Exam2 sp10 - Exam 2 Practice Questions PDF

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Exam 2 Practice Questions...

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Physics 101

Classical Physics

Spring 2010

Exam 2 Instructions: The answer sheets must be handed in as soon as time is called. You have until 10:20am. Answer the following four multiple choice questions. Each question is worth 4 points. 1. A ball of mass 0.3 kg hits a wall and rebounds. Initially the magnitude of the ball’s velocity is 7 m/s, but after rebound the magnitude of the velocity is 5 m/s. What is the impulse imparted to the ball by the wall? (a) 1.8 kg m/s, (b) 2.1 kg m/s, (c) 3.6 kg m/s, (d) 0.6 kg m/s, (e) 1.5 kg m/s 2. An object initially at rest breaks into two pieces as the result of an explosion. One piece has twice the kinetic energy of the other piece. Which of the following is the ratio of the masses of the two pieces? (a) 1:1, (b) 2:1, (c) 4:1, (d) 16:1, (e) more information is needed 3. A flywheel rotating with an initial angular velocity of 12 rev/s is brought to rest in 6 s. If the angular acceleration is constant during this time, what is its value? (a) -4 rad/s2 , (b) -4π rad/s2 , (c) -2 rad/s2 , (d) -1/π rad/s2 , (e) -72 rad/s2 4. The Earth wobbles—the axis about which it rotates each day actually rotates its direction over time (this is a phenomenon called ‘precession’). While right now it points toward the star Polaris (the North Star), in 13,000 years it circles around and and will eventually point toward the star Vega in the opposite part of the sky. 13,000 years after that, it will have circled all the way back and point toward Polaris again. Which of the following statements is most likely to describe why this does or does not violate the conservation of angular momentum? (a) The speed of rotation does not change, so the angular momentum is constant and therefore conserved. (b) Angular momentum does not have to be conserved, because the Earth is in space, far away from anything else. (c) The Earth is being acted on by an external torque from the gravity of the Moon and the Sun, and so this changes the Earth’s angular momentum. (d) Angular momentum is conserved, because the axis eventually gets back to where it started so the net change is zero. (e) None of these.

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5. A spinning bicycle wheel is brought to a stop by a hand pushing on the tire with a constant force. The only other point of contact for the wheel is at its axle. If the bicycle wheel were a perfect ‘hoop’, it would have a rotational inertia of mR2 , but because of the spokes of the wheel it is not exactly mR 2 . If the force provided by the hand slows the wheel down in a time t, how would the time to slow down a perfect hoop (with I = mR2 exactly and the same mass and radius as the bicycle wheel) compare to t, if the same force is applied by the hand? (a) The time to slow down the hoop would be shorter than t (b) The time to slow down the hoop would be exactly t (c) The time to slow down the hoop would be longer than t (d) The hoop would never stop. (e) The hoop would travel at a constant angular velocity.

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For the following problems, Use g = −10m/s2 .

you must show your work to receive full credit.

6. A ball of mass m collides perfectly elastically with a second ball of the same mass that serves as the pendulum bob—the ball is attached to a string of length L that is suspended from the ceiling. Both masses have m = 3 kg, and the first ball is initially traveling in the positive x-direction at 2m/s. The collision is not a glancing collision but is exactly ‘head-on’, and you should ignore the effects of the string at the instant of collision, and just consider it after that. (a) What is the velocity of the first ball, immediately after the collision?

(b) How high does the pendulum bob rise?

(c) When the pendulum bob comes back down, it collides elastically with the first ball. What is the magnitude of the first ball’s velocity after the collision?

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7. A block of mass m = 4 kg sits on an incline plane whose angle is θ = 30◦ relative to the horizontal, and the mass is held in place so that it compresses a spring (of spring constant k = 300N/m) a distance d = 0.1 m (measured along the plane) from its equilibrium position. At t = 0 the mass is released so that the spring begins to push it up the plane. (This is similar to a pinball machine’s ‘launcher’, only to simplify the problem we are using a heavy block instead of a little silver ball).

(a) If the plane is frictionless (µk = 0), what is the velocity of the block when the spring gets to its equilibrium position?

(b) Again for the case of no friction, how far up the plane will the block travel before coming to rest, relative to the initial starting point (where the spring was compressed)?

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(c) If the plane instead has a coefficient of kinetic friction of µk = 2 3, how far up the plane will the block travel before coming to rest, relative to the initial starting point (where the spring was compressed)?

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8. A solid cylinder of length L and radius R has a weight W . Two cords are wrapped around the cylinder, one near each end (each at the same distance form their respective end) and the cord ends are attached to hooks on the ceiling. The cylinder is held horizontally with the two cords exactly vertical and then released. For a solid cylinder rotating around an axis through its center, the rotational inertia is given by I = 21 MR2 . Assume there is no slipping or stretching of the cords.

(a) What is the tension in each cord as they unwind in terms of the weight of the cylinder?

(b) When the cylinder has dropped a distance y = 0.1 m, what is the velocity of its center of mass?

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9. A uniform plank with length L = 3 m and mass m = 2 kg on which a heavy (m = 7 kg) power saw is sitting is supported by two sawhorses, one of which is at the far end of the plank opposite the power saw.

(a) How close can the second sawhorse be to the first so that the saw does not tip the plank over?

(b) If now the second sawhorse is a distance d = 2 m away from the first, what is the largest mass that the power saw can have and the plank not tip over?

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