Which of the following best describes how to calculate the average acceleration of any object?
Average acceleration is always equal to the change in velocity of an object divided by the time interval.
The figure shows the velocity versus time graph for a car driving on a straight road. Which of the following best describes the acceleration of the car?
The acceleration of the car is positive and decreasing.
...
...
On a straight road, a car speeds up at a constant rate from rest to 20 m/s over a 5 second interval and a truck slows at a constant rate from 20 m/s to a complete stop over a 10 second interval. How does the distance traveled by the truck compare to that
The truck travels twice as far as the car.
Suppose you are hiking along a trail. Make a comparison between the magnitude of your displacement and your distance traveled.
The magnitude of your displacement can be equal to your distance traveled.
The magnitude of your displacement can be less than your distance traveled
Suppose a runner completes one lap around a 400-m track in a time of 50 s. Calculate the magnitude of the average velocity of the runner.
0 m/s (his displacement is zero if his starting point = his ending point)
Suppose a runner completes one lap around a 400-m track in a time of 50 s. Calculate the average speed of the runner.
8 m/s
Consulting the graph shown in (Figure 1) , determine the object's average velocity over the time interval from 2 to 4 seconds.
5 m/s
Which of the motion diagrams in the figure below best matches the motion of the bungee jumper shown in the video?
C (Because the video only follows the free fall portion of the jump, the correct motion diagram shows constant downward acceleration.)
Which of the following best describes the acceleration of a bungee jumper during free fall?
constant (Free fall acceleration is constant and has a value of 9.8 m/s^2)
Three cars drive around a perfectly circular track. The speedometers in the figure below show the speed of each car over the same 10-s time interval. Which of the cars are accelerating?
Cars A, B, and C (All three cars are accelerating because the directions of their velocity vectors change constantly as they drive in a circle. In addition, the speeds of cars A and B are changing, which also indicates acceleration.)
Four cars undergo acceleration as described by the data in the following table.
Car B, Car A, Car D, Car C (Correct
The average accelerations, from most positive to most negative, are as follows: (B) 4 m/s2, (A) 3 m/s2, (D) 2.5 m/s2, and (C) ?3 m/s2.)
Suppose that you toss a rock upward so that it rises and then falls back to the earth. If the acceleration due to gravity is 9.8 m/sec2, what is the rock's acceleration at the instant that it reaches the top of its trajectory (where its velocity is moment
The rock has a downward acceleration of 9.8m/s^2
On Mars, where air resistance is negligible, an astronaut drops a rock from a cliff and notes that the rock falls about d meters during the first t seconds of its fall. Assuming the rock does not hit the ground first, how far will it fall during the first
16d
On the Moon, where air resistance is negligible, an astronaut drops a rock from a cliff and notes that the rock has a speed v after falling from its point of release for a time t. Assuming that the rock does not hit the ground first, how fast will it be m
4v
Which of the following equations correctly expresses the relation between vectors A? , B? , and C? shown in the figure? (problem 1)
B? =A? +C?
Vector A? has a magnitude of 2.00 m and vector B? has a magnitude of 5.00 m. If the direction of each vector is unknown, what is the largest possible value for the magnitude of A? ?B? ?
7.00 m
Which of the following equations correctly expresses the relation between vectors A? , B? , and C? shown in the figure? (problem 2)
A? +B? +C? =0
Vector A? has a magnitude of 3.00 and is directed parallel to the negative y-axis and vector B? has a magnitude of 3.00 and is directed parallel to the positive y-axis. Determine the magnitude and direction angle (as measured counterclockwise from the pos
C = 6.00; ? = 270?
Suppose that C? =A? ?B? . Under what circumstances is the length of C? has to equal to the sum of the lengths of A? has and B? has?
When A? and B? point in opposite directions
Starting from your campsite you walk 3.0 km east, 6.0 km north, 1.0 km east, and then 4.0 km west. How far are you from your campsite?
6.0 km
Which of the following is a vector quantity?
acceleration
velocity
momentum
force
displacement
The sum of two vectors is the largest when the two vectors are _____.
pointing in the same direction
The sum of the x components of vectors A and B in (Figure 1) is ___.
4
A swimmer is determined to cross a river that flows due south with a strong current. Initially, the swimmer is on the west bank desiring to reach a camp directly across the river on the opposite bank. In which direction should the swimmer head?
The swimmer should swim northeast.
As an airplane taxies on the runway with a speed of 17.0 m/s , a flight attendant walks toward the tail of the plane with a speed of 1.22 m/s. What is the flight attendant's speed relative to the ground?
v(rel) = 15.8 m/s
A police car travels at 37.8 m/s due east while in pursuit of a vehicle that is traveling at 33.4 m/s due east. What is the velocity of the vehicle relative to the police car?
-4.4 m/s (x^)
What is the velocity of the police car relative to the vehicle?
