Phys Final

A projectile is launched with an initial speed v0 at an angle of θ to the horizontal. What is the speed of this projectile when it reaches its highest point? (A) 0 m/s (B) v0 cos θ (C) v0 sin θ (D) v0 tan θ (E) v0

B

A box of mass m is pressed against (but is not attached to) a spring, compressing it. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this with a box of mass 2m and compress the spring by the same distance, then which statement is true? (A) The lighter box will go twice as high up the incline as the heavier box. (B) As it leaves the spring, the lighter box will move twice as fast as the heavier box. (C) Both boxes will have the same speed just as they move free of the spring. (D) Both boxes will reach the same maximum height on the incline.

A

A horse refuses to pull a cart. The horse reasons, "According to Newton's Third Law, whatever force I exert on the cart, the cart will exert an equal and opposite force on me, so I have no chance of accelerating the cart." Which of the following statements about this situation are true? I. The force of the cart on the horse is not relevant to the acceleration of the cart. II. The magnitude of the force of the ground on the horse is equal to magnitude of the force of the horse on the cart. III. The magnitude of the force of the ground on the cart is equal to the magnitude of the force of the horse on the cart. (a) Statement I only. (b) Statement II only. (c) Statement III only. (d) Statements I and II only. (e) Statements II and III only.

A

A lifeguard standing on a ramp at the edge of the water pulls a rope at a constant speed of 1 m/s toward himself. There is a swimmer attached to the other end of the rope. The guard is 3 m above the water level. When the swimmer is at a distance of 5 m from the shore the speed of the swimmer toward the shore is (a) 0.86 m/s (b) 0.51 m/s (c) 1 m/s (d) 0.6 m/s

A

A solid ball is released from rest at the top of the left ramp (height H from ground) and begins rolling smoothly (no slip) down the ramp. The ball then rolls smoothly along the ground before it slides up a frictionless ramp (on the right) as it continues spinning. How does the maximum vertical height h that the spinning ball reaches on the frictionless ramp compare to the height H from which it was released on the first ramp? (A) H > h (B) H = h (C) H < h (D) not enough information is given

A

A uniform solid cylinder (mass M and radius R) is released from rest on top of a ramp (height h)and rolls down smoothly (no slip). The center of mass velocity at the bottom of the ramp is observed to be V1.After we drill a through hole (of radius r = R/2) in the center of the cylinder and repeat the same experiment(same height, also no-slip), the center of mass velocity at the bottom of the ramp is observed to be V2. What statement below is true? (A) V1 > V2 (B) V1 = V2 (C) V1 < V2 (D) not enough information is given

A

3.0 kg mass attached to a spring oscillates with an amplitude of 4.0 cm and a period of 2.0 s. What is the maximum speed of the object? (a) 0.11 m/s (b) 0.13 m/s (c) 0.15 m/s (d) 0.17 m/s (e) 0.19 m/s

B

A 1000 kg load is being moved up by a crane. What is the approximate tension in the cable if the load moves upward with a speed decreasing by 4 m/s each second? (a) 4000 N (b) 6000 N (c) 10 000 N (d) 14 000 N

B

A child first holds a stone in her hand at rest and then lifts the stone, accelerating it upward. Which statement below is true concerning the force (magnitude) of the child's hand on the stone, FS,H, and the force (magnitude) of the stone on the child's hand, FH,S? (A) While at rest, FS,H = FH,S, but while the stone is being lifted, FS,H > FH,S. (B) When at rest and when the stone is lifted, FS,H = FH,S. (C) FS,H > FH,S at all times. (D) FS,H < FH,S at all times. (E) While at rest, FS,H = FH,S, but while the stone is being lifted, FS,H < FH,S.

B

A closed railroad car is at rest on a flat frictionless track. Cannon located inside the car and that is attached to the front end points to the rear wall and fires. The projectile, which has a mass of 1/4 of the cannon, is completely absorbed in the rear wall. (a) The final position of the car has not changed (b) The final position of the car has moved in the direction of the front of the car (c) The final position of the car has moved in the direction of the rear of the car (d) The car is now moving.

B

A cruise ship passenger uses a shuffleboard cue to push a shuffleboard disk of mass 0.40 kg horizontally along the deck so that the disk leaves the cue with a speed of 8.5 m/s. The disk then slides a distance of 8.0 m before coming to rest. What is the coefficient of kinetic friction between the disk and the deck? (a) 0.41 (b) 0.46 (c) 0.53 (d) 0.59 (e) 0.64

B

An object hangs from a spring with spring constant k attached to the ceiling, and makes one full oscillation in time T. Now it is hung from four parallel springs attached to the ceiling, each one of them has the same spring constant k. What is the period now? (a) T/4 (b) T/2 (c) T (d) 2T

B

Four circular objects (a disc, a hoop, a solid sphere, and a hollow sphere) all have the same mass and roll, without slipping, at the same linear speed. Which one of these has the greatest total kinetic energy? (A) disc (B) hoop (C) solid sphere (D) hollow sphere (E) They all have the same total kinetic energy.

