PHYS1100: Exam II Practice Questions

A 1.0 kg rubber ball traveling horizontally to the left (negative x) at 10. m/s hits a wall and bounces back with a velocity of 6.0 m/s to the right (positive x). The total impulse exerted by the wall on the ball is A) +16 Ns B) -16 Ns C) 0.0 Ns D) +8.0 Ns E) -8.0 Ns

A) +16 Ns

A 3.50 kg book slides along a rough horizontal surface. Initially the book is traveling at 2.25 m/s. At some later point, the book is traveling at 0.75 m/s. The work done on the book is closest to A) - 7.9 J B) 7.9 J C) - 4.5 J D) 4.5 J E) 0.0 J

A) - 7.9 J

(Q. 2-3) An object is moving along the x-axis and is acted on by a conservative force Fx(x). The figure at right shows the graph of the potential energy function U (x) associated with that force. The object has a mass m = 2.0 kg, and at x = 0.0 m its velocity is v = +2.0 m/s. What is the force acting on the object at x = 1.5 m? A) -0.67 N B) -1.0 N C) 0.0 N D) +0.67 N E) +1.0 N

A) -0.67 N

A 4.0 kg mass is released from rest at the top of a frictionless ramp 2.0 m above ground. It slides down the ramp to a level, horizontal portion of frictionless track and then collides with a stationary 8.0 kg mass. Immediately after the collision the larger mass has a velocity v8 = +3.5 m/s (i.e., heading to the right). The velocity v4 of the smaller mass just after the collision is A) -0.74 m/s B) +0.74 m/s C) -2.6 m/s D) +2.6 m/s E) 0 m/s

A) -0.74 m/s

A 3.0 kg mass is traveling at 1.0 m/s and a 2.0 kg mass is traveling in the opposite direction at 2.0 m/s. What is the speed of the center of mass of the two masses? A) 0.20 m/s B) 0.68 m/s C)0.71 m/s D) 0.98 m/s E) 1.4 m/s

A) 0.20 m/s

A torque of 12 N-m is applied to a solid, uniform disk (I = MR2/2) of mass 17 kg, causing the disk to accelerate at 5.7 rad/s2. What is the radius of the disk? A) 0.50 m B) 1.0 m C) 1.5 m D) 4.3 m E) 2.7 m

A) 0.50 m

The elastic potential energy U of an ideal spring is related to the displacement x from a reference equilibrium position 0 in one dimension as U = 1/2kx2, where k is the spring constant. The conservative force that an ideal spring exerts on a body as a function of x is A) 1 B) 2 C) 3 D) 4 E) 5

A) 1

A clay block of mass M1 = 4.0 kg slides to the left along a straight and level frictionless track at speed |V1|. Another clay block of mass M2 = 12 kg slides to the right on the same track at speed |V2|.The blocks collide and stick together, moving as a single unit. The total kinetic energy of the system after the collision is A) 1.1 J. B) 5.2 J. C) 10 J. D) 0.28 J. E) 21 J.

A) 1.1 J.

A ceiling fan with 0.500 m radius blades is turning at 6.28 rad/s. It takes 25.0 s for the fan to stop after it is turned off, what is the linear speed of the tip of a blade 15.0 s after the fan is turned off? A) 1.26 m/s B) 2.54 m/s C) 2.99 m/s D) 3.33 m/s E) 3.67 m/s

A) 1.26 m/s

A 570. kg car moving at 13.3 m/s is hit from behind by a 480. kg car moving at 14.4 m/s in the same direction. If the new speed of the heavier car is 14.0 m/s, what is the speed of the lighter car after the collision? Assume that this two-car system is isolated. A) 13.6 m/s B) 10.5 m/s C) 19.9 m/s D) 5.24 m/s E) 7.94 m/s

A) 13.6 m/s

A torque of 12 N • m is applied to a solid, uniform disk of radius R = 0.50 m, causing the disk to accelerate at 5.7 rad/s2. What is the mass of the disk? (The moment of inertia of the disc about an axis passing through its center of mass is ½ MR2.) A) 17 kg B) 13 kg C) 8.5 kg D) 4.3 kg E) 5.9 kg

A) 17 kg

A torque of 12 N-m is applied to a solid, uniform disk (I = MR2/2) of radius 0.50 m, causing the disk to accelerate at 5.7 rad/s2 . What is the mass of the disk? A) 17 kg B) 13 kg C) 8.5 kg D) 4.3 kg E) 2.7 kg

A) 17 kg

A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire), the velocity of the tape with respect to the road is: A) 2v. B) v. C) 1.5v. D) zero. E) The velocity depends on the radius of the tire.

A) 2v.

