PHYSICS AP CLASSROOM CLAVE
a 1 kg crate accelerates down an inclined plane at .6 m/s^2. which of the following statements are true? select two answers.
- increasing the mass of the crate will decrease the acceleration down the plane since Newton's second law applies - increasing the angle will not change the acceleration since it will not change the net force
an elevator moves upward at a constant speed. Which of the following statements is correct?
- the kinetic energy of the elevator car is constant but not the gravitational potential energy - the upward force on the elevator car is constant
the figure shows a graph of the positioin of a moving object as a function of time. what is the velocity of the object at 5.5 s?
-40 m/s
The Atwood's machine shown consists of two blocks of mass m1 and m2 that are connected by a light string that passes over a pulley of negligible friction and negligible mass. The block of mass m1 is a distance h1 above the ground, and the block of mass m2 is a distance h2 above the ground. m2 is larger than m1. The two-block system is released from rest. Which of the following claims correctly describes the outcome after the blocks are released from rest but before the block of m2 reaches the ground? Select two answers.
-For the system consisting of the two blocks, the change in the kinetic energy of the system is equal to the work done by gravity on the system. - For the system consisting of the two blocks, the pulley, and Earth, the change in the total mechanical energy of the system is zero.
When a 45-kg person steps on a scale in an elevator, the scale reads a steady 480 N. Which of the following statements must be true? (There could be more than one correct choice.)
-the elevator is accelerating upward at a constant rate - from the given information, we cannot tell if the elevator is moving up or down
A 50 kg athlete running at speed v grabs a light rope that hangs from a 10-meter-high platform and swings to a maximum of 1.8 m above the ground. Later, a 100 kg athlete, running at the same speed, grabs a similar rope hanging from a 5-meter-high platform. What is the maximum height to which the 100 kg athlete swings?
1.8 m
An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational force on the object after it has been moved to a distance of 4R from the center of the planet?
1/16 W
Disk Y of rotational inertia IY=12MYRY2 is held at rest above disk X of rotational inertia IX=12MXRX2 that rotates about its center with an angular velocity of +ω0. Disk Y is slowly lowered onto disk X until both disks are in contact and travel together with a common angular velocity ωf. Which of the following equations could a student use to correctly solve for the final angular velocity of the two-disk system immediately after the collision? Justify your selection.
1/2MXRX2ω0=(1/2MXRX2+12MYRY2)ωf, because the initial momentum of disk XX is equal to the sum of the final momentum of disk XX and the final momentum of disk YY.
a .5 kg stone is moving in a vertical circular path attached to a string that is 75 cm long. The stone is moving around the path at a constant frequency of 2.20 revs/s. At the moment the stone is overhead, the stone is released. The magnitude and directioin of the velocity of the stone when it leaves the circular path is
10.4 m/s, horizontal
a bucket filled with water has a mass of 23 kg and is attached to a rope, which in turn, is wound around a .050m radius cylinder at the top of a well. What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate?
11 Nm
The graph above shows velocity v as a function of time t for a 0.50 kg object traveling along a straight line. The graph has three segments labeled 1, 2, and 3. A rope exerts a constant force of magnitude FT on the object along its direction of motion the whole time. During segment 2 only, a frictional force of magnitude Ff is also exerted on the object. For another identical object initially at rest, no frictional force is exerted during segment 2 (between t = 2 s and t = 4 s). A rope exerts the same constant force of magnitude FT as in the previous scenario. What is the change in the object's kinetic energy during segment 2?
12 J
a knight swings a mace of radius 1m in two complete circles. What is the distance traveled by the mace?
12.6 m
A force F is exerted on a 5 kg block to move it across a rough surface, as shown above. The magnitude of the force is initially 5 N, and the block moves at a constant velocity. While the block is moving, the force is instantaneously increased to 12 N. How much kinetic energy does the block now gain as it moves a distance of 2 m?
14 J
A large spring requires a force of 150 N to compress it only 0.010 m. What is the spring constant of the spring?