B

Two men are standing in the exact middle of a boat that is at rest in the middle of a lake. The two men then begin to walk to opposite sides of the boat, with the 80 kg man walking east and the 60 kg man walking west. Both men stop when they reach the end of the boat. After the men stop, which of the following statements is true: (A) The boat has moved slightly to the east. (B) The boat has moved slightly to the west. (C) The boat will end up in the same position. (D) The final position of the boat will depend on the momentum of each man as they walk. (E) The direction the boat moves depends on whether it is lighter or heavier than the men.

B

Two stones are thrown simultaneously from a height of 500 m. The first stone is thrown vertically downward at a speed of 10 m/s, while the second stone is thrown vertically upward at a speed of 10 m/s. Immediately after the two stones are thrown, the difference in their speeds will . During the time interval that both stones are in flight the difference in their velocities will. (A) increase with time, increase (B) increase with time, stay the same (C) stay the same, stay the same (D) decrease with time, increase (E) decrease with time, decrease

B

What force(s) perform a non-zero amount of work at any point during the motion of a simple pendulum, i.e., a mass hanging from a string that swings back and forth? (A) The tension in the string (B) Gravity (C) The centripetal force (D) Both gravity and the string's tension (E) All three forces: gravity, tension, and centripetal force

B

A satellite moves at a constant speed in a circular orbit about the center of the Earth and near the surface of the Earth. Assume that the acceleration of gravity on this satellite is g = 9.81 m/s2 and that the radius of the Earth is 6370 km. How long does it take for this satellite to make one complete revolution around the Earth? (a) 67.1 minutes (b) 76.5 minutes (c) 84.3 minutes (d) 92.1 minutes (e) 101. minutes

C

An acrobat sliding down a vertical pole tightens her grip as she speeds up such that (the upward) frictional force between her hands and the pole increases. At the point where the frictional force equals her weight, she maintains a constant grip (and hence her frictional force remains unchanged). Describe her motion after this point. (A) The acrobat comes to an immediate stop. (B) The speed of the acrobat gradually decreases. (C) The acrobat descends the pole at a constant speed. (D) The acrobat falls off the pole. (E) Cannot be determined without additional information.

C

An automobile has 60% of its weight on the front wheels. The front and back wheels are separated by 3 m. What distance from the front wheels is the center of mass? (a) 1 m (b) 1.1 m (c) 1.2 m (d) 1.3 m

C

An elevator begins accelerating upward from rest due to a constant force supplied by an elevator motor before traveling at a constant velocity. At which point in the elevator's motion does the motor supply the most power? (A) Just when the elevator starts accelerating. (B) Halfway through the period when the elevator is accelerating. (C) Just before the elevator reaches its final, greatest velocity. (D) After the elevator has finished accelerating and is traveling at its greatest velocity.

C

Rank the following angular momenta from largest to smallest. I: A 1.0 kg mass located 1.0 m north of the axis of rotation, moving directly east at 2.0 m/s II: A 2.0 kg mass located 1.0 m west of the axis of rotation, moving directly east at 2.0 m/s III: A 1.0 kg mass located 1.4 m northwest of the axis of rotation, moving directly east at 2.0 m/s IV: A 2.0 kg mass located 1.0 m east of the axis of rotation, moving directly east at 1.0 m/s (a) I > III > IV > II (b) III > I > II = IV (c) I > III > II = IV (d) III > I > II > IV (e) IV > I > III > II

C

Two identical cylindrical disks have a common axis of rotation. Initially, one of the disks is spinning with angular momentum Li and rotational kinetic energy Ki. The other disk is stationary. When the two disks are brought into contact, they stick together. Which of the following concerning Lf and Kf for the final system of two rotating disks is true? (a) Lf=Li and Kf=Ki (b) Lf=Li/2 and Kf=Ki/2 (c) Lf=Li and Kf=Ki/2 (d) Lf=Li/2 and Kf=Ki

C

What physical principle lies behind stars spinning faster after they collapse into neutron stars? (The star starts as a solid sphere of mass M and radius R and ends as a neutron star of the same mass M but radius r << R.) (A) Energy Conservation (B) Linear Momentum Conservation (C) Angular Momentum Conservation (D) External Torque Theorem (E) Kepler's First Law