4.4 m/s (x^)
For general projectile motion, which of the following best describes the horizontal component of a projectile's acceleration? Assume air resistance is negligible.
The horizontal component of a projectile's acceleration is zero.
For general projectile motion, which of the following best describes the vertical component of a projectile's acceleration? Assume air resistance is negligible.
The vertical component of a projectile's acceleration remains a nonzero constant
At what angle, above the horizon, should a cannon be fired in order for the cannon ball to obtain the greatest horizontal range? Assume air resistance is negligible.
The cannon should be fired at an angle of 45� above the horizon.
A football player kicks a football in a field goal attempt. When the football reaches its maximum height, what is the relationship between the direction of the velocity and acceleration vectors? Assume air resistance is negligible.
At the maximum height, the velocity and acceleration vectors are perpendicular to each other.
Use the motion diagram in (Figure 1) showing the trajectory of a human cannonball to answer Parts A through D. No air resistance acts on the human cannonball. How does the vertical acceleration at point A compare to the vertical acceleration at point C?
Both accelerations are equal to free fall acceleration.
How does the magnitude of the horizontal velocity change as the human cannonball passes through points A, B, C, D, and E?
It does not change.
Is the vertical component of velocity ever zero? If so, where?
Yes, it is zero at point C
When launched, the human cannonball's initial velocity has a positive x-component and a positive y-component. Rank the vertical velocity components at points A through E from most positive to most negative.
A, B, C, D, E
An object is moving with constant velocity. Which of the following best describes the force(s) acting on the object?
The net force acting on the object is zero.
A large truck collides head-on with a small car. The car is severely damaged as a result of the collision. According to Newton's third law, how do the forces acting between the truck and car compare during the collision?
The force on the truck is equal to the force on the car.
Recall the portion of the video in which the girl pushes her brother on the sled at constant velocity. The pushing force she exerts on the sled is _____ the frictional force the ground exerts on the sled.
equal to
According to Newton's first law, when the net force acting on an object is zero, the object must _____
Have constant velocity.
An elevator moves straight upward at a constant speed. Newton's first law predicts that the net force acting on the elevator will _____.
be zero.
Imagine holding a basketball in both hands, throwing it straight up as high as you can, and then catching it when it falls. At which points in time does a zero net force act on the ball? Ignore air resistance.
When you hold the ball still in your hands after catching it
When you hold the ball still in your hands before it is thrown
The video identifies the force pair produced when an apple falls through the air. Which force belongs in a free-body diagram of the apple?
force of Earth on apple
A force pair is produced when a tennis racket strikes a tennis ball. Which of the following best explains why the tennis ball does not have zero net force acting on it?
Each half of the force pair acts on a different object.
What explains the dramatically different magnitudes of accelerations that result when a mosquito collides head on with a moving truck?
unequal masses of the bus and the mosquito
The same net force is applied to two different objects. The second object has twice the mass of the first object. Compare the acceleration of the two objects.
The acceleration of object 1 is twice the acceleration of object 2
An object is at rest on a tabletop. Earth pulls downward on this object with a force equal in magnitude to mg. If this force serves as the action force, what is the reaction force in the action-reaction pair?
the object pulling upward on Earth
You are pulling your little sister on her sled across an icy (frictionless) surface. When you exert a constant horizontal force of 110 N , the sled has an acceleration of 2.4 m/s2 . If the sled has a mass of 9.0 kg , what is the mass of your little sister
m = 37 kg
An ant walks slowly away from the top of a bowling ball, as shown in the figure.If the ant starts to slip when the normal force on its feet drops below one-half its weight, at what angle ? does slipping begin?
? = 60�
Suppose a rocket launches with an acceleration of 32.0 m/s2 . What is the apparent weight of an 95-kg astronaut aboard this rocket
w(a) = 4000 N
A packing crate is sitting at rest on an inclined loading ramp. How does the magnitude of the force of static friction compare to the other forces acting on the crate?
The magnitude of the force of static friction is equal to the magnitude of the component of the weight of the crate parallel to the inclined ramp
In general, how does the coefficient of static friction compare to the coefficient of kinetic friction for the same two materials?
The coefficient of static friction is greater than the coefficient of kinetic friction.
You push two identical bricks across a tabletop with constant speed, v, as shown in the figure. In case 1, you place the bricks end to end; in case 2, you stack the bricks one on top of the other.(Figure 1) Is the force of kinetic friction in case 1 great
equal to
Choose the best explanation from among the following:
The normal force is the same in the two cases, and friction is independent of surface area.
Two drivers traveling side-by-side at the same speed suddenly see a deer in the road ahead of them and begin braking. Driver 1 stops by locking up his brakes and screeching to a halt; driver 2 stops by applying her brakes just to the verge of locking, so
greater than
Choose the best explanation from among the following:
Locked-up breaks lead to sliding (kinetic) friction, which is less than rolling (static) friction.