The moment of inertia of a uniform disk (see figure) about an axis coming out of the page and passing through the point C at the center of the disk is IC = 1/2MR2. What is the moment of inertia of the disk about an axis coming out of the page and passing through the point E at the edge? A) 3/2MR2 B) 5/2MR2 C) 3/5MR2 D) 2MR2 E) 1/2MR2

A) 3/2MR2

A uniform solid disk (I = MR2/2) of radius 1.60 m rolls without slipping to the bottom of an inclined plane. If the angular velocity of the disk is 5.35 rad/s at the bottom, what is the height of the inclined plane? A) 5.61 m B) 4.21 m C) 4.94 m D) 6.73 m E) 3.24 m

A) 5.61 m

(Q.24-25) A hollow sphere of mass M = 1.5 kg and radius R = 0.50 m rolls without slipping down an inclined surface at an angle of 30° with respect to the horizontal. The hollow sphere starts from rest at the top of the inclined surface and the height above the ground is 3.0 m. The moment of inertia of the hollow sphere about its center of mass is I = 2/3MR2. When the sphere arrives at the bottom of the inclined surface the speed of it about the center of mass is A) 5.9 m/s B) 9.7 m/s C) 12 m/s D) 29 m/s E) 37 m/s

A) 5.9 m/s

As shown in the figure, a 15 g bullet hits a 2.0 kg block and penetrates the block. The maximum height of the combined block and bullet moving upward is 8.0 mm after the bullet hits the block. Assume that air resistance is negligible. What is the speed of the bullet just before it hits the block? A) 53 m/s B) 33 m/s C) 29 m/s D) 17 m/s E) 8.3 m/s

A) 53 m/s

The four forces shown all have the same magnitude: F1 = F2 = F3 = F4 and are acting on a horizontal rod. Which force produces the greatest magnitude of torque about the point O (marked by the black dot)? A) F1 B) F2 C) F3 D) F4 E) Not enough information is given to decide.

A) F1

Which of the following forces is considered a conservative force? A) Gravity B) The force of tension C) The force of friction D) The force of someone pushing an object E) The force of someone pulling an object

A) Gravity

The standard units of momentum are kg∙m/s. Which of these is an alternate way to express these units? A) N∙s B) s/(kg∙m) C) N∙m D) N/s E) kg∙m 2

A) N∙s

The moment of inertia of an object depends on which of the following factors? A) The axis about which the object is rotated. B) The torque applied to the object. C) The angular acceleration of the object. D) Where the force is applied. E) The angular velocity of the object.

A) The axis about which the object is rotated.

A solid sphere is rolling without sliding about its center of axis with moment of inertia 2MR2 /5 along a flat, horizontal plane. The center of mass of the sphere is moving toward the south at constant velocity. Which one of the following statements concerning the translational and rotational kinetic energies of the sphere is true? A) The translational kinetic energy is greater than the rotational kinetic energy. B) The translational kinetic energy is less than the rotational kinetic energy. C) The translational kinetic energy is equal to the rotational kinetic energy. D) The sum of the translational and rotational kinetic energies equals the gravitational potential energy of the cylinder. E) The sum of the translational and rotational kinetic energies equals zero joules.

A) The translational kinetic energy is greater than the rotational kinetic energy.

What is true about the work done by a conservative force? A) The work done by a conservative force is always path independent. B) The work done by a conservative force is always path dependent. C) The work done by a conservative force will always increase the total mechanical energy of a system. D) The work done by a conservative force will always decrease the total mechanical energy of a system. E) The work done by a conservative force along any closed path is not zero.

A) The work done by a conservative force is always path independent.

The graph shows the potential energy U for a particle that moves along the x-axis. The only force that acts on the particle is the force associated with U. The particle is initially at x = d and moves in the negative x-direction. At which of the labeled x-coordinates is the particle slowing down? A) a B) b C) c D) d E) More than one of these points.

A) a

The momentum of a system is conserved only if A) no net external force is exerted on the system. B) no internal forces between objects in the system are exerted. C) the momentum of each object in the system stays exactly the same. D) no force is exerted on the system. E) no conservative force is exerted on the system.

A) no net external force is exerted on the system.

A cylinder is rolling without slipping up an inclined plane and slowing down. The VCOM is the linear velocity of the center of mass of the cylinder. The friction at the contact point P is A) static and points up the inclined plane. B) static and points down the inclined plane. C) kinetic and points up the inclined plane. D) kinetic and points down the inclined plane. E) zero because it is rolling without slipping.

A) static and points up the inclined plane.

