Cars a and B Travel on Circular Race Tracks of Radii 100 and 200 Meters, Respectively

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Problem 1 (20 points)

Initially, a block of mass 4m moves with velocity vo to the right on a frictionless surface. A block of mass m drops straight down (no initial horizontal velocity, vertical velocity irrelevant) onto the larger block. After landing, the smaller block slips under kinetic friction, but eventually comes to rest without falling off the larger block.

(a) After the smaller block stops slipping, both smaller and larger blocks travel with a common velocity vF. What is vF? Express your answers only in terms of m and vo. (6 points)

(b) What is the work done by kinetic friction on the smaller block during the time it is slipping? Express your answers only in terms of m and vo, and clearly indicate the sign of your answer.(7 points)

(c) What is the work done by kinetic friction on the larger block during the same time interval as in part (b)?Express your answers only in terms of m and vo, and clearly indicate the sign of your answer.(7 points)

Print Name: ______

Problem 2 (20 points)

A cart of mass 4m and length 2 meters sits on a frictionless surface. It is initially at rest, with aball of mass 3mat its center (also at rest). The mass 3m explodes into two pieces of mass 2m and m, which stick to the opposite sides of the cart.

(a) Take the speed of 2m after the explosion (but before sticking) to be +v. How much stored energy is released in the explosion? Express your answer in terms of m and v only. (6 points)

(b) The mass 2m hits the end of the cart after the mass m. Assuming the interior of the cart is frictionless, how much energy is lost when the mass 2m lands? Express your answer in terms of m and v only. (8 points)

(c) What is the displacement of the cartafter both masses have stuck to its ends? Remember the cart has mass 4m and be careful to indicate the correct sign relative to the x-axis shown. (6 points)
Print Name: ______

Problem 3 (20 points)

A 1.00 kg mass sits on a frictionless, horizontalsurface. On the left it is attached to a spring with constant k= 20.0 N/m, and on the right it is connected to a 4.00 kg mass by a massless rope and two massless, frictionless pulleys as shown. The masses are released from rest with the spring initially unstretched.

(a) What distance has the 4.00 kg mass fallen when it reaches its lowest point? (6points)

(b) What is the speed of the 4.00 kg mass after it has fallen0.25 meters?(Note—you do NOT need your numerical answer from part (a) to solve this part.) (7 points)

On this formula sheet, often ‘1’ denotes ‘initial’ and ‘2’ denotes ‘final’.