C

Which vector describes a displacement of 10 units in a direction 30◦ below the positive x-axis? (A) 10i − 10j (B) 5.0i − 8.6j (C) 8.6i − 5.0j (D) 10(i + j) (E) 0.5i − 0.4j m

C

You swing a bucket of water over your head making an arc of radius r. The minimum speed required for the water to remain in the bucket is (a) gr (b) gr^2 (c) sqrt(gr) (d) g^2r (e) g*sqrt(r)

C

You throw a rock horizontally from the top of a vertical cliff 40 m high. It lands on level ground 100 m from the base of the cliff. How fast did you throw it? (a) 70 km/hr (b) 100 km/hr (c) 130 km/hr (d) 160 km/hr

C

piano on a wooden floor has a coefficient of static friction which is larger than its co-efficient of kinetic friction. A force is applied that is large enough to start the piano sliding. If this same force continues to be applied, the piano will (A) eventually stop moving. (B) move at constant velocity. (C) speed up at a constant rate. (D) move in a series of jerks. (E) none of the above.

C

A 3.0 kg object attached to a spring oscillates with an amplitude of 4.0 cm and a period of 2.0 s. What is the total energy of this system? (a) 0.0060 J (b) 0.012 J (c) 0.018 J (d) 0.024 J (e) 0.030 J

D

A ball is thrown straight up in the air with an initial speed v, rising to a maximum height h in a time interval T . If the ball had been thrown straight up at four times this speed (4v) ,it would reach a maximum height in a time interval. (A) 4h, 2T (B) 4h, 4T (C) 4h, 16T (D) 16h, 4T (E) 16h, 16T

D

At some initial time, an object is located at the origin. At a later time, the object's position is found to be 10 meters from the origin in the +x direction. What statement concerning the relationship between the object's average speed and the magnitude (i.e., absolute value)of the object's velocity, |Vavg|, during this time interval must be true?(A) average speed < |Vavg| (B) average speed ≤ |Vavg| (C) average speed > |Vavg| (D) average speed ≥ |Vavg| (E) Its average speed could be greater than, less than, or equal to |Vavg|.

D

Chuck Norris, Mr. T, and Angus Young walk into a bar. Unable to contain that much awesomeness, the bar spontaneously explodes, sending a 10.0 kg bar stool straight up into the sky to a max height of 10.0 km. How much kinetic energy was transferred to the bar stool during the explosion? (A) 370 kJ (B) 560 kJ (C) 740 kJ (D) 980 kJ (E) 1100 kJ

D

The force exerted by an expanding gas is what propels a bullet out of a gun barrel. Suppose a force that has an average magnitude F propels the bullet so that it has a speed vat the instant it reaches the end of the barrel. What magnitude of force would be required to increase the speed of the bullet to 4v for the same gun? (A) 2F (B) 4F (C) 8F (D) 16F (E) 32F

D

The instantaneous power delivered by force ~F acting on an object moving with a velocity v = (2 m/s)i + (3 m/s)j is found to be 6 W. Which of these could not be the applied force? (A) (2 N)j (B) (3 N)i + (2 N)k (C) (-3 N)i + (4 N)j (D) (1.5 N)i + (1.5 N)j (E) (2 N)j + (2 N)k

D

Two carts of unequal mass lie on a frictionless track and are connected to each other by a massless spring. The carts are pulled apart, stretching the spring, and then they are released from rest. At one point in time, the velocity of cart 1 is 2v and that of cart 2 is −3v. If at another moment of time cart 1's velocity is −6v, what would be the velocity of cart 2 at this moment assuming no external forces had acted on the system during the interval over which the velocity measurements were taken? (A) 2v/3 (B) 4v (C) 5v (D) 9v (E) Not enough information provided.

D

Which of the following statements in true? I. Circular motion can be described parametrically as simple harmonic motions in x and y that are 90° out of phase. II. In simple harmonic motion, the period is independent of the amplitude. III. In simple harmonic motion, the velocity is independent of the phase, because the phase is a constant and the derivative of a constant is zero. (a) Statement I only. (b) Statement II only. (c) Statement III only. (d) Statements I and II only. (e) Statements II and III only.