A 12.0 kg box resting on a horizontal frictionless surface is attached to a 5.00 kg weight by a thin wire that passes over a frictionless pulley. See figure. The pulley has the shape of a uniform solid disk of mass M = 2.00 kg and radius 0.250 m. The rotational inertia of a disk is 1/2MR2. After the system is released, find the linear acceleration of the box. A) 3.95 m/s2 B) 2.72 m/s2 C) 2.40 m/s2 D) 1.95 m/s2 E) 1.54 m/s2

B) 2.72 m/s2

(Q.24-25) A hollow sphere of mass M = 1.5 kg and radius R = 0.50 m rolls without slipping down an inclined surface at an angle of 30° with respect to the horizontal. The hollow sphere starts from rest at the top of the inclined surface and the height above the ground is 3.0 m. The moment of inertia of the hollow sphere about its center of mass is I = 2/3MR2. The frictional force on the sphere as it rolls down the ramp is A) 1.1 N B) 2.9 N C) 3.6 N D) 4.6 N E) 7.6 N

B) 2.9 N

A futuristic design for a car is to have a large solid disk-shaped flywheel within the car storing kinetic energy. The uniform flywheel (I = MR2/2) has mass 370. kg with a radius of 0.500 m and can rotate up to 230. rev/s. Assuming all of this stored kinetic energy could be transferred to the linear velocity of the 1600. kg car, find the maximum attainable speed of the car. A) 18.0 m/s B) 246 m/s C) 5.75 m/s D) 348 m/s E) None of the above

B) 246 m/s

The figure shows a plot of the time dependent force Fx(t) acting on an 1.0 kg particle in motion along the x-axis. The initial speed of the particle is 2.0 m/s. What is the speed of the particle at t = 1.0 s? A) 2.0 m/s B) 3.0 m/s C) 4.0 m/s D) 5.0 m/s E) 6.0 m/s

B) 3.0 m/s

A 12.0 kg box resting on a horizontal frictionless surface is attached to a 5.00 kg weight by a thin wire that passes over a frictionless pulley. See figure. The pulley has the shape of a uniform solid disk of mass M = 2.00 kg. The rotational inertia of a disk is 1/2MR2. After the system is released, what is the tension acting on the 5.0 kg mass? A) 3.95 N B) 35.4 N C) 24.0 N D) 19.5 N E) 127 N

B) 35.4 N

A truck has a brake failure while going down an icy mountain road of a constant downward slope angle a = 30. Initially the truck is sliding downhill at speed Vo = 20 m/s. After sliding downhill at distance L = 100 m with negligible friction, the truck driver steers the runaway vehicle onto a runaway truck ramp of a constant upward slope angle b = 30. The truck slides up the truck ramp which has a coefficient of friction uT = 0.6. There is no rolling involved. What is the distance D that the truck moves up before coming to a halt? A) 66 m B) 69 m C) 75 m D) 78 m E) 89 m

B) 69 m

A hoop of mass M and R = 0.600 m is released from rest and rolls without slipping down an incline that is at an angle of 60° above the horizontal. The moment of inertia of a hoop about its center of mass is I = MR2. When the hoop has traveled a distance S = 4.0 m down the incline, the magnitude of its angular velocity about its center is A) 7.38 rad/s. B) 9.71 rad/s. C) 11.2 rad/s. D) 10.4 rad/s. E) 14.8 rad/s.

B) 9.71 rad/s.

You are riding your bicycle due east. You slow down your bicycle. What are the directions of angular velocity and angular acceleration of bicycle wheels during slowing down? A) Both angular velocity and angular acceleration point NORTH. B) Angular velocity points NORTH and angular acceleration points SOUTH. C) Angular velocity points EAST and angular acceleration points WEST. D) Both angular velocity and angular acceleration point SOUTH. E) None of the above.

B) Angular velocity points NORTH and angular acceleration points SOUTH.

When a rigid body rotates about a fixed axis, all the points in the body have the same A) tangential speed. B) angular displacement. C) tangential acceleration. D) linear displacement. E) centripetal acceleration.

B) angular displacement.

A light cart and a heavy steel cart are both pushed with the same force for the same time interval, starting from rest. After the force is removed, the momentum of the light plastic cart is: A) greater than that of the heavy steel cart. B) equal to that of the heavy steel cart. C) less than that of the heavy steel cart. D) can't say. It depends on how big the force is. E) can't say. It depends on the masses of the carts.

B) equal to that of the heavy steel cart.

The change in an object's momentum during a certain time interval is equal to A) the change in the speed of the object times the mass of the object. B) the net force exerted on the object times the duration of the time interval. C) the net force exerted on the object times the distance the object travels in that time. D) the change in the object's kinetic energy. E) work done by a friction force.

B) the net force exerted on the object times the duration of the time interval.

Two objects with different masses collide with and stick to each other on a frictionless surface. Compared to before the collision, the system of two objects after the collision has A) the same amount of total momentum and the same total kinetic energy. B) the same amount of total momentum but less total kinetic energy. C) less total momentum but the same amount of total kinetic energy. D) less total momentum and less total kinetic energy. E) Not enough information is given to decide.

