Question

4. Energy and Momentum for 15 points: A 200 gram lab cart is initially at rest on top of a 50 cm ramp, as shown. Note that the wheels are very light and the axle has no friction in it. You push the cart as it moves through a distance of 20 cm with a constant force of 10N in a direction oriented 20 degrees below horizontal. After you stop pushing on the cart, it encounters a ramp, and rolls down to collide with a block. Use the coordinate system that the +x direction points to the right. +x 50cm Ice here, no friction Friction present here, y unknown (a) Find the speed of the lab cart at the bottom of the ramp, but before the collision. (b) When the lab cart is on the ice, it collides with a 1 kg block that is initially at rest. After the collision, the 1 kg block has a speed of 1.5 m/s. Find the velocity vector of the 200 g cart after the collision (e) After the collision, the block slides off of the ice, and slides an additional 50cm before coming to rest. Find the value of the coefficient of kinetic friction between the block and the ground.

Answer 1

(a)

Work done by external constant force on the cart = 10 cos(20) * 0.2 m = 1.88 J

Work done by gravity = mgh = 0.2 *9.8*0.5 = 0.98 J

Net work = change in kinetic energy

1/2 *0.2*v^2 = 1.88+0.98

v = 5.347 m/s

(b)

Conservation of momentum

0.2 * 5.347 = 0.2 v + 1*1.5

v = -2.1527 m/s

speed = 2.1527 m/s to the left

(c) Work dne by friction on the block = -umgd

d = 0.5 m

1/2 m v^2 = ukmgd

uk = 0.5 * 1.5*1.5/9.8*0.5

uk = 0.2296 (coefficient of kientic friction)