15000 N/m
a car starts from rest and travels a distance of 100 m in 10 s. What is the acceleration of the car?
2 m/s^2
how long must a 100 N net force act to produce a change in momentum of 200 kg m/s?
2.0 s
a force of 10 N stretches a spring that has a spring constant of 20 N/m. The potential energy stored in the spring is
2.5 J
what is the linear displacement of a wheel if the radius is 8 m and the angular displacement of the wheel is 3 rads.
24 m
what is the linear displacement of a wheel if the radius is 8m ad the angular displacement of the wheel is 3 rads?
24 m
a 3.00 kg toy falls from a height of 1.00 m. what will the kinetic energy of the toy be just before the toy hits the ground?
29.4 J
Three different experiments are conducted that pertain to the oscillatory motion of a pendulum. For each experiment, the length of the pendulum and the mass of the pendulum are indicated. In all experiments, the pendulum is released from the same angle with respect to the vertical. The pendulum in Experiment 2 is released from rest at an angle of θ0 with respect to the vertical. What is the magnitude of the change in kinetic energy of the pendulum from its lowest point to the highest point along its arc?
2Mg(L−Lcosθ0)
a 30 kg child who is running at 4 m/s jumps onto a stationary 10 kg skateboard. The speed of the child and the skateboard is approximately:
3 m/s
a freight car is moving freely along a railroad track at 7 m/s and collides with a tanker car that is at rest. After the collision, the two cars stick together and continue to move down the track. What is the magnitude of the final velocity of the cars if the freight car has a mass of 1200 kg and the tanker car has a mass of 1600 kg?
3 m/s
a 2 kg object initially moving with a constant velocity is subjected to a force of magnitude F in the direction of motion. A graph of F as a function of time t is shown. What is the increase, if any, in the velocity of the object during the time the force is applied?
3.0 m/s
a CD has a diameter of 12 cm. If the CD is rotating at a constant angular velocity of 20 rads/s, then the frequency of the rotational motion is
3.18 Hz
if the net force on an object were doubled while at the same time the mass of the object was halved, then the acceleration of the object is
4 times greater
a compressed spring has 16 J of potential energy. What is the maximum speed it can impart to a 2 kg object?
4.0 m/s
a bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 10^-2 kg m^2 and a radius of .10m. If it rolls down the lane without slipping at a linear speed of 4.0 m/s, what is its angular speed?
40 rad/s
a 4 kg mass is moving in a circular path of radius 4.10 with a constant angular velocity of 5 rad/s. the centripetal force on the mass is
410 N
A satellite of mass 1000 kg is in a circular orbit around a planet. The centripetal acceleration of the satellite in its orbit is 5 ms2. What is the gravitational force exerted on the satellite by the planet?
5000 N
a stellite is in a circular orbit about the earth at a distance of one earth radius above the surface. what is the speed of the satellite (r of earth is 6.4 10^6 and G=6.610^-11)
5600 m/s
A uniform, rigid rod of length 2m lies on a horizontal surface. One end of the rod can pivot about an axis that is perpendicular to the rod and along the plane of the page. A 10N force is applied to the rod at its midpoint at an angle of 37°. A second force F is applied to the free end of the rod so that the rod remains at rest, as shown in the figure. The magnitude of the torque produced by force F is most nearly
6.0 Nm
a ball is attached to a string and rotates in a circle. If it takes 1 second to complete 1 revolution what is the angular speed of the ball?
6.28 rad/s
A rope of negligible mass supports a block that weighs 30 N, as shown above. The breaking strength of the rope is 50 N. The largest acceleration that can be given to the block by pulling up on it with the rope without breaking the rope is most nearly
6.7 m/s^2
A rod of length ℓ and rotational inertia Ir about one end may freely rotate about a pivot that is attached to the ceiling and upper end of the rod. A sphere of mass M and radius R is launched horizontally with velocity v0 toward the rod. It collides with the bottom of the rod, as shown in Figure 1. After colliding with the rod, the sphere momentarily comes to rest before it falls vertically to the ground. The rod swings upward with an angular speed ω2, as shown in Figure 2. The rotational inertia of the sphere is Is. Which of the following mathematical procedures, if any, can a student use to determine ω2 immediately after the sphere collides with the rod? Justify your selection.