B) the same amount of total momentum but less total kinetic energy.

(Q. 2-3) An object is moving along the x-axis and is acted on by a conservative force Fx(x). The figure at right shows the graph of the potential energy function U (x) associated with that force. The object has a mass m = 2.0 kg, and at x = 0.0 m its velocity is v = +2.0 m/s. What is the speed of the object at x = 3.0 m? A) -1.0 m/s B) 0.0 m/s C) +1.4 m/s D) +2.2 m/s E) +3.4 m/s

C) +1.4 m/s

A particle moves along the x axis. Its momentum px is graphed as a function of time t. What is the force acting on the particle at t = 2.0 s? A) -1.0 N B) +1.0 N C) -2.0 N D) +2.0 N E) 0.0 N

C) -2.0 N

A 2.50 kg stone is dropped from rest at a height of 3.75 m. What is the impulse of the stone from the instant it is dropped until just before it hits the ground? (Assume that negligible air resistance and take the upward direction as the positive direction.) A) 8.20 N•s B) 21.4 N•s C) -21.4 N•s D) -8.20 N•s E) Cannot be calculated with the information provided.

C) -21.4 N•s

Consider a particle of mass m = 0.2 kg that is revolving with an angular speed w = 10 rad/s around a vertical axis. The perpendicular distance from the particle to the axis is R = 0.1 m. What is the kinetic energy of the rotating particle? A) 1.8 J B) 2.2 J C) 0.1 J D) 3.7 J E) 4.0J

C) 0.1 J

A solid flat disk of mass M = 4.0 kg and radius R = 0.20 m is rotating about an axis passing through its center as shown in the right figure. The moment of inertia of the disc about an axis passing through center of mass is 1/2MR2. What is the moment of inertia of the disc about an axis passing through its edge? A) 0.08 kg m2 B) 0.16 kg m2 C) 0.24 kg m2 D) 0.08 kg m2 E) None of the above.

C) 0.24 kg m2

An object starting from rest travels 200. m down an inclined surface that has a 30.0° slope and a constant friction force. When the object reaches the bottom of the surface, the object's speed is 30.0 m/s. What is the coefficient of kinetic friction between the surface and the object? A) 0.124 B) 0.265 C) 0.312 D) 0.578 E) 0.783

C) 0.312

Block A on the left has mass 1.00 kg. Block B on the right has mass 3.00 kg. Block A is initially moving to the right at 6.00 m/s, while block B is initially at rest. The surface they move on is level and frictionless. What is the velocity of the center of mass of the two blocks before the blocks collide? A) 3.00 m/s, to the right B) 3.00 m/s, to the left C) 1.50 m/s, to the right D) 1.50 m/s, to the left E) Zero

C) 1.50 m/s, to the right

A wheel released from rest is rotating about an axis with a constant angular acceleration of 2.06 rad/s 2. The angular velocity of the wheel after 5.00 s is A) 3.12 rad/s B) 4.52 rad/s C) 10.3 rad/s D) 13.0 rad/s E) 19.0 rad/s

C) 10.3 rad/s

You are riding in a car. As the car rounds a flat curve at a constant speed, an air freshener suspended from the ceiling of the car by a string is found to hang at an angle 40.0ᵒ with respect to the vertical. The air freshener is located 20.0 m from the curve's center of curvature. The speed of the car is closest to A) 10.2 m/s B) 11.3 m/s C) 12.8 m/s D) 15.3 m/s E) 23.2 m/s

C) 12.8 m/s

Questions 7 and 8 deal with a particle moving along the x -axis. For x ≥ 0 m a conservative force F(x) is acting on the particle. The figure on the right shows the graph of the potential energy U associated with that force over the range x = 0 m to x = 7 m. The particle has a mass m = 2 kg, and at x = 3 m its velocity v = + 2 m/s. What is the speed of the particle at x = 5 m? A) 0 m/s B) 1 m/s C) 2 m/s D) 3 m/s E) 4 m/s

C) 2 m/s

The angular acceleration of a spinning wheel with moment of inertia I = 1.00 kg m2 about a fixed axis is displayed as a function of time t in the graph. If the wheel's angular velocity at t = 0.0 s is -22.5 rad/s, what is its rotational kinetic energy at t = 6 s? A) 400 J B) -400 J C) 200 J D) -200 J E) Need more information.

