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

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 the instant the ball is

Explanation / Answer

5 oz = 0.3125 lb

180 mi/hr = 264 ft/s

Initial KE = 1/2*mv^2 = 1/2*0.3125*264^2 = 10890 lb-ft^2/s^2

Friction force = 0.2*(100+2+0.3125)*32.2 = 658.8925 lb-ft/s^2

a)

Energy conservation gives, Initial KE = Work done by friciton

10890 = 658.8925*d

Distance d = 16.527 ft

b)

Momentum conservation:

Initial momentum = final momentum

0.3125*264 = (100+2+0.3125)*v

velocity v = 0.806 ft/s

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