A large crate filled with physics laboratory equipment must be moved up an incline onto a truck. (Figure 1). The crate is at rest on the incline. What can you say about the force of friction acting on the crate?
The frictional force points up the incline
A physicist attempts to push the crate up the incline. The physicist senses that if he applies slightly more force the crate will move up the incline but cannot muster enough strength to get the motion started. What can you say now about the force of fric
The frictional force points down the incline
The first physicist gets a second physicist to help. They both push on the crate, parallel to the surface of the incline, and it moves at constant speed up the incline. How does the force exerted by the two physicists on the crate compare with the force o
F(two physicists) is greater than F(friction)
An object is hanging by a string from the ceiling of an elevator. The elevator is moving upward with a constant speed. What is the magnitude of the tension in the string?
The magnitude of the tension in the string is equal to the magnitude of the weight of the object.
An object is hanging by a string from the ceiling of an elevator. The elevator is slowing down while moving upward. What is the magnitude of the tension in the string?
The magnitude of the tension in the string is less than the magnitude of the weight of the object
Consider the video tutorial you just watched. Suppose that we duplicate this experimental setup in an elevator. What will the spring scale read if the elevator is moving upward at constant speed?
18 N (Since the elevator is not accelerating, the reading on the scale is the same as in the video.)
To hang a pot of flowers, a gardener uses two wires - one attached horizontally to a wall, the other sloping upward at an angle ? of and attached to the ceiling.(Figure 1) Which of the three graphs (A, B, or C) in the figure shows an accurate plot of the
Graph B
Choose the best explanation from among the following:
T2 is greater than T1 at all angles, and is equal to mg at ? = 90�
Atwood's machine consists of two masses connected by a string that passes over a pulley, as shown in the figure.(Figure 1)
The acceleration of the masses for general m1 and m2 is a=(m2?m1m2+m1)g. In the specific case m1 = 3.1kg and m2 = 4.4kg acceleration
decrease
Choose the best explanation from among the following:
The net force acting on the blocks is the same, but the total mass that must be accelerated is greater.
In the situation shown in the figure, a person is pulling with a constant, nonzero force F? on string 1, which is attached to block A. Block A is also attached to block B via string 2, as shown.
For this problem, assume that neither string stretches and t
Both blocks will have the same acceleration
How does the magnitude of the tension in string 1, T1, compare with the tension in string 2, T2?
T1 > T2
An object moves in a circular path at a constant speed. What is the direction of the net force acting on the object?
The net force is directed toward the center of the circular path
An object moves in a circular path at a constant speed. What is the relationship between the directions of the object's velocity and acceleration vectors?
The velocity and acceleration vectors are perpendicular
A car drives with constant speed on an elliptical track, as shown in the figure (Figure 1) .Rank the points A, B, and C in order of decreasing likelihood that the car might skid.
Rank the points from most likely to least likely for car to skid. To rank it
A, B, C
A puck attached to a string undergoes circular motion on an air table. If the string breaks at the point indicated in the figure (Figure 1) , is the subsequent motion of the puck best described by path A, B, C, or D?
B
A Human Centrifuge To test the effects of high acceleration on the human body, the National Aeronautics and Space Administration (NASA) has constructed a large centrifuge at the Manned Spacecraft Center in Houston. In this device, astronauts are placed in
v = 36 m/s
Consider the video demonstration that you just watched. Which of the following changes would make it more likely for the ball to hit both the white can and the green can?
None of the above
Two identical cars are driving in opposite directions at the same speed. Their kinetic energies have ____.
The same magnitude and sign
A motorcycle drives up a steeply inclined ramp. The work done on the motorcycle by the Earth's gravitational force is ____.
negative
During a certain time interval, the net work done on an object is zero joules. We can be certain that ____.
the object's final speed was the same as its initial speed
The amount of kinetic energy an object has depends on its mass and its speed.
Rank the following sets of oranges and cantaloupes from least kinetic energy to greatest kinetic energy. If two sets have the same amount of kinetic energy, place one on top of
mass 4m speed 1/4v, total mass 2m speed 1/2v, mass m speed v, total mass 4m speed v = mass 4m speed v
A graph depicts force versus position. What represents the work done by the force over the given displacement?
The work done is equal to the area under the curve
If the net work done on an object is positive, what can you conclude about the object's motion? Assume the object is in the absence of any other forces or friction.
The object is speeding up
A person applies a 50 N force on a crate, causing it to move horizontally at a constant speed through a distance of 10 m. What is the net work done on the crate
The net work done on the crate is zero joules
A ball is thrown straight upward. How does the sign of the work done by gravity while the ball is traveling upward compare with the sign of the work done by gravity while the ball is traveling downward?
Work done by gravity is negative while the ball is traveling upward and positive while the ball is traveling downward.