C) 200 J

Consider a sphere with mass M and radius R rolls without slipping on an inclined plane with angle of inclination θ = 30.0˚ as shown in the figure. What is the acceleration of the center of mass of the sphere? (The moment of inertia of the sphere about its center of mass is 2/5MR2.) A) 1.01 m/s 2 B) 2.45 m/s 2 C) 3.50 m/s2 D) 4.50 m/s 2 E) 5.34 m/s

C) 3.50 m/s2

Consider a sphere with mass M and radius R rolls without slipping on an inclined plane with angle of inclination θ = 30.0˚ as shown in the figure. What is the acceleration of the center of mass of the sphere? (The moment of inertia of the sphere about its center of mass is 2/5MR2.) A) 1.01 m/s 2 B) 2.45 m/s 2 C) 3.50 m/s2 D) 4.50 m/s 2 E) 5.34 m/s 2

C) 3.50 m/s2

A 15.0 kg block is attached to an ideal spring of unknown spring constant k and is resting on a smooth horizontal table as shown in the figure below. Suddenly it is struck by a 3.00 kg stone traveling horizontally at 8.00 m/s to the right, whereupon the stone rebounds at 2.00 m/s horizontally to the left. After the collision the maximum distance that the block will compress the spring is 0.430 m. Find the spring constant k. A) 135 N/m B) 254 N/m C) 325 N/m D) 512 N/m E) 613 N/m

C) 325 N/m

The figure shows a plot of the time dependent force Fx (t) acting on a 1.0 kg particle in motion along the x-axis. The initial speed of the particle is 1.0 m/s. What is the speed of the particle at t = 8.0 s? A) 2.5 m/s B) 3.5 m/s C) 4.5 m/s D) 5.5 m/s E) 6.5 m/s

C) 4.5 m/s

Far in outer space where the gravity is negligible, a 425.0 kg spacecraft traveling at 75.00 m/s fires its engines. The figure shows the thrust force, Fthrust as a function of time. The mass lost by the spacecraft during the 30.00 s burn is negligible. At what time does the spacecraft reach its maximum speed and what is its maximum speed? A) At t = 10 s, the max speed is 86.76 m/s. B) At t = 10 s, the max speed is 98.53 m/s. C) At t = 30 s, the max speed is 110.3 m/s. D) At t = 30 s, the max speed is 145.6 m/s. E) None of the above.

C) At t = 30 s, the max speed is 110.3 m/s.

Two solid spheres of different radii and different masses roll down an incline surface without slipping, starting from rest at the same height. Sphere A has a greater mass and sphere B has a greater radius. Which reaches the bottom first? A) Sphere A. B) Sphere B. C) Both at the same time. D) Cannot be determined unless we know the angular accelerations of both spheres. E) Cannot be determined unless we know the angular velocities of both spheres.

C) Both at the same time.

Two equal point masses, m, connected by a rod of negligible mass and length r. If I1 is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I2 is the moment of inertia with respect to an axis passing through one of the masses which of the following is TRUE? A) I1 = I2 B) I1 > I2 C) I2 > I1 D) I1 > 0 but I2 = 0 E) I1 = 0 but I2 > 0

C) I2 > I1

When an object is moving only under the influence of conservative forces, which of the following statement is TRUE? A) Its kinetic energy does not change. B) Its potential energy does not change. C) Its mechanical energy does not change. D) The sum of its kinetic and potential energies changes. E) Its momentum does not change.

C) Its mechanical energy does not change.

A thin, very light wire is wrapped around a drum that is free to rotate. The free end of the wire is attached to a ball of mass m. The drum has the same mass m. Its radius is R, and its moment of inertia is I = (1/2) mR2. As the ball falls, the drum spins. At an instant that the ball has translational kinetic energy K, what is the rotational kinetic energy of the drum? A) K B) 2K C) K/2 D) K/4 E) 3K

C) K/2

The fan blade shown in the figure is slowing down. What are the directions of the angular velocity of the fan blade and the torque acting on the blade? A) The angular velocity is out of the page and the torque is out of the page. B) The angular velocity is out of the page and the torque is into the page. C) The angular velocity is into the page and the torque is out of the page. D) The angular velocity is into the page and the torque is into the page. E) Need more information.

C) The angular velocity is into the page and the torque is out of the page.

A block that is attached to an ideal massless spring oscillates vertically. When the speed of the block is a maximum, which of following statements is TRUE? A) the magnitude of the acceleration is a maximum. B) the magnitude of the displacement is a maximum. C) the magnitude of the force is zero. D) the potential energy is a maximum. E) the kinetic energy is zero.

C) the magnitude of the force is zero.

If a quantity X is conserved for a certain system and during a certain process, that means A) any change in the quantity X for that system during that process is offset by an equal but opposite change for the quantity X of the surroundings. B) the initial value of the quantity X equals its final value, even though the quantity X changes during that process. C) the quantity X for that system does not change in any way during that process. D) the value of the quantity X for each part of the system must change in the same way during that process. E) the quantity X for that system changes during that process.

C) the quantity X for that system does not change in any way during that process.

