Phys C Exam Part 1
A frictionless pendulum of length 3 m swings with an amplitude of 10°. At its maximum displacement, the potential energy of the pendulum is 10 J. What is the kinetic energy of the pendulum when its potential energy is 5 J?
5 J
A block of mass m is accelerated across a rough surface by a force of magnitude F that is exerted at an angle 𝜙 with the horizontal, as shown above. The frictional force on the block exerted by the surface has magnitude f. What is the coefficient of friction between the block and the surface?
f/(mg−Fsinϕ)
An object of mass m moves with acceleration a down a frictionless incline that makes an angle with the horizontal, as shown above. If N is the normal force exerted by the plane on the block, which of the following is correct?
a=gsinθ
The following graph represents a hypothetical potential energy curve for a particle of mass m. If the particle is released from rest at position r0 , its speed at position 2r0 is most nearly
sqrt(4U0/m)
A skier slides at constant speed down a slope inclined at an angle ϕ to the horizontal, as shown above. If air resistance is negligible, the coefficient of friction µ between the skis and the snow is equal to
tan ϕ
In the system of two blocks and a spring shown above, blocks 1 and 2 are connected by a string that passes over a pulley. The initially unstretched spring connects block 1 to a rigid wall. Block 1 is released from rest, initially slides to the right, and is eventually brought to rest by the spring and by friction on the horizontal surface. After block 1 comes to rest, the force exerted on it by the spring must be equal in magnitude to
the vector sum of the forces on block 1 due to friction and tension in the string
A ball is thrown and follows a parabolic path, as shown above. Air friction is negligible. Point Q is the highest point on the path. Which of the following best indicates the direction of the acceleration, if any, of the ball at point Q?
arrow straight downwards
A ball is thrown and follows a parabolic path, as shown above. Air friction is negligible. Point Q is the highest point on the path. Which of the following best indicates the direction of the net force on the ball at point P?
arrow straight downwards
A dart gun is used to fire two rubber darts with different but unknown masses, M1 and M2. The gun exerts the same constant force on each dart, but its magnitude F is unknown. The magnitudes of the accelerations of both darts, a1 and a2, respectively, are measured. Which of the following can be determined from these data?
The ratio of M1 and M2 only
A car is traveling along a straight, level road when it runs out of gas at time t = 0. From this time on, the net force on the car is a resistive force of -kv, where v is velocity and k is a constant. Which of the following pairs of graphs best represents the speed v and position x of the car as functions of time after t = 0 ?
decreasing graph of -ln(x), increasing graph of ln(x)
A uniform ladder of weight W leans without slipping against a wall making an angle 𝜽 with a floor as shown above. There is friction between the ladder and the floor, but the friction between the ladder and the wall is negligible. The magnitude of the friction force exerted by the ladder on the floor is
W/2 cot θ
A block of mass m is accelerated across a rough surface by a force of magnitude F that is exerted at an angle 𝜙 with the horizontal, as shown above. The frictional force on the block exerted by the surface has magnitude f. What is the acceleration of the block?
(Fcosϕ−f)/m
Two blocks of masses M and m, with M > m, are connected by a light string. The string passes over a frictionless pulley of negligible mass so that the blocks hang vertically. The blocks are then released from rest. What is the acceleration of the block of mass M ?
(M-m)g/(M+m)
A disc of mass m slides with negligible friction along a flat surface with a velocity v. The disc strikes a wall head-on and bounces back in the opposite direction with a kinetic energy one-fourth of its initial kinetic energy. What is the final velocity of the disc?
-v/2
A spring has a force constant of 100 N/m and an unstretched length of 0.07 m. One end is attached to a post that is free to rotate in the center of a smooth table, as shown in the top view above. The other end is attached to a 1 kg disc moving in uniform circular motion on the table, which stretches the spring by 0.03 m. Friction is negligible. What is the work done on the disc by the spring during one full circle?
0 J
A person throws a ball of mass 0.20 kg. The ball starts from rest, accelerates horizontally and uniformly through a distance of 0.90 m, and leaves the person's hand at 30 m/s. The average horizontal force applied to the ball by the person's hand is
100 N
Three blocks, A, B, and C, of masses 1, 2, and 3 kg, respectively, are initially at rest on a frictionless surface as indicated in the figure above. What force F has to be applied on block C to accelerate the three blocks at 2 m/s^2?