An object weighing 20 N moves horizontally toward the right a distance of 5.0 m. What is the work done on the object by the force of gravity?
The work done on the object by the force of gravity is zero joules.
Person B does twice the work of person A, and in one-half of the time . How does the power output of person B compare to person A?
Person B has four times the power output of person A.
Which of the following statements is/are true?
Power can be considered the rate at which energy is transformed.
A person's power output limits the amount of work that he or she can do in a given time span.
Power can be considered the rate at which work is done.
The SI unit of power is the watt.
Which of the following statements is/are true?
The work done by a nonconservative force depends on the the path taken.
A potential energy function can be specified for a conservative force.
A conservative force permits a two-way conversion between kinetic and potential energies
The work done by a conservative force is indicated in the figure for a variety of different paths connecting the points A and B. What is the work done by this force on path 1?
W1 = -3 J
What is the work done by this force on path 2?
W2 = -4 J
Ball 1 is thrown to the ground with an initial downward speed; ball 2 is dropped to the ground from rest. Assuming the balls have the same mass and are released from the same height, is the change in gravitational potential energy of ball 1 greater than,
equal to the change in gravitational potential energy of ball 2
Choose the best explanation from among the following:
The gravitational potential energy depends only on the mass of the ball drop height.
The work-energy theorem states that a force acting on a particle as it moves over a ______ changes the ______ energy of the particle if the force has a component parallel to the motion.
distance/kinetic
To calculate the change in kinetic energy, you must know the force as a function of _______. The work done by the force causes the kinetic energy change.
position
To illustrate the work-energy concept, consider the case of a stone falling from xi to xf under the influence of gravity.
Using the work-energy concept, we say that work is done by the gravitational _____, resulting in an increase of the ______ energy of
force/kinetic
Rather than ascribing the increased kinetic energy of the stone to the work of gravity, we now (when using potential energy rather than work-energy) say that the increased kinetic energy comes from the ______ of the _______ energy.
change/potential
This process happens in such a way that total mechanical energy, equal to the ______ of the kinetic and potential energies, is _______.
sum/conserved
During which interval is the largest amount of energy required to stretch the spring?
From x = 2d to x = 3d
A spring is stretched from x=0 to x=d, where x=0 is the equilibrium position of the spring. It is then compressed from x=0 to x=?d. What can be said about the energy required to stretch or compress the spring?
The same amount of energy is required to either stretch or compress the spring
Now consider two springs A and B that are attached to a wall. Spring A has a spring constant that is four times that of the spring constant of spring B. If the same amount of energy is required to stretch both springs, what can be said about the distance
Spring A must stretch half the distance spring B stretches.
Two identical springs are attached to two different masses, MA and MB, where MA is greater than MB. The masses lie on a frictionless surface. Both springs are compressed the same distance, d, as shown in the figure. Which of the following statements desci
Spring A requires the same amount of energy as spring B
Two objects are moving at equal speed along a level, frictionless surface. The second object has twice the mass of the first object. They both slide up the same frictionless incline plane. Which object rises to a greater height?
The two objects rise to the same height
Two identical balls are thrown vertically upward. The second ball is thrown with an initial speed that is twice that of the first ball. How does the maximum height of the two balls compare?
The maximum height of the second ball is four times that of the first ball
Which of the following statements is/are true?
Check all that apply.
Mechanical energy can be dissipated to nontechnical forms of energy
The total mechanical energy of a system is constant only if all the forces doing work on it are conservative
Is the mechanical energy of the shuttle-Earth system when the shuttle lands greater than, less than, or the same as when it is in orbit?
less than when it is in orbit
Choose the best explanation from among the following:
A portion of the mechanical energy has been converted to heat energy.
Suppose that we repeat the experiment in the video, but this time (1) the loop's diameter is twice that of the original loop and (2) the ball's starting position is twice as high above the table as that in the video. The initial height is sufficiently hig
?(2)v0
In the opening scenes of the prelecture video, we outlined some of the key properties of momentum. Which of the following statements are consistent with these properties?
Momentum is a vector quantity
An object's momentum is equal to the product of its mass and its velocity
Object A has a mass m and a speed v, object B has a mass m/2 and a speed 4v, and object C has a mass 3m and a speed v/3. Rank the objects according to the magnitude of their momentum.
Rank from smallest to largest. To rank items as equivalent, overlap the
Object A = Object C, Object B
A 1700kg rhino charges at a speed of 50.0km/h. What is the magnitude of the average force needed to bring the rhino to a stop in 0.50s?
4.7x10^4 N
A 3.6-kg chihuahua charges at a speed of 3.3m/s. What is the magnitude of the average force needed to bring the chihuahua to a stop in 0.50s?
24 N
Shown below is a graph of a force applied to a small object as a function of time. If the object has a mass of 5.0kg and is at rest at t=0s, how fast is the object moving at t=4.0s?