(Q. 2 - 3) An object is moving along the x-axis. For x ≥ 0 m it is acted on by a conservative force F(x). The figure at right shows the graph of the potential energy function U (x) associated with that force over the range x = 0.0 m to x = 4.0 m. The particle has a mass m = 2.5 kg, and at x = 0.0 m its velocity is v = +2.0 m/s. What is the speed of the object at x = 3.0 m? A) -1.0 m/s B) 0.0 m/s C) +1.0 m/s D) +2.2 m/s E) +3.4 m/s

D) +2.2 m/s

A 50.0 kg skier starting from rest travels 200. m down a hill that has a 30.0° slope and a uniform surface. When the skier reaches the bottom of the hill, the skier's speed is 30.0 m/s. How much work is done by friction as the skier comes down the hill? A) 1.10 × 10^4 J B) 2.65 × 10^4 J C) -1.10 × 10^4 J D) -2.65 × 10^4 J E) 0 J

D) -2.65 × 10^4 J

Questions 7 and 8 deal with a particle moving along the x -axis. For x ≥ 0 m a conservative force F(x) is acting on the particle. The figure on the right shows the graph of the potential energy U associated with that force over the range x = 0 m to x = 7 m. The particle has a mass m = 2 kg, and at x = 3 m its velocity v = + 2 m/s. What is the force acting on the particle at x = 2 m? A) -2 N B) -1 N C) 0 N D) 1 N E) 2 N

D) 1 N

A roller coaster car moves on its track with negligible friction. Portions of the track are at different heights above the ground, as shown in the figure. If the speed of the car at point A is VA = 7.00 m/s, what is its speed at B? A) 27.8 m/s B) 16.0 m/s C) 23.0 m/s D) 17.4 m/s E) 11.3 m/s

D) 17.4 m/s

A force F is applied to a 3.0 kg box parallel to the x -axis as it moves in a straight line. The force varies with the x -coordinate of the box as shown in the figure. Initially, at x = 0 m, the box is traveling at a speed of 1.0 m/s. What is the speed of the box at x = 5.0 m? A) 7.0 m/s B) 5.6 m/s C) 3.7 m/s D) 2.4 m/s E) 1.2 m/s

D) 2.4 m/s

In the figure, point P is at rest when it is on the x-axis. The time t, when P returns to the original position on the x-axis, is closest to A) 13 s. B) 18 s. C) 25 s. D) 35 s. E) 50 s.

D) 35 s.

A uniform disk of mass M is free to rotate about a fixed axis passing through point O as shown in the figure. A tangential force (F) applied at a distance r (point A) from the axis produces an angular acceleration α. What would be the angular acceleration if the same tangential force is applied at 3r (point B) distance from the same axis? A) α B) 9α C) α/3 D) 3α E) α/9

D) 3α

A 0.5 kg rubber ball traveling horizontally to the left (negative x) at 10 m/s hits a wall and bounces back with a velocity of 6 m/s to the right (positive x). The total impulse exerted by the wall on the ball is A) 6 Ns B) -6 Ns C) 0 Ns D) 8 Ns E) -8 Ns

D) 8 Ns

Two objects, one of mass m and the other of mass 2m, are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance. Which statement about these objects is true? A) The heavier object will go twice as high as the lighter one because it initially had twice as much kinetic energy. B) Both objects will reach the same height because they initially had the same amount of kinetic energy. C) At their highest point, both objects will have the same gravitational potential energy because they reach the same height. D) At its highest point, the heavier object will have twice as much gravitational potential energy as the lighter one because it is twice as heavy. E) The lighter object will reach its maximum height sooner than the heavier one.

D) At its highest point, the heavier object will have twice as much gravitational potential energy as the lighter one because it is twice as heavy.

The force vector F can be applied to the wheel in one of four possible locations, as shown. At which location should the force be applied in order to produce the most torque around the central axis of the wheel? A) A B) B C) C D) D

D) D

The force vector F can be applied to the wheel in one of four possible locations, as shown. At which location should the force be applied in order to produce the most torque around the central axis of the wheel? A) A B) B C) C D) D E) Any of them

D) D

Which one of the following statements is true? A) Momentum can be positive or negative but is not a vector. B) Momentum is a vector but can only have a magnitude and not a direction. C) Momentum is a scalar, with a magnitude and direction. D) Momentum is a vector, with a magnitude and a direction. E) The direction of momentum of an object and the direction of a force acting on the object are always in the same direction.

D) Momentum is a vector, with a magnitude and a direction.