Angular momentum is conserved, so calculate the initial angular momentum of the sphere as measured from the pivot, and set that equal to the angular momentum of the rod immediately after the collision.
An object rotates with an angular speed that varies with time, as shown in the graph. How can the graph be used to determine the magnitude of the angular acceleration α of the object? Justify your selection.
Determine the slope of the line from 0s0s to 2s2s, because the slope represents ΔωΔt
A block on a horizontal surface of negligible friction is placed in contact with an ideal spring, as shown above. The block is moved to the left so that the spring is compressed a distance x from equilibrium and then released from rest. The block has kinetic energy K1 when it separates from the spring. When the spring is compressed a distance 2x and the block is released from rest, the kinetic energy of the block when it separates from the spring is
EK1
Two blocks of the same mass but made of different material slide across a horizontal, rough surface and eventually come to rest. A graph of the kinetic energy of each block as a function of position along the surface is shown. Which of the following is a true statement about the frictional force Ff that is exerted on the two blocks?
Ff2=2Ff1, since the force of friction is represented as the slope for each of the two curves.
A student is asked to determine the work done on a block of wood when the block is pulled horizontally using an attached string. The student is supplied with a spring scale, a stopwatch, and a meterstick. Which of the following graphical analysis techniques will allow the student to determine the work done on the block by the string?
Graphing the force as a function of distance and calculating the area under the curve
A box of mass m hangs from massless strings, as shown in the figure above. The angle between strings 1 and 2 is 90o, and the angles that the strings make with the ceiling are Ѳ1 and Ѳ2, respectively. If T1 is the tension in string 1, which of the following are the magnitudes of the horizontal and vertical components of the tension in string 2 ?
Horizontal: T1costheta1 Vertical mg-T1sintheta1
the sum of the forces on the object is zero in which of the cases?
I and II only
in which of the following situations would an object be accelerated?
II and III only
the magnitude of momentum of the object is increasing in which of the cases?
III only
Two boxes are tied together with a string. They are thrown onto a layer of ice such that they spin around their center of mass C as they slide horizontally across the icy surface, as shown in the figure. The system has an angular momentum L⃗ 0 and an angular velocity ω⃗ 0 at a time t=0s. A graph of the two-block system's center of mass velocity as a function of time is shown. Which of the following predictions are correct about the angular momentum L⃗ 4 and angular velocity ω⃗ 4 at t=4s ?
L0=L4 and w0=w4
A lump of clay of mass mclay with speed vclay=8 m/s travels toward various spheres that are suspended from the ceiling by lightweight strings of different lengths, as shown in the figure. For the three scenarios, the clay collides with the suspended sphere and sticks to it. Which of the following correctly relates the angular momentum L of the clay-bob system immediately after the collision for each scenario, where the angular momentum is taken about the point where the string is attached to the ceiling?
L1>L2>L3
The center of mass of a uniform meterstick is placed on a fulcrum. Two objects of known mass, m1 and m2, are hung at known positions on the meterstick. One end of a string is attached to one end of the meterstick, and the other end of the string is looped around a pulley and connected to hanging object X of unknown mass, as shown in the figure. The meterstick does not rotate and is level with the horizontal. Which of the following measuring devices, if any, should be used to make measurements to determine the unknown mass of object X? Justify your selection.
No additional equipment or measurements are needed, because the force due to gravity exerted on objects m1m1 and m2m2 and the distance between where the force is applied and the tip of the fulcrum are already known.
Two students wish to determine the value of g, the acceleration due to gravity at Earth's surface. The students have a collection of blocks of different masses, a string of negligible mass, a pulley of negligible mass, and a device for measuring acceleration. The students attach two of the blocks to the ends of the string and pass the string over the pulley so the blocks hang vertically on either side. The blocks are then released from rest, and their acceleration is measured. The students' data for one trial are shown below, with m1 and m2 equal to the masses of the blocks. Considering the gravitational forces acting on the blocks, do the data provide a reasonable determination of the value of g, and what is a possible justification for why or why not?