7.2 m/s
Suppose a constant force is the only force applied to an object of unknown mass. What quantities do we need to know in order to find the object's change in momentum?
We need to know the magnitude of the force
We need to know the time interval during which the force acts
In a lab environment, you are investigating the impulse of a force exerted on a brick when the brick's speed is reduced from 2.5 m/s to a complete stop. First, you allow the brick to slam into a secured piece of wood, bringing the brick to a sudden stop.
The impulse is the same in both situations
A lump of putty and a rubber ball have equal mass. Both are thrown with equal speed against a wall. The putty sticks to the wall. The ball bounces back at nearly the same speed with which it hit the wall. Which object experiences the greater momentum chan
The ball experiences the greater momentum change
The video shows an animated billiards experiment in which a cue ball strikes a glued-in-place eight-ball. Which of the following explains why the momentum of the eight-ball is conserved?
The "glue force" cancels the collision force.
Which statement must be true for the momentum of a system to be conserved?
The net external force on the system is zero.
Bumper cars A and B undergo a collision during which the momentum of the combined system is conserved. Which equation(s) correctly states the principle of conservation of momentum?
P? A,i+P? B,i=P? A,f+P? B,f
?P? A+?P? B=0
While goofing off at the ice skating rink, a student takes off her shoes and places each of them on the ice. Her friend, a hockey player, then shoots a hockey puck at each shoe. The first puck immediately comes to rest after it collides with the left shoe
The right shoe
For an elastic collision, which of the following statements are true?
Momentum is conserved
Kinetic energy is conserved
A freight car moves along a frictionless level railroad track at constant speed. The freight car is open on the top. A large load of sand is suddenly dumped into the freight car. What happens to the speed of the freight car?
The speed of the freight car decreases
A red ball with a velocity of +3.0 m/s collides head-on with a yellow ball of equal mass moving with a velocity of ?2.0 m/s. What is the velocity of the two balls after the elastic collision?
The velocity of the red ball is -2.0m/s; the velocity of the yellow ball is +3.0 m/s
When a person steps forward out of a small boat onto a dock, the boat recoils backward in the water. Why does this occur?
The total momentum of the system is conserved.
Two particles of masses m1 and m2 (m1<m2) are located 10 meters apart. Where is the center of mass of the system located?
More than 5 meters but less than 10 meters from the particle of m1
For the system of three particles shown, which have masses M, 2M, and 3M as indicated, where is the center of mass located?
between the particle of mass 2M and the particle of mass 3M
For the system of particles described in Part B, find the x coordinate xcm of the center of mass. Assume that the particle of mass M is at the origin and the positive x axis is directed to the right.
x(CM) = 8L/6
Let us now consider a two-dimensional case. The system includes three particles of equal mass M located at the vertices of an isosceles triangle as shown in the figure. Which arrow best shows the location of the center of mass of the system? Do not calcul
4
What is the x coordinate xcm of the center of mass of the system described in Part D?
Express your answer in terms of L.
x(CM) = L/3
A system of four buckets forms a square as shown in the figure. Initially, the buckets have different masses (it is not known how these masses are related). A student begins to add water gradually to the bucket located at the origin. As a result, what hap
The x coordinate decreases the y coordinate decreases.
Find the x coordinate xcm of the center of mass of the system of particles shown in the figure.
x(CM) = 0.56 m
Find the y coordinate of the center of mass of the system of particles described in the previous part.
Express your answer in meters to two significant figures.
y(CM) = 0.40 m
Is the center of mass of the midair drops higher than, lower than, or equal to the halfway distance between the tip of the stalactite and the cave floor?
higher than
Choose the best explanation from among the following:
Though equally spaced in time, the drops are closer together higher up.
A girl and a boy are riding on a merry-go-round that is turning at a constant rate. The girl is near the outer edge, and the boy is closer to the center. Who has greater angular displacement?
Both the girl and the boy have the same nonzero angular displacement
Rank the following in order of decreasing angular speed: an automobile tire rotating at 2.00�103deg/s, an electric drill rotating at 400.0 rev/min, and an airplane propeller rotating at 40.0 rad/s.
Rank from largest to smallest angular speed. To rank item
Electric drill, airplane propeller, automobil tire
In answering the following questions, assume that the angular acceleration is constant and nonzero: ??0. True or false: The quantity represented by ? is a function of time (i.e., is not constant)
TRUE
True or false: The quantity represented by ?i is a function of time (i.e., is not constant).
FALSE
True or false: The quantity represented by ?i is a function of time (i.e., is not constant).
FALSE
True or false: The quantity represented by ? is a function of time (i.e., is not constant).
TRUE
Which of the following equations is NOT an explicit function of time t, that is, does not involve t as a variable, and is therefore useful when you do not know or do not need the time?
?2=?20+2?(???0)
In the equation ?=?0+?t, what does the time variable t represent?