The figure shows two blocks suspended by a cord over a pulley. The mass of block B is twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. The pulley's axle is frictionless, and the cord's weight can be ignored. The tensions in both parts of the cord are different. Let TR be the tension in the right cord and TL the tension in the left cord. If R is the radius of the pulley, what is the net torque τnet acting on the pulley? Take the positive direction of torques to be out of page. A) Zero B) R (TR - TL) C) R TR D) R (TL - TR) E) R TL

D) R (TL - TR)

A brother and sister are riding on a merry-go-round at the park. The brother rides on the outer edge of the merry-go-round and the sister rides closer to the center. While the merry-go-round rotates with a constant angular velocity, which of following statement is TRUE? A) They both have the same non-zero centripetal (radial) acceleration. B) They both have the same non-zero tangential acceleration. C) They both have the same non-zero angular acceleration. D) The brother has the greater centripetal (radial) acceleration. E) The brother has the greater tangential acceleration.

D) The brother has the greater centripetal (radial) acceleration.

You throw a ball upward. When the ball is moving up, what can you conclude about the gravitational force exerted on the ball? A) The gravitational force does positive work on the ball and decreases its kinetic energy. B) The gravitational force does negative work on the ball and increases its kinetic energy. C) The gravitational force does positive work on the ball and increases its kinetic energy. D) The gravitational force does negative work on the ball and decreases its kinetic energy. E) The gravitational force does not work on the ball and decreases its kinetic energy.

D) The gravitational force does negative work on the ball and decreases its kinetic energy.

What is true about the work done by a conservative force? A) The work done by a conservative force will decrease the total mechanical energy of a system. B) The work done by a conservative force will increase the total mechanical energy of a system. C) The work done by a conservative force is always path dependent. D) The work done by a conservative force along any closed path is zero. E) The work done by a conservative force along any closed path is not zero.

D) The work done by a conservative force along any closed path is zero.

Three forces are applied to a wheel of radius R. One force F1 is tangent to it, one force F2 makes a 30.0 angle with the radius R, and one force F3 is perpendicular to the rim. Assume that the magnitudes of three forces are equal, rank order the magnitude of the torque t associated with the force. A) t1 = t2 = t3 B) t1 = t2 > t3 C) t1 = t3 > t2 D) t1 > t2 > t3 E) t3 > t2 > t1

D) t1 > t2 > t3

(Q. 2 - 3) An object is moving along the x-axis. For x ≥ 0 m it is acted on by a conservative force F(x). The figure at right shows the graph of the potential energy function U (x) associated with that force over the range x = 0.0 m to x = 4.0 m. The particle has a mass m = 2.5 kg, and at x = 0.0 m its velocity is v = +2.0 m/s. What is the force acting on the object at x = 1.5 m? A) -2.0 N B) -1.0 N C) 0.0 N D) +1.0 N E) +2.0 N

E) +2.0 N

The amount of work required to bring a rotating object at 5.00 rad/s to a complete stop is -300. J. What is the moment of inertia of this object? A) -24.0 kg-m 2 B) -14.4 kg-m 2 C) +6.0 kg-m 2 D) +14.4 kg-m 2 E) +24.0 kg-m 2

E) +24.0 kg-m 2

A 4.0 kg mass is released from rest at the top of a frictionless ramp 2.0 m above ground. It slides down the ramp to a level, horizontal portion of frictionless track and then collides with a stationary 8.0 kg mass. Immediately after the collision the larger mass has a velocity v8 = +3.5 m/s (i.e., heading to the right). The velocity v4 of the smaller mass just after the collision is A) 3.3 m/s. B) 4.5 m/s. C) -2.6 m/s. D) 13 m/s. E) -0.74 m/s.

E) -0.74 m/s.

A block of mass 5.6 kg is attached to a horizontal spring on a rough floor. Initially the spring is compressed 3.5 cm. The spring has a force constant of 1040 N/m. The coefficient of kinetic friction between the block and the floor is 0.26. The block is released from rest. The speed of the block after it has traveled 0.020 m is A) 0.089 m/s B) 0.11 m/s C) 0.17 m/s D) 0.23 m/s E) 0.29 m/s

E) 0.29 m/s

A wheel rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel? A) 0.616 rad/s2 B) 5.45 rad/s2 C) 111 rad/s2 D) 22.5 rad/s2 E) 10.9 rad/s2

E) 10.9 rad/s2

A force of 0.0200 N acts on the edge of a solid uniform sphere (I = 2/5MR2) of mass 205 g and radius 2.15 cm. What is the angular acceleration of the sphere? A) 13.4 rad/s2 B) 12.7 rad/s2 C) 21.2 rad/s2 D) 15.2 rad/s2 E) 11.3 rad/s2

E) 11.3 rad/s2

The angular acceleration of a spinning wheel as a function of time is displayed in the graph at right. If the wheel's angular velocity at t = 0.0 s is 10.0 rad/s, its angular velocity at t = 8.00 s is A) 52.5 rad/s. B) 7.50 rad/s. C) 17.5 rad/s. D) 2.50 rad/s. E) 13.5 rad/s.

E) 13.5 rad/s.

