A pitcher on the UMassD baseball team throws a 5 oz baseball with a diameter of

ID: 1860339 • Letter: A

Question

A pitcher on the UMassD baseball team throws a 5 oz baseball with a diameter of 3 inches at a speed of 180 miles per hour at a 2 pound catchers mitt fastened to a 100 pound block of wood. The mitt is fastened by nails directly to the block of wood. The block is sitting on smooth vinyl surface with an 0.2 coefficient of kinetic friction. The ball hits the mitt and is retained in the mitt.

a. How far will the mitt and wood block slide before coming to a stop?

b. What is the velocity of the ball, mitt, and wood block at ther instant the ball is

Explanation / Answer

The problem is about the conservation of momentum.

The initial momentum of the ball = velocity * mass = (5* 0.0625) * ( 180 * 1.467) pound. ft /s = 82 . 52 p. ft/s

Suppose when the ball is catched , the wood block , the mitt and the mitt move togrhter with a velocity , 'v'.

so final momentum = (100 + 0.0625*5 + 2) * v = 102. 3125 v pounds ft /s

According to conservation of momentum.

INtial momentum = final momentum

so, 82 . 52 = 102 .3125 v

so, v = 0.807 ft /s = 0.55 miles per hour . ----- answer (b)

The friction force acting on the wood block , the mitt and the mitt = 0.2 * (102.3125) * 32.174

the deceleration caused by this force = force/ mass = 0.2 * 32.174 = 6.435 ft/s^2

Using eqautions of motion,

0.807 ^2 - 0 = 2 *(6.435) * d , where d = distance slid by the wood block ,

d = 0.051 ft ----- answer (a)

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A pitcher on the UMassD baseball team throws a 5 oz baseball with a diameter of

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A pitcher on the UMassD baseball team throws a 5 oz baseball with a diameter of

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