No, because the calculated value of gg is too small, possibly due to an additional force exerted on the blocks-string system.
A ball of mass M swings in a horizontal circle at the end of a string of radius R at an initial tangential speed v0 as it undergoes uniform centripetal motion. A student gradually pulls the string inward such that the radius of the circle decreases, as shown in the figure. Which of the following predictions is correct regarding the angular momentum and rotational inertia of the ball about the axis of revolution as the ball is pulled inward?
The angular momentum of the ball remains constant. The rotational inertia of the ball about the axis of revolution decreases.
In an experiment, an external torque is applied to the edge of a disk of radius 0.5m such that the edge of the disk speeds up as it continues to rotate. The tangential speed as a function of time is shown for the edge of the disk. The rotational inertia of the disk is 0.125kg⋅m2. Can a student use the graph and the known information to calculate the net torque exerted on the edge of the disk?
Yes, because the change in tangential speed per unit of time can be multiplied by the rotational inertia divided by the radius of the disk.
an object moving in a circle at constant speed is
accelerating toward the center of the circle
for the wheel and axle system shown above, which of the following expresses the condition required for the system to be in static equilibrium?
am1=bm2
which of the following statements about the block is correct
at X=A, its displacement is at a maximum
a car is travelling on a road in hilly terrain, see figure to the right. Assume the car has speed v and the tops and bottoms of the hills have the radius of curvature R. the driver of the car is most likely to feel weightless:
at the top of the hill when v>rootgR
A helium atom collides with another helium atom in an elastic collision. Which of the following is true?
both momentum and kinetic energy are conserved
Two toy cars with different masses originally at rest are pushed apart by a spring between them. Which of the following statements would NOT be true?
both toy cars will acquire equal kinetic energies
net impulse is best related to
change in momentum
a centripetal force F is applied to an object moving at a constant speed v in a horizontal circle of radius r. If the radius is quadrupled and the speed is doubled, what happens to the centripetal force?
does not change
a spider sits on a turntable that is rotating at a constant 33 rpm. The velocity, v, of the spider is
greater the farther the spider is from the central axis
what does the moment of inertia describe?
how a mass of an object is distributed about a rotational axis
during an inelastic collision between two balls, which of the following statements is correct?
momentum is conserved, but kinetic energy is not conserved
Planet X is in a stable circular orbit around a star, as shown in the figure. Which of the following graphs best predicts the angular momentum of the planet as a function of its horizontal position from point A to point B if the planet is moving counterclockwise as viewed in the figure above?
straight horizontal line on positive
if the ball is replaced with a disk of rotational inertia (1/2)MR^2, how will the velocity at the bottom change?
the disk will travel slower
Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force has a greater magnitude?
the first force (at the midpoint)
A student initially at rest on a frictionless frozen pond throws a 1 kg hammer in one direction. After the throw, the hammer moves off in one direction while the student moves off in the other direction. Which of the following correctly describes the above situation?
the hammer will have the greater kinetic energy
how are frequency and period related in simple harmonic motion?
they are inversely related
a ball is whirled in a horizontal circle of radius r and speed v. The radius is increased to 2r keeping the speed of the ball constant. The period of the ball changes by a factor of
two
a push broom of mass m is pushed across a rough horizontal floor by a force of magnitude T directed at angle theta as shown above. The coefficient of friction between the broom and the floor is u. the frictional force on the broom has magnitude
u(mg+Tsintheta)
the amount of force needed to keep a .1 kg hockey puck moving at a constant velocity of 5 m/s on frictionless ice is
zero
Two identical wheels, wheel 1 and wheel 2, initially at rest begin to rotate with constant angular accelerations α. After rotating through the same angular displacement, Δθ0 , the angular velocity of wheel 1 is ω1 and the angular velocity of wheel 2 is ω2=3ω1 . How does the angular acceleration of wheel 2, α2, compare to the angular acceleration of wheel 1, α1 ?