D

A beetle safely rides near the edge of a tire (radius = R) of a car that is moving with a constant linear speed v. At a specific instant in time, the beetle lies directly above the tire's center, at the highest point of the tire. Determine the total linear speed of the beetle with respect to the road at this instant. (A) 0 (B)√v2R (C) v2R (D) √2 v (E) 2v

E

A car initially moving at a speed v skids to a stop over a distance D on a level surface. If the initial speed of the car had been 3v, what would have been the distance required for it to skid to a stop? (A) D/3 (B) √3 D (C) 1.5 D (D) 3 D (E) 9 D

E

A car undergoing uniform acceleration with magnitude a = 4.0 m/s2 is travelling at a speed of 40 m/s as it enters a tunnel. When the car exits the tunnel, its speed is 72 m/s. How long is the tunnel? (A) 7 m (B) 21 m (C) 197 m (D) 378 m (E) 448 m

E

A child is riding on a freely spinning merry-go-round, which is initially rotating clockwise(as seen from above), somewhere between its center and its edge. To increase the rotational speed of the merry-go-round, the child could I. walk toward the edge of the merry-go-round. II. walk toward the center of the merry-go-round. III. walk in the clockwise direction about the merry-go-round's center. IV. walk in a counterclockwise direction about the merry-go-round's center. (A) I or III (B) II or III (C) I or IV (D) II or IV (E) IV only

E

A disk rotates with an initial angular velocity of 2 radians/s about a frictionless shaft. This disk is solid with a mass of 2 kg and a radius of 10 cm. A second disk with a mass of 1 kg and a radius of 5 cm is dropped onto the first disk. Friction between the disks causes them to rotate at the same angular velocity. This velocity is (a) 0 (b) (20/9) radians/s (c) 1 radian/s (d) 2 radians/s (e) (16/9) radians/s

E

A pilot of mass 60 kg comes out of a nose dive at a speed of 100 m/s, making a circular arc of radius 200 m. At the bottom of this arc, the total upward normal force of his chair on him is (A) 50 N. (B) 600 N. (C) 2400 N. (D) 3000 N. (E) 3600 N.

E

One end of a 1.0-m long string is fixed, the other end is attached to a 2.0-kg stone. The stone is then swung in a vertical circle, passing through the lowest point with a speed of 4.0 m/s. The tension force of the string at this point is about: (A) 0 (B) 12 N (C) 20 N (D) 32 N (E) 52 N

E

Rank the follow torques from largest to smallest. I: A 20 N force applied at 90° at the end of a 0.2 m long wrench II. A 20 N force applied at 90° at the end of an 0.15 m long wrench III. A 20 N force applied at 60° at the end of a 0.2 m long wrench IV. A 40 N force applied at 90° at the end of a 0.1 m long wrench (a) IV > I > III > II (b) IV > II > I > III (c) I > IV > II > III (d) I = IV > II > III (e) I = IV > III > II

E

Rank the force on a wall in the following four collisions from largest to smallest. Collision A: A 1 kg mass traveling at 2 m/s hits a wall and sticks to it in a collision lasting 0.05 s. Collision B: A 1 kg mass traveling at 2 m/s hits a wall and recoils at 2 m/s in a collision lasting 0.10 s. Collision C: A 1 kg mass traveling at 1 m/s hits a wall and sticks to it in a collision lasting 0.025 s. Collision D: A 1 kg mass traveling at 1 m/s hits a wall and sticks to it in a collision lasting 0.05 s. (a) A > B > C > D (b) A > C > B > D (c) B > A > C > D (d) B > C > D > A (e) A = B = C = D

E

Which of the following statements is true about simple harmonic motion? I. If you double the amplitude and double the period, the maximum velocity is unchanged. II. For a pendulum, the period is proportional to the square root of the length. III. For a spring oscillator, the angular frequency is independent of the amplitude. (a) Statement I only (b) Statement II only (c) Statement III only (d) Statements I and III (e) Statements I, II and III

E

Which of the following statements is true? I. If two balls are launched at identical speeds above a flat field, the ball launched at an angle of 60° above the horizontal will travel further than the ball launched at 30° above the horizontal. [Neglect air resistance.] II. If a ball is thrown straight up and passes a window with velocity v, it will pass the same window with velocity -v on its way down. III. Neglecting air resistance, the horizontal distance that a projectile travels is independent of its mass. (a) Statement I only. (b) Statement II only. (c) Statement III only. (d) Statements I and II only. (e) Statements II and III only.

E

You jump off a platform 134 m above the surface of the Zambezi River, which flows between Zambia and Zimbabwe, while attached to a bungee cord with an unstretched length of 40 m. You then fall another 80 m before the bungee cord, which obeys Hooke's Law, brings you to a stop and then starts pulling you upward. What is your net acceleration in units of g (9.81 m/s2) due to the bungee cord and gravity at the lowest point where your velocity is zero? (a) 1.2 g (b) 1.4 g (c) 1.6 g (d) 1.8 g (e) 2.0 g

E