Choose the answer that is always true. Several of the statements may be true in a particular problem, but only one is always true.
the time elapsed from when the angular velocity equals ?0 until the angular velocity equals ?
Suppose you are asked to find the amount of time t, in seconds, it takes for the turntable to reach its final rotational speed. Which of the following equations could you use to directly solve for the numerical value of t?
More information is needed before t can be found.
You are now given an additional piece of information: It takes five complete revolutions for the turntable to speed up from 3313rpm to 45rpm. Which of the following equations could you use to directly solve for the numerical value of the angular accelerat
?2=?20+2?(???0)
Rank these graphs on the basis of the angular velocity of each object. Rank positive angular velocities as larger than negative angular velocities.
Rank from largest to smallest. To rank items as equivalent, overlap them.
B, C, A=F, D=E,
Rank these graphs on the basis of the angular acceleration of the object. Rank positive angular accelerations as larger than negative angular accelerations.
A = B = C = D = E = F.
Two racecars are driving at constant speeds around a circular track. Both cars are the same distance away from the center of the track, but car 2 is driving twice as fast as car 1. The acceleration of car 2 is ___________ the acceleration of car 1.
four times
Two children are riding on a merry-go-round that is rotating with a constant angular speed. Abbie is one meter from the center of the merry-go-round, whereas Zak is two meters from the center. Abbie's acceleration is ___________ Zak's acceleration.
half of
Four racecars are driving at constant speeds around a circular racetrack. The data table gives the speed of each car and each car's distance from the center of the track at one instant.
Acceleration of car C, Acceleration of car D, Acceleration of car A, Acceleration of car B
Cheryl is riding on the edge of a merry-go-round, 2m from the center, which is rotating with an increasing angular speed. Cheryl's tangential acceleration is 3.0m/s2. At the instant that Cheryl's linear speed is 4.0m/s, what is Cheryl's total acceleration
8.5 m/s^2
A girl and a boy are riding on a merry-go-round that is turning at a constant rate. The girl is near the outer edge, and the boy is closer to the center. Who has greater linear speed?
The girl has greater linear speed
A girl and a boy are riding on a merry-go-round that is turning at a constant rate. The girl is near the outer edge, and the boy is closer to the center. Who has greater tangential acceleration?
Both the girl and the boy have zero tangential acceleration
Which of the graphs corresponds to x position versus time?
Graph F
Which of the graphs corresponds to angular position versus time?
Graph A
Which of the graphs corresponds to y velocity versus time?
Graph F
Which of the following graphs corresponds to angular velocity versus time?
Graph C
Which child moves with greater magnitude of linear velocity?
Bobby has the greater magnitude of linear velocity
Who moves with greater magnitude of angular velocity?
Both Ana and Bobby have the same magnitude of angular velocity
Who moves with greater magnitude of tangential acceleration?
Both Ana and Bobby have the same magnitude of tangential acceleration
Who has the greater magnitude of centripetal acceleration?
Bobby has the greater magnitude of centripetal acceleration
A baseball bat can be rotated around many different axes of rotation. Three such possibilities are shown in (Figure 1) . Rank the baseball bat's moment of inertia about each of these three axes of rotation.
Rank the moment of inertia from largest to small
B, A, C
Given the same baseball bat and possible axes of rotation shown in (Figure 1) , for which axis of rotation would it be the easiest to rotate the bat from rest?
C
A girl spins around in a circle trying to make herself dizzy. Without changing her position, she starts spinning twice as fast. By how much did her rotational kinetic energy change?
It quadrupled
A solid sphere and a hollow sphere (spherical shell) of the same mass and same radius rotate with the same amount of kinetic energy. Which one is rotating faster?
The solid sphere
Starting from rest, a solid sphere rolls without slipping down an incline plane. At the bottom of the incline, what does the angular velocity of the sphere depend upon?
The angular velocity depends on the mass of the sphere
The angular velocity depends on the height of the incline
Suppose a bicycle wheel is rotated about an axis through its rim and parallel to its axle. Is its moment of inertia about this axis greater than, less than, or equal to its moment of inertia about its axle?
greater than
Suppose a bicycle wheel is rotated about an axis through its rim and parallel to its axle. Choose the best explanation from among the following:
Mass is farther from the axis when the wheel is rotated about the rim
When the ball comes to rest on the no-slip surface, is its height greater than, less than, or equal to the height from which it was released?
less than
An electric fan spinning with an angular speed of 11 rad/s has a kinetic energy of 4.7 J . What is the moment of inertia of the fan?
Express your answer using two significant figures.
I = 7.8�10?2 kg?m2
Two equal forces are applied perpendicular to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Which force exerts the greater torque?
The force applied at the doorknob exerts the greater torque
A constant net torque is applied to a rotating object. Which of the following best describes the object's motion?
The object will rotate with constant angular acceleration.