A 50. kg mass is at rest on a frictionless surface. An unknown force pushes the mass for 5.0 seconds until the mass reaches a velocity of 3.0 m/s. What was the magnitude of the impulse acting on the mass? A) 17 kg-m/s B) 10. kg-m/s C) 30. kg-m/s D) 80 kg-m/s E) 150 kg-m/s

E) 150 kg-m/s

A 20.0-kg body is moving through space with a velocity V = 200 m/s i, when, due to an internal explosion, it breaks into three parts. One part, with a mass m1 = 10.0 kg, moves away from the point of explosion with a velocity V1 = 100 m/s j. A second part, with a mass m2 = 4.00 kg, has a velocity V2 = 500 m/s i. The third part has a mass m3 = 6.00 kg. What is the velocity V3 of the third part? A) 2000 m/s i - 1000 m/s j. B) 500 m/s i - 250 m/s j. C) -2000 m/s i + 1000 m/s j. D) 550 m/s i - 280 m/s j. E) 333 m/s i - 167 m/s j.

E) 333 m/s i - 167 m/s j.

As shown in the figure, ball of putty with mass M attached to one end of a massless rod of length L = 1.00 m. The other end of the rod is attached to a massless, frictionless axle that can pivot freely in a vertical plane. Initially, the rod and ball are at rest and level with the horizontal. The system is then released, and the ball and rod swing downward, due to gravity. The speed of the ball when the rod and ball are at an angle of 60.0° below the horizontal is A) 3.67 m/s. B) 2.91 m/s. C) 1.21 m/s. D) 2.06 m/s. E) 4.12 m/s.

E) 4.12 m/s.

A wheel has a radius of 0.40 m and is mounted on frictionless bearings. A block is suspended from a rope that is wound on the wheel and attached to it (see figure). The wheel is released from rest and the block descends 1.5 m in 2.00 s without any slipping of the rope. The tension in the rope during the descent of the block is 20 N. What is the moment of inertia of the wheel? A) 3.5 kg • m2 B) 3.7 kg • m2 C) 3.9 kg • m2 D) 4.1 kg • m2 E) 4.3 kg • m2

E) 4.3 kg • m2

A constant nonzero net torque is exerted on an object that is free to rotate. Which of the following is constant? A) Angular position B) Angular velocity C) Rotational kinetic energy D) Centripetal acceleration E) Angular acceleration.

E) Angular acceleration.

Which of following statements is TRUE about momentum? A) It can be positive or negative but is not a vector. B) It is a vector but can only have a magnitude and not a direction. C) It is a scalar, with a magnitude and a direction. D) It is a scalar, with a magnitude. E) It is a vector, with a magnitude and a direction.

E) It is a vector, with a magnitude and a direction.

When an object travels in a circular path at constant speed, which one of the following statements is wrong? A) The direction of the object's acceleration is directed toward the center of the circular path. B) The object's velocity and acceleration are perpendicular. C) The object's velocity is changing. D) The object's acceleration is changing. E) The object's acceleration is zero.

E) The object's acceleration is zero.

You get on a ride where you stand against the inner wall of a hollow vertical cylinder with a radius of 3.5 m. The cylinder begins to rotate and speed up until a constant rotation rate of 1 revolution every 2.0 seconds is reached. Once the cylinder gets up to speed the floor drops out from below you and you remain pinned to the wall, no longer touching the floor. The minimum coefficient of static friction required to keep you from sliding down. A) 0.01 B) 0.28 C) 0.41 D) 0.57 E) None of the above

B) 0.28

A mass m = 0.200 kg sits on a frictionless horizontal surface, connected to a spring with force constant k = 4.50 N/m. You pull on the mass, stretching the spring, and then release it with no initial velocity. The mass begins to move back toward its equilibrium position (x = 0). What must the initial displacement of the mass be if its maximum speed in the subsequent motion is to be 2.50 m/s? A) 0.149 m B) 0.527 m C) 0.797 m D) 0.932 m E) 1.32 m

B) 0.527 m

In the figure, a mass of 31.77 kg is attached to a light string that is wrapped around a disk of radius R = 0.1000 m and moment of inertia I = 4.000 kg • m2 . The disk is suspended from the ceiling, and the mass is then released. What is the magnitude of the acceleration of the mass? A) 0.4256 m/s2 B) 0.7211 m/s2 C) 1.265 m/s2 D) 3.549 m/s2 E) 5.456 m/s2

B) 0.7211 m/s2

The moment of inertia I of a solid sphere is (2/5) mR2. This sphere rolls without slipping down an inclined plane with an inclination angle = 30.0 from the horizontal direction. The mass of the sphere is 1.00 kg. What is the friction force between the inclined plane and the sphere? A) 1.90 N B) 1.40 N C) 1.70 N D) 1.10 N E) 0.65 N

B) 1.40 N