α2=9α1
in another scenario there is friction between the ball and incline so that the ball rolls down without slipping. How fast is the ball traveling at the bottom of the incline?
√10gh/7
how fast is the ball traveling at the bottom of the incline?
√2gh
a particle of mass m moving in a straight line on a smooth, frictionless surface experiences an increase in velocity. This increase in velocity indicates
- the presence of a force with a component in the same direction as the direction of the velocity vector - that work was done on the particle, increasing its kinetic energy
a .2 kg hockey puck is sliding along the ice with an initial speed of 12 m/s when a player strikes it with his stick, causing it to reverse its direction and giving it a speed of 23 m/s. The impulse the stick applies to the puck is most nearly
-7Ns
The figure above shows the net force exerted on an object as a function of the position of the object. The object starts from rest at position x = 0 m and acquires a speed of 3.0 m / s after traveling a distance of 0.090 m. What is the mass of the object?
.030 kg
a block with initial velocity 4.0 m/s slides 8.0 m across a rough horizontal floor before coming to rest. The coefficient of friction is
.10
A group of students must study the oscillatory motion of a pendulum. One end of a light string is attached to the ceiling, and the other end of the string is attached to a mass hanger so that small disks of various masses may be stacked on the hanger, as shown in the figure. Students are provided with data in which an experiment was conducted to determine the relationship between the length of the pendulum and the period of oscillation. The data include a pendulum of length 0.5m, for which it took 81 s for the pendulum bob to oscillate 10 times. However, the experiment was conducted at a location that is not near Earth's surface. The gravitational field strength where the experiment was conducted is most nearly
.3 N/kg
a 50kg skater at rest on a frictionless rink throws a 2 kg ball, giving the ball a velocity of 10 m/s. which statement describes the skater's subsequent motion?
.4 m/s in the opposite direction of the ball
The cart of mass 10 kg shown above moves without frictional loss on a level table. A 10 N force pulls on the cart horizontally to the right. At the same time, a 30 N force at an angle of 60° above the horizontal pulls on the cart to the left. What is the magnitude of the horizontal acceleration of the cart?
.5 m/s^2
a bicycle tire of diameter of .4 m rotates 600 times in 800 s. The average tangential speed of the valve stem is approximately
.94 m/s
A cart of mass 2.0kg on a horizontal surface is attached to a horizontal spring of negligible mass. A 1.0kg block is secured on top of the of the 2.0kg cart. The other end of the spring is attached to a wall, and there is negligible friction between the cart-block-spring system and the horizontal surface. The cart-block-spring system then experiences simple harmonic motion as described by the graph that shows the velocity of the cart-block system as a function of time. The maximum spring potential energy of the cart-block-spring system is most nearly
.96 J
A student is at rest on a stool that may freely spin about its central axis of rotation. As the stool spins, the student holds onto two dumbbells as the stool spins at an angular speed of 1.2 rad/s with the student's arms completely stretched out from the student's body. At this instant, the student-dumbbell system has rotational inertia of 6 kg⋅m2. The student then brings their arms close to their body, and rotational inertia of the student-dumbbell system is changed to 2 kg⋅m2. What is the new angular speed of the student?
3.6 rad/s
a bat striking a .125 kg baseball is in contact with the ball for a time of .03 seconds. The ball travels in a straight line as it approaches and then leaves the bat. If the ball arrives at the bat with a speed of 4.5 m/s and leaves with a speed of 6.5 m/s in the opposite direction, what is the magnitude of the average force acting on the ball?
45.83 N
robin hood aims his longbow horizontally at a target's bull's eye 30 m away. if the arrow strikes the target exactly 2 m below the bull's eye, how fast did the arrow move as it was shot from the bow? assume air resistance is neglible
47 m/s
A block on a horizontal surface is placed in contact with a light spring with spring constant k, as shown in Figure 1. When the block is moved to the left so that the spring is compressed a distance d from its equilibrium length, the potential energy stored in the spring-block system is Em . When a second block of mass 2m is placed on the same surface and the spring is compressed a distance 2d, as shown in Figure 2, how much potential energy is stored in the spring compared to the original potential energy Em ? All frictional forces are considered to be negligible.