Rank these forces (A through F) on the basis of the magnitude of the torque they apply to the wrench, measured about an axis centered on the bolt.
Rank from largest to smallest. To rank items as equivalent, overlap them.
D, B=E, F
To tighten a spark plug, it is recommended that a torque of 30 N?m be applied. If a mechanic tightens the spark plug with a wrench that is 15 cm long, what is the minimum force necessary to create the desired torque?
F = 200 N
Assume that the mass of the swing bar, as shown in the figure, is negligible.(Figure 1)
Find the magnitude of the angular acceleration ? of the seesaw.
Express your answer in terms of some or all of the quantities m1, m2, l, as well as the acceleration du
? =
[2(m1?m2)g](m1+m2)l
In what direction will the seesaw rotate, and what will the sign of the angular acceleration be?
The rotation is in the counterclockwise direction and the angular acceleration is positive.
Now consider a similar situation, except that now the swing bar itself has mass mbar.(Figure 2)
Find the magnitude of the angular acceleration ? of the seesaw.
Express your answer in terms of some or all of the quantities m1, m2, mbar, l, as well as the a
? =
6g(m1?m2)(3(m1+m2)+mbar)l
In what direction will the seesaw rotate and what will the sign of the angular acceleration be?
The rotation is in the counterclockwise direction and the angular acceleration is positive.
An extended object is in static equilibrium if __________.
both the net force acting on the object is zero and the net torque acting on the object is zero
Two children want to balance horizontally on a seesaw. The first child is sitting one meter to the left of the pivot point located at the center of mass of the seesaw. The second child has one-half the mass of the first child. Where should the second chil
2 m to the right of the pivot (Whether the seesaw is balanced or not depends upon whether there is any net torque about its pivot point. This can be determined either by explicitly calculating the torque due to each child about that point, or by finding t
Rank in order, from least stable to most stable, the three glasses of water shown.
tall, narrow glass, tapered glass, short, fat glass.
A heavy boy and a lightweight girl are balanced on a massless seesaw. The boy moves backward, increasing his distance from the pivot point. What happens to the seesaw?
The side the boy is sitting on will tilt downward.
Suppose we replace the mass in the video with one that is four times heavier. How far from the free end must we place the pivot to keep the meter stick in balance?
90 cm (10 cm from the weight)
Suppose the person climbs higher on the ladder. As a result, is the ladder more likely, less likely, or equally likely to slip?
more likely
Choose the best explanation from among the following:
the magnitude of f2 must increase as the person moves upward
Does the pivot point (i.e., the triangle in the diagram upon which the ruler balances) exert a force on the ruler? Does it exert a nonzero torque about the pivot?
yes/no
Although the pivot exerts a force on the ruler it does not exert a torque with respect to the pivot point. Why not?
Because the distance from the exerted force to the pivot is zero.
Find the mass M2.
Express your answer for the unknown mass numerically, in grams, to two significant digits.
M2 = 18 g
Five locations labeled A through E are indicated on the diagram. Which of these, if any, is a possible location of the object's center of mass (center of gravity)?
C
Is the tension in the string on the left-hand rotating system greater than, less than, or equal to the tension in the string on the right-hand rotating system?
Greater than
Choose the best explanation from among the following:
The mass in the right-hand system has the greater downward acceleration
When the block is allowed to fall, does it stay on the center line, move toward the right, or move toward the left?
move toward the left
Choose the best explanation from among the following:
The wheel has the greater moment of inertia and unwinds more slowly than the disk.
A 2.80 kg bucket is attached to a disk-shaped pulley of radius 0.131 m and mass 0.692 kg . If the bucket is allowed to fall. What is its linear acceleration?
a = 8.73 m/s2
What is the angular acceleration of the pulley?
? = 66.6 rad/s2
How far does the bucket drop in 1.50 s ?
?y = 9.82 m
Initially, the baton is spinning about an axis through its center at angular velocity 3.00 rad/s . (Figure 1) What is the magnitude of its angular momentum about a point where the axis of rotation intersects the center of the baton?
1.92�10?2 kg?m2/s
With a skillful move, the majorette changes the rotation of her baton so that now it is spinning about an axis passing through its end at the same angular velocity 3.00 rad/s as before. (Figure 2) What is the new amplitude of the angular momentum of the r
7.68�10?2 kg?m2/s
What is the magnitude of the jogger's linear momentum?
p = 236 kg?m/s
What is the magnitude of the jogger's angular momentum with respect to the origin, O?
L = 1180 kg?m2/s
Calculate the angular momentum of the Earth about its own axis, due to its daily rotation. Assume that the Earth is a uniform sphere.
L = 7.05�1033 kg?m2/s
A girl moves quickly to the center of a spinning merry-go-round, traveling along the radius of the merry-go-round. Which of the following statements are true?