12 N
During a certain time interval, a constant force delivers an average power of 4 watts to an object. If the object has an average speed of 2 meters per second and the force acts in the direction of motion of the object, the magnitude of the force is
2 N
The position of a toy locomotive moving on a straight track along the x-axis is given by the equation x = t3 - 6t2 + 9t, where x is in meters and t is in seconds. The net force on the locomotive is equal to zero when t is equal to
2 s
Two 0.60-kilogram objects are connected by a thread that passes over a light, frictionless pulley, as shown above. The objects are initially held at rest. If a third object with a mass of 0.30 kilogram is added on top of one of the 0.60-kilogram objects as shown and the objects are released, the magnitude of the acceleration of the 0.30-kilogram object is most nearly
2.0 m/s^2
A ball is thrown upward. At a height of 10 meters above the ground, the ball has a potential energy of 50 joules (with the potential energy equal to zero at ground level) and is moving upward with a kinetic energy of 50 joules. Air friction is negligible. The maximum height reached by the ball is most nearly
20 m
The maximum mass that can be hung vertically from a string without breaking the string is 10 kg. A length of this string that is 2 m long is used to rotate a 0.5 kg object in a circle on a frictionless table with the string horizontal. The maximum speed that the mass can attain under these conditions without the string breaking is most nearly
20 m/s
A block slides from rest with negligible friction down the track above, descending a vertical height of 5.0 m to point P at the bottom. It then slides on the horizontal surface. The coefficient of friction between the block and the horizontal surface is 0.20. How far does the block slide on the horizontal surface before it comes to rest?
25 m
A spring has a force constant of 100 N/m and an unstretched length of 0.07 m. One end is attached to a post that is free to rotate in the center of a smooth table, as shown in the top view above. The other end is attached to a 1 kg disc moving in uniform circular motion on the table, which stretches the spring by 0.03 m. Friction is negligible. What is the centripetal force on the disc?
3 N
The following graph represents a hypothetical potential energy curve for a particle of mass m. If the potential energy function is given by U(r) = br^-3/2 + c, where b and c are constants, which of the following is an expression for the force on the particle?
3b/2 r^−5/2
A toy car of mass 6 kg, moving in a straight path, experiences a net force given by the function F = −3t. At time t = 0, the car has a velocity of 4 m/s in the positive direction and is located +8 m from the origin. The car will come instantaneously to rest at time t equal to
4 s
A block of mass 3 kg, initially at rest, is pulled along a frictionless, horizontal surface with a force shown as a function of time t by the graph above. The speed of the block at t = 2s is
4/3 m/s
A block of mass 3 kg, initially at rest, is pulled along a frictionless, horizontal surface with a force shown as a function of time t by the graph above. The acceleration of the block at t = 2s is
4/3 m/s^2
Two identical massless springs are hung from a horizontal support. A block of mass 1.2 kilograms is suspended from the pair of springs, as shown above. When the block is in equilibrium, each spring is stretched an additional 0.15 meter. The force constant of each spring is most nearly
40 N/m
A block of mass 5 kilograms lies on an inclined plane, as shown above. The horizontal and vertical supports for the plane have lengths of 4 meters and 3 meters, respectively. The coefficient of friction between the plane and the block is 0.3. The magnitude of the force F necessary to pull the block up the plane with constant speed is most nearly
42 N
The velocity v of an elevator moving upward between adjacent floors is shown as a function of time t in the graph above. At which of the following times is the force exerted by the elevator floor on a passenger the least?
6 s
To stretch a certain nonlinear spring by an amount x requires a force F given by F = 40x - 6x2 , where F is in newtons and x is in meters. What is the change in potential energy when the spring is stretched 2 meters from its equilibrium position?
64 J
A small box is on a ramp tilted at an angle 𝜽 above the horizontal. The box may be subject to the following forces: frictional ( 𝑓 ), gravitational ( 𝑚𝘨 ), pulling or pushing ( 𝐹𝑃 ) , and normal ( 𝑁 ). In the following free-body diagrams for the box, the lengths of the vectors are proportional to the magnitudes of the forces. Which figure best represents the free-body diagram for the box if it is at rest on the ramp?
Figure C
A small box is on a ramp tilted at an angle 𝜽 above the horizontal. The box may be subject to the following forces: frictional ( 𝑓 ), gravitational ( 𝑚𝘨 ), pulling or pushing ( 𝐹𝑃 ) , and normal ( 𝑁 ). In the following free-body diagrams for the box, the lengths of the vectors are proportional to the magnitudes of the forces. Which figure best represents the free-body diagram for the box if it is sliding down the ramp at constant speed?
Figure C
A small box is on a ramp tilted at an angle 𝜽 above the horizontal. The box may be subject to the following forces: frictional ( 𝑓 ), gravitational ( 𝑚𝘨 ), pulling or pushing ( 𝐹𝑃 ) , and normal ( 𝑁 ). In the following free-body diagrams for the box, the lengths of the vectors are proportional to the magnitudes of the forces. Which figure best represents the free-body diagram for the box if it is accelerating up the ramp?
Figure E
An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The flywheel rotates clockwise on a horizontal shaft S with constant angular velocity 𝜔 . As the wheel rotates, the ant revolves past the stationary points I, II, III, and IV. The ant can adhere to the wheel with a force much greater than its own weight. It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points?
III
An object with initial velocity v0, as shown above, slides up and then down a long, frictionless, inclined plane. Which of the following is true of the object as it moves?
It has the same acceleration as it moves up and down the plane.
An object of mass 100 kg is initially at rest on a horizontal frictionless surface. At time t = 0, a horizontal force of 10 N is applied to the object for 1 s and then removed. Which of the following is true of the object at time t = 2 s if it is still on the surface?
It is moving at a constant speed.