4Em
A 2kg block on a horizontal surface is attached to a horizontal spring of negligible mass. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. The block is released from rest after the spring is stretched such that the block-spring system experiences simple harmonic motion, as shown in the graph that represents the block's velocity as a function of time. How could a student use the known information and the graph to determine the magnitude of the change in spring potential energy of the system from the release point of the block to the moment when the system's spring potential energy is zero?
By determining the kinetic energy of the block at 2s2s by using K=12mv2
A group of students must study the oscillatory motion of a pendulum. One end of a light string is attached to the ceiling, and the other end of the string is attached to a mass hanger so that small disks of various masses may be stacked on the hanger, as shown in the figure. The students perform four experiments, as described. Experiment 1: Determine the relationship between the mass of the pendulum and the period of oscillation. Experiment 2: Determine the relationship between the displacement of the pendulum and the period of oscillation. Experiment 3: Determine the relationship between the period of oscillation and the length of the pendulum. Experiment 4: Determine the relationship between the vertical release height of the hanger-disk system and its speed at the lowest point of its arc. The students collect data to create the graph that is shown, but the horizontal and vertical axes are not labeled. Which experiments could be represented by the graph?
Experiment 3 and Experiment 4
A uniform horizontal beam of mass M and length L0 is attached to a hinge at point P, with the opposite end supported by a cable, as shown in the figure. The angle between the beam and the cable is θ0. What is the magnitude of the torque that the cable exerts on the beam?
MgL0/2
Two objects, X and Y, accelerate from rest with the same constant acceleration. Object X accelerates for twice the time as object Y. Which of the following is true of these objects at the end of their respective periods of acceleration?
Object X has traveled four times as far as object Y.
which of the following is not evidence that kinetic energy has been lost in a collision?
One of the objects is at rest after the collision
two cars collide, lock bumpers, and move together after the collision. What kind of collision is this?
Perfectly inelastic collision
A student must determine how the mass of a block affects the period of oscillation when the block is attached to a vertical spring. The value of the spring constant is known. The student writes the following experimental procedure. Use an electronic balance to measure the mass of the block. Attach the block to the vertical spring. Displace the block from the system's equilibrium position to a new vertical position. Release the block from rest. Use a meterstick to measure the vertical displacement of the center of mass of the block from the system's equilibrium position to its maximum vertical position above the equilibrium position. Use a stopwatch to measure the time it takes for the system to make ten complete oscillations. Repeat the experiment for different vertical displacements and block masses. Which of the following steps of the procedure should the student revise to make the determination? Justify your selection.
Step 7, because the experiment should not be repeated for different vertical displacements and block masses.
A rod of length 2D0 and mass 2M0 is at rest on a flat, horizontal surface. One end of the rod is connected to a pivot that the rod will rotate around if acted upon by a net torque. A sphere of mass m0 is launched horizontally toward the free end of the rod with velocity v0, as shown in the figure. After the sphere collides with the rod, the sphere sticks to the rod and both objects rotate around the pivot with a common angular velocity. Which of the following predictions is correct about angular momentum and rotational kinetic energy of the sphere-rod system immediately before the collision and immediately after the collision?
The angular momentum immediately before the collision is equal to the angular momentum immediately after the collision. The rotational kinetic energy immediately before the collision is greater than the rotational kinetic energy immediately after the collision.
Two students, X and Y, sit on a seesaw that is in static equilibrium, as shown in the figure. A fulcrum is located at the center of the seesaw. The mass mY of Student Y is known. A third student, Z, must determine the mass of Student X. Which of the following measurements should Student Z make in order to determine the mass of Student X? Justify your selection.
The distance that Student XX is from the center of the seesaw and the distance that Student YY is from the center of the seesaw, because these are the distances from the fulcrum to the location of the forces exerted on the two-student-seesaw system.