The moment of inertia of the system decreases
The angular speed of the system increases
Suppose that we repeat the experiment in the video but use hand-held weights of different masses and different initial speeds. In each of the cases below, the demonstrator starts with her arms extended (rotating at angular speed ?0) and then pulls her arm
Initial angular speed 0.5?0, mass m=Initial angular speed 0.5?0, mass 0.5m, Initial angular speed ?0, mass m=Initial angular speed ?0, mass 2m, Initial angular speed 2?0, mass m= Initial angular speed 2?0, mass 2m
Suppose you now grab the edge of the wheel with your hand, stopping it from spinning.
It begins to rotate counterclockwise (as observed from above)
The experimenter from the video rotates on his stool, this time holding his empty hands in his lap. You stand on a desk above him and drop a long, heavy bean bag straight down so that it lands across his lap, in his hands. What happens?
He spins slower
What is the final angular velocity, ?f, of the two disks?
?f = It/(It+Ir) ?i
Because of friction, rotational kinetic energy is not conserved while the disks' surfaces slip over each other. What is the final rotational kinetic energy, Kf, of the two spinning disks?
Kf = Ki (It/It+Ir)
Two objects attract each other gravitationally. If the distance between their centers decreases by a factor of 2, how does the gravitational force between them change?
The gravitational force increases by a factor of 4.
Which of the following statements are true?
The gravitational force between two objects is proportional to the product of the masses of the two objects
The gravitational force between two objects is inversely proportional to the square of the distance between the two objects.
Two objects attract each other gravitationally. If the mass of each object doubles, how does the gravitational force between them change?
The gravitational force increases by a factor of 4
Two planets, planet A and planet B, have the same surface gravity. However, planet B has twice the radius of planet A. How does the mass of planet B compare to the mass of planet A?
The mass of planet B is four times the mass of planet A
A hypothetical planet has a mass one-third of and a radius three times that of Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity on Earth?
The acceleration due to gravity is g/27
Consider the earth following its nearly circular orbit (dashed curve) about the sun.(Figure 2) The earth has mass mearth=5.98�1024kg and the sun has mass msun=1.99�1030kg. They are separated, center to center, by r = 93million miles = 150 million km. What
3.53x10^22 N
At the moment shown in the figure of the earth and sun (Figure 2) , what is the direction of the gravitational force acting on the earth? The possible directions are displayed in this figure (Figure 3) .
A
What is the magnitude of the gravitational force acting on the sun due to the earth?
The earth exerts 3.53�1022N of force on the sun, exactly the same amount of force the sun exerts on the earth found in Part A.
Which of the following changes to the earth-sun system would reduce the magnitude of the force between them to one-fourth the value found in Part A?
Reduce the mass of the earth to one-fourth its normal value
Reduce the mass of the sun to one-fourth its normal value
Reduce the mass of the earth to one-half its normal value and the mass of the sun to one-half its normal value.
With the sun and the earth back in their regular positions, consider a space probe with mass mp=125kg launched from the earth toward the sun. When the probe is exactly halfway between the earth and the sun along the line connecting them, what is the direc
The force is towards the sun.
What is the value of the composite constant (Gmer2e), to be multiplied by the mass of the object mo in the equation above?
9.80 m/s^2
Earth's orbit around the Sun is slightly elliptical. Thus, Earth actually gets closer to the Sun during part of the year. What happens to Earth's orbital speed when it is closer to the Sun?
Earth's orbital speed is greater when it is closer to the Sun than when it is farther from the Sun
A planet is discovered orbiting around a star in the galaxy Andromeda at the same distance from the star as Earth is from the Sun. If that star has four times the mass of our Sun, how does the orbital period of the planet compare to Earth's orbital period
The planet's orbital period will be one-half Earth's orbital period.
Which of the following statements are true?
The path of the planets around the Sun is elliptical in shape
The Sun is located and one of the foci of the planets' elliptical orbits.
Why does a satellite in a circular orbit travel at a constant speed?
There is no component of force acting along the direction of motion of the satellite.
Which of the following statements are true?
The launch speed of a satellite determines the shape of its orbit around Earth
A satellite's motion is independent of its mass
Two identical satellites orbit the earth in stable orbits. One satellite orbits with a speed v at a distance r from the center of the earth. The second satellite travels at a speed that is less than v. At what distance from the center of the earth does th
At a distance greater than r.
Now assume that a satellite of mass m is orbiting the earth at a distance r from the center of the earth with speed ve. An identical satellite is orbiting the moon at the same distance with a speed vm. How does the time Tm it takes the satellite circling
Tm is greater than Te
Is the amount of energy required to get a spacecraft from the Earth to the Moon greater than, less than, or equal to the energy required to get the same spacecraft from the Moon to the Earth?
greater than
Choose the best explanation from among the following:
The escape speed of the Moon is less than that of the Earth; therefore, less energy is required to leave the Moon