A wheel with rotational inertia I is mounted on a fixed, frictionless axle. The angular speed 𝜔 of the wheel is increased from zero to 𝜔𝑓 in a time interval T. What is the average net torque on the wheel during this time interval?
Iωf/T
A wheel with rotational inertia I is mounted on a fixed, frictionless axle. The angular speed 𝜔 of the wheel is increased from zero to 𝜔𝑓 in a time interval T. What is the average power input to the wheel during this time interval?
Iωf^2/2T
Two identical massless springs are hung from a horizontal support. A block of mass 1.2 kilograms is suspended from the pair of springs, as shown above. When the block is in equilibrium, each spring is stretched an additional 0.15 meter. When the block is set into oscillation with amplitude A, it passes through its equilibrium point with a speed v. In which of the following cases will the block, when oscillating with amplitude A, also have speed v when it passes through its equilibrium point? The block is hung from only one of the two springs. The block is hung from the same two springs, but the springs are connected in series rather than in parallel. A 0.5-kilogram mass is attached to the block.
None
In the system of two blocks and a spring shown above, blocks 1 and 2 are connected by a string that passes over a pulley. The initially unstretched spring connects block 1 to a rigid wall. Block 1 is released from rest, initially slides to the right, and is eventually brought to rest by the spring and by friction on the horizontal surface. Which of the following is true of the energy of the system during this process?
The potential energy lost by block 2 is greater in magnitude than the potential energy gained by the spring.
An object is released from rest at time t = 0 and falls through the air, which exerts a resistive force such that the acceleration a of the object is given by a = g - bV, where V is the object's speed and b is a constant. If limiting cases for large and small values of t are considered, which of the following is a possible expression for the speed of the object as an explicit function of time?
V = g(1 - e^-bt)/b
A uniform ladder of weight W leans without slipping against a wall making an angle 𝜽 with a floor as shown above. There is friction between the ladder and the floor, but the friction between the ladder and the wall is negligible. The magnitude of the normal force exerted by the floor on the ladder is
W
A toy car of mass 6 kg, moving in a straight path, experiences a net force given by the function F = −3t. At time t = 0, the car has a velocity of 4 m/s in the positive direction and is located +8 m from the origin. Which of the following best shows a graph of position d versus time t for the car?
graph with positive y-intercept in negative parabolic arc
A horizontal force F pushes a block of mass m against a vertical wall. The coefficient of friction between the block and the wall is μ . What value of F is necessary to keep the block from slipping down the wall?
mg/μ
A car travels forward with constant velocity. It goes over a small stone, which gets stuck in the groove of a tire. The initial acceleration of the stone, as it leaves the surface of the road, is
vertically upward
The following questions are related to this scenario: The following pairs of equations show how the x- and y-coordinates of a particle vary with time t. In the equations, A, B, and ω are nonzero constants. Choose the pair of equations that best answers each of the following questions. A choice may be used once, more than once, or not at all. Which pair of equations can describe the path of a particle that moves with a constant speed and with a nonzero acceleration that is constant in magnitude?
x = A cos ωt y = A sin ωt
The following questions are related to this scenario: The following pairs of equations show how the x- and y-coordinates of a particle vary with time t. In the equations, A, B, and ω are nonzero constants. Choose the pair of equations that best answers each of the following questions. A choice may be used once, more than once, or not at all. Which pair of equations can describe the path of a particle moving with zero acceleration?
x = At y = Bt
The following questions are related to this scenario: The following pairs of equations show how the x- and y-coordinates of a particle vary with time t. In the equations, A, B, and ω are nonzero constants. Choose the pair of equations that best answers each of the following questions. A choice may be used once, more than once, or not at all. Which pair of equations can describe the path of a particle moving with an acceleration that is perpendicular to the velocity of the particle at t = 0 and remains constant in magnitude and direction?
x = At y = Bt^2
Suppose that the potential energy of a particle constrained to move along the x-axis can be described by the function U(x)= 1/2kx^2 - αx where 𝑘 and α are positive constants. Stable equilibrium points, about which the particle oscillates, are located at
x=α/k only
A block of mass m is pulled across a rough surface, as shown above. The coefficient of friction between the block and the surface is µ𝑘 . The force F that pulls the block is exerted at the angle 𝜙 shown. Which of the following is an expression for the magnitude of the frictional force on the block if it is moving at constant speed?
µ𝑘 (𝑚𝘨 - 𝐹 sin 𝜙 )
A block of mass m is placed against the inner wall of a hollow cylinder of radius R that rotates about a vertical axis with a constant angular velocity ω, as shown above. In order for friction to prevent the mass from sliding down the wall, the coefficient of static friction μ between the mass and the wall must satisfy which of the following inequalities?
μ≥g/ω^2R
An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The flywheel rotates clockwise on a horizontal shaft S with constant angular velocity 𝜔 . As the wheel rotates, the ant revolves past the stationary points I, II, III, and IV. The ant can adhere to the wheel with a force much greater than its own weight. What is the magnitude of the minimum adhesion force necessary for the ant to stay on the flywheel at point III?
𝑚𝜔^2𝑟 + 𝑚𝘨