Physics 71 Recit 9

TWHFX-×, 2nd sem, A.Y. 2014-2015

March 27, 2015

Instructions: Answer all problems. Show your complete solution unless otherwise stated. The instructor has the rightto deem your answer wrong if your solution is incomplete and/or unclear. University rules apply for cheating.

This is a take-home recit, meant to be solved individually. Deadline is on April 8, 2015 (Wednesday).

1. A flywheel rotates at a constant angular acceleration. At time t = 1.38 s, it rotates with a speed of ω = 2.40 rad/sin the clockwise direction. At time t = 5.97 s, it rotates with a speed of ω = 2.40 rad/s in the counter-clockwisedirection. What is its angular displacement from t = 0.00 s to t = 7.00 s? What is the tangential acceleration of apoint on the flywheel 0.223 m from the axis?

2. An Atwood’s machine consists of a 4.00- kg block ini-tially on the ground and a 12.0- kg block initially hang-ing 4.00 m above the ground. They are connected bya taut string through a cylindrical pulley with mass3.00 kg and radius 0.10 m (Icm = 1

2MR2). After theblocks are released from rest, What is the speed of the12.0- kg block just as it hits the ground? (Hint: Whensetting up conservation of energy equation, one mustinclude the sum of the kinetic and potential energiesof the two blocks and the pulley.)

3. A solid, uniform, spherical boulder(Icm = 2

5MR2)

starts from rest and rolls down a 50.0- m-high hill. Thetop half of the hill is rough enough to cause the boulderto roll without slipping, but the lower half is coveredwith ice and there is no friction. What is the speed ofthe boulder’s center of mass...

(a) halfway down the hill?

(b) at the bottom of the hill? (Hint: the linear speedof its center of mass will increase, but the boul-der’s angular speed won’t change.)

4. On a frictionless air hockey table, a puck of mass 5.0 kgmoving at 2.0 m/s approaches an identical puck thatis stationary. After collision, the first puck moves at30.◦ above the original line of motion; the second puckmoves 60.◦ below.

(a) What are the speeds of the puck after collision?

(b) Was the collision elastic?

5. A 45.0- kg woman stands up in a 60.0- kg canoe 6.00 mlong. She walks from a point 1.00 m from one end toa point 1.00 m from the other end. If you ignore anykind of resistance on the canoe, how far does the canoemove during this process? (Hint: since the woman-canoe system experiences zero net force, its center ofmass shoudn’t move.)

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