A person holds a 4.0 kg block at position A shown above on the left, in contact with an uncompressed vertical spring with a spring constant of 500 N/m. The person gently lowers the block from rest at position A to rest at position B. Which of the following describes the change in the energy of the block-spring-Earth system as a result of the block being lowered?
The energy decreases by approximately 1.5 J.
A block of mass 1.0kg on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 100N/m. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the spring is unstretched, the block is located at x=0m. The block is then pulled to x=0.5m and released from rest so that the block-spring system oscillates between x=−0.5m and x=0.5m, as shown in the figure. Which of the following descriptions about the system are correct? Select two answers.
The spring potential energy of the system at x=0.25m is nearly 3.13 J The sum of the spring potential energy of the system and the kinetic energy of the block at x=0.4m is nearly 12.5J.
An object initially at rest falls from a height H until it reaches the ground. Two of the following energy bar charts represent the kinetic energy K and gravitational potential energy Ug of the object-Earth system at two positions. The first position is when the object is initially released, and the second position is when the object is halfway between its release point and the ground. Which two charts could represent the mechanical energy of the object-Earth system? Select two answers.
U all the way up, then equal to K
A disk-shaped platform has a known rotational inertia ID. The platform is mounted on a fixed axle and rotates in a horizontal plane with an initial angular velocity of ωD in the counterclockwise direction, as shown. After an unknown time interval, the disk comes to rest. A single point on the disk revolves around the center axle hundreds of times before the disk comes to rest. Frictional forces are considered to be constant. In a different experiment, the original disk is replaced with a disk for which frictional forces are considered to be negligible. The disk is set into motion such that it rotates with a constant angular speed. As the disk spins, a small sphere of clay is dropped onto the disk, and the sphere sticks to the disk. Which of the following claims is correct about the angular momentum and the total kinetic energy of the disk-sphere system immediately before and immediately after the collision?
angular motion- the same kinetic energy- greater before
a racing car is moving around the circular track of radius 300 m shown above. at the instant when the car's velocity is directed due west, its acceleration is directed due south and has a magnitude of 3 m/s2. when viewed from above, the car is moving
clockwise at 30 m/s
An axle passes through a pulley. Each end of the axle has a string that is tied to a support. A third string is looped many times around the edge of the pulley and the free end attached to a block of mass mb , which is held at rest. When the block is released, the block falls downward. Consider clockwise to be the positive direction of rotation, frictional effects from the axle are negligible, and the string wrapped around the disk never fully unwinds. The rotational inertia of the pulley is 12MR2 about its center of mass. How many forces are applied to the pulley-axle system, and how many torques are applied to the pulley about its center when the block is released from rest?
forces- 4 torques -1
a centripetal force F is applied to an object moving at a constant speed v in a horizontal circle of radius r. if the radius is doubled and the speed is doubled, what happens to the centripetal force?
increased by a factor of 2
A rocket is continuously firing its engines as it accelerates away from Earth. For the first kilometer of its ascent, the mass of fuel ejected is small compared to the mass of the rocket. For this distance, which of the following indicates the changes, if any, in the kinetic energy of the rocket, the gravitational potential energy of the Earth-rocket system, and the mechanical energy of the Earth-rocket system?
increasing, increasing , increasing
a tennis ball is dropped from 1 m, bounces off the ground, and rises to .85m. What kind of collision occurred between the ball and the ground?
inelastic collision
how does an air mattress protect a stunt person landing on the ground after a stunt?
it lengthens the stopping time of the stunt person and reduces the force applied during the landing
A rod of length 2D0 and mass 2M0 is at rest on a flat, horizontal surface. One end of the rod is connected to a pivot that the rod will rotate around if acted upon by a net torque. A lump of clay of mass m0 is launched horizontally toward the center of the rod with velocity v0, as shown in the figure. After the clay collides with the rod, the clay sticks to the rod and both objects rotate around the pivot with the common angular velocity ωf. The rotational inertia of the clay-rod system is Is. Which of the following equations could a student use to solve for the common angular velocity ωf immediately after the collision? Justify your selection.
m0v0D0=Isωf, because the clay hits the rod a distance D0D0 from the pivot.
