinetic energy when it reaches x = 4 m?
Which force does the most work?
A crane raises a steel girder into place at a construction site. The girder moves with constant speed. Consider the
work Wg done by gravity and the work WT done by the tension in the cable. Which of the following is correct?
Work and Energy Page 86
a. Wg and WT are both zero.
b. Wg is negative and WT is negative.
c. Wg is negative and WT is positive.
d. Wg is positive and WT is positive.
e. Wg is positive and WT is negative.
A crane raises a steel girder into place at a construction site. The girder is moving downward and slowing down.
Which of the following statements about the girder are true.
a. The kinetic energy is increasing
b. The kinetic energy is decreasing
c. The work from the cable is positive
d. The work from the cable is negative
e. The work from gravity is positive
f. The work from gravity is negative
g. The magnitude of the work from the cable is greater than that from gravity
h. The magnitude of the work from the cable is less than that from gravity
i. The magnitude of the work from the cable is equal to that from gravity
A 2-kg-block, initially at rest, is being pulled horizontally by a 5-N tension force. The coefficient of static and kinetic
friction between the block and the surface is 0.5 and 0.2, respectively. What are the sign of the following quantities?
A. Work from gravity
B. Work from the normal force
C. Work from the tension
D. Work from the friction
Work and Energy Page 87
D. Work from the friction
Now sliding in direction of tension, what are the signs of the following quantities?
A. Work from gravity
B. Work from the normal force
C. Work from the tension
D. Work from the friction
A cart on an air track is moving at 0.5 m/s when the air is suddenly turned off. The cart comes to rest after
traveling 1 m. The experiment is repeated, but now the cart is moving at 1 m/s when the air is turned off.
How far does the cart travel before coming to rest?
Work and Energy Page 88
A pendulum bob swings in a complete vertical circle. At what point does the tension in the string do the
most work?
a. Bottom of the loop
b. Top of the loop
c. The tension does no work
Two people are on low friction carts, throwing a medicine ball back and forth, speeding up the rate at which
they move away from each other.
What is the sign of the work of the ball on person A while they catch the ball?
Work and Energy Page 89
a. positive
b. negative
c. zero
What is the sign of the work of the ball on person A while they throw the ball?
a. positive
b. negative
c. zero
The diagram depicts two pucks on a frictionless table. Puck II is four times as massive as puck I. Starting from rest, the
pucks are pushed across the table by two equal forces. The forces are active all the way to the finish line.
Which puck will have the greater kinetic energy upon reaching the finish line?
a. Puck I
b. Puck II
c. Both will have the same.
d. There is not enough information to decide.
Work and Energy Page 90
The diagram depicts two pucks on a frictionless table. Puck II is four times as massive as puck I. Starting from rest, the
pucks are pushed across the table by two equal forces. The forces act on both of them for 6.0 s.
Rank the final kinetic energy of the two pucks.
A cart on an air track is moving at 0.5 m/s when the air is suddenly turned off. The cart comes to rest after traveling 1 m.
The experiment is repeated, but now the cart is moving at 1 m/s when the air is turned off. How far does the cart travel
before coming to rest?
A pendulum bob swings in a complete vertical circle. At what point does the tension in the string do the most work?
a. Bottom of the loop
Work and Energy Page 91
a. Bottom of the loop
b. Top of the loop
c. The tension does no work
A stuntman is sliding toward a brick wall with wind blowing down and against their motion. Strapped to their back is a
rocket providing thrust.
What is the sign of the work for each force acting on the stuntman?
Work and Energy Page 92
A truck is accelerating with a box in the bed of the truck.
What is the sign of the following work?
A. friction from road on truck
B. friction from the truck on the box
C. normal force from the truck on the box
D. friction from the box on the truck
E. normal force from the box on the truck
A gondola with a box inside is accelerating up and at an angle from the horizontal.
What is the sign of the following work?
A. gravity on box
B. gravity on gondola
C. normal force on box
D. normal force on gondola
E. friction on box
F. friction on gondola
G. tension from cable on box
Work and Energy Page 93
Starting from rest, two identical 2-kg masses slide down different angle frictionless inclines.
If the angle from the horizontal in the first case is 30 o and the incline is 20.0 m long, how much work does gravity do on the
first mass while sliding down the incline?
Starting from rest, two identical 2-kg masses slide down different angle frictionless inclines.
If the angle from the horizontal in the second case is 65o and the incline is 11.03 m long, how fast will the mass be moving
when it reaches the bottom of the incline?
Work and Energy Page 94
Work and Energy Page 95
Starting from rest, two identical 2-kg masses slide down different angle inclines that both have identical coefficients of kinetic
friction.
Which mass will have the greater final kinetic energy when reaching the bottom.
1. 1
2. 2
3. same
4. not enough information
A 2-kg mass is compressed 1 m against a spring whose spring constant k is 20 N/m. Once released the mass
slides down a frictionless ramp then back up to another spring with the same spring constant. After
compressing the second spring it comes to rest and is held in place. Rank the work done by the normal force
from the ground during the following intervals.
•
•
•
•
a to b
b to c
c to d
d to e
>
What is the speed in m/s of the mass at point c?
Work and Energy Page 96
(J)
a
K
Ug
b
c
d
e
Work and Energy Page 97
Us
Etot
A box of mass m starts from rest on a horizontal surface on a
planet with an acceleration of gravity g. Wind applies a constant
horizontal force Fw on the box. After traveling a distance d on the
horizontal surface the box encounters an inclined plane that
makes an angle of θ up from the horizontal. To what height h will
the box reach before momentarily coming to rest? All surfaces are
frictionless.
Work and Energy Page 98
Two masses are connected via a simple pulley. m1 is on a horizontal surface while m2 is on
an incline. If you were trying to determine the final speed of the second mass once its
traveled some distance down the incline, which of the following physics are useful in the
analysis?
1.
2.
3.
4.
Kinematics
Newton's 2nd Law Mechanics
Impulse and Momentum
Conservation of Energy
Draw a line to define a
system boundary that would
have zero non-conservative
work being done in it.
Work and Energy Page 99
Three students are discussing the concept of work in regards to a situation where a dude is
standing at rest holding some books. Which student do you agree with most?
1. “The books aren't moving so there is no way any work is being done on
them.”
2. “That doesn't make sense because the dudes arms would be getting
tired and thus he must be losing energy, if energy is being lost then
work must be done on the dude”
3. “The only force connecting the books and that dude are the normal
force, so if the books have no work being done on them but the dude
does have work being done on him it can’t be due to the normal force
from the books.”
4. All are correct statements
A 50-kg person stands on a 25-kg platform. He pulls on the rope that is attached to the platform via
the frictionless pulley system shown here. If he pulls the platform up at a steady rate, and pulls the
rope through a distance of 2 meters, how much work does the rope do on the man? Ignore friction
and assume g = 10 m/s2.
Work and Energy Page 100
Tarzan is in the path of a pack of stampeding elephants when Jane swings in to the rescue on a
rope vine, hauling him off to safety. If the length of the vine is 25 m, and Jane starts her swing with
the rope horizontal, how fast is she traveling right before picking up Tarzan?
If Jane’s mass is 54 kg, and Tarzan’s is 82 kg, to what height above the ground will the pair swing
after she grabs him. Answer: 3.94 m
Work and Energy Page 101
Potential Energy Functions
Work and Energy Page 102
Work and Energy Page 103
Work and Energy Page 104
Work and Energy Page 105
Work and Energy Page 106