An object of mass m is attached to a spring on a frictionless inclined plane that makes an angle θ with the horizontal, as shown above. The object is released from rest with the spring in its unstretched position. As the object moves on the plane, its displacement from the unstretched position is x. What is the magnitude of the work done by gravity as the object slides down the incline?
mgx Sin theta
A simple pendulum consisting of a small object of mass m attached to a string of length l has a period T. A pendulum with which of the following combinations of object mass and string length will also have period T ?
object mass- m/2 length- l
A solid metal bar is at rest on a horizontal frictionless surface. It is free to rotate about a vertical axis at the left end. The figures below show forces of different magnitudes that are exerted on the bar at different locations. In which case does the bar's angular speed about the axis increase at the fastest rate?
one F arrow pointing up furthest from center
a 2.5 kg body slides across a frictionless horizontal tabletop that is 1.2 m above the level of the floor with a speed of 2.1 m/s. Relatie to the tabletop, the mechanical energy associated with the body is
only kinetic energy as it slides on the frictionless surface
a merry-go-round completes one revolution in 40s. WHat is the centripetal acceleration of a rider located at a distance 2 m from the center of the merry go-round
pi^2/200
to increse the moment of inertia of a body about an axis, you must
place part of the body farther from the axis
the frictional force of the floor on a large suitcase is least when the suitcase is
pulled by a force directed at an angle theta above the floor
An astronaut performs an experiment near the surface of a moon by releasing an object at rest above a motion detector such that data can be collected about the object's vertical velocity as a function of time. The data are provided in the table. Which of the following graphs most likely represents the shape of the curve of the magnitude of the gravitational field strength near the surface of the moon as a function of time?
straight horizontal, positive
a student initially at rest on a frictionless frozen pond throws a 1 kg hammer in one direction. After the throw, the hammer moves off in one direction while the student moves off in the other direction. Which of the following correctly describes the above situation?
the hammer will have the greater kinetic energy
a wooden box is first pulled across a horizontal steel plate as shown in the diagram A. The box is then pulled across the same steel plate while the plate is inclined as shown in diagram B. how does the force required to overcome friction in teh inclined case (B) compare to the horizontal case (A)
the inclined case has less frictional force
a bullet moving with an initial speed of vi strikes and embeds itself in a block of wood which is suspended by a string, causing the bullet and block to rise to a maximum height h. Which of the following statements is true of the collision?
the kinetic energy of the bullet and block immediately after the collision is equal to the potential energy of the bullet and block at the instant they reach the maximum height h.
A crate is on a horizontal frictionless surface. A force of magnitude F is exerted on the crate at an angle θ to the horizontal, as shown in the figure above, causing the crate to slide to the right. The surface exerts a normal force of magnitude FN on the crate. As the crate slides a distance d, it gains an amount of kinetic energy ∆K. While F is kept constant, the angle θ is now doubled but is still less than 90o. Assume the crate remains in contact with the surface.
the new gain is less than deltaK
a car slides up a frictionless inclined plane. How does the normal force of the incline on the car compare with the weight of the car?
the normal force must be less than the car's weight
which of the following statements about energy is correct?
the potential energy of the spring is at a minimum at x=0
which of the following is true for a simple pendulum?
the total energy is constant
an object of mass M travels along a horizontal air track at a constant speed v and collides elastically with an object of identical mass that is initially at rest on the track. Which of the following statements is true for the two objects after the impact?
the total momentum is Mv and the total kinetic energy is 1/2Mv^2
Two swimmers relax close together on air mattresses in a pool. One swimmer's mass is 48 kg, and the other's mass is 55 kg. If the swimmers push away from each other,
their momenta are equal but opposite
A mass m has speed v. It then collides with a stationary object of mass 2m. If both objects stick together in a perfectly inelastic collision, what is the final speed of the newly formed object?
v/3
a mass attached to a spring vibrates back and forth. At the equilibrium position, the
velocity reaches a maximum
