Practice Test Problem 13.1 During a baseball game, a batter approaches the plate

Question

Practice Test Problem 13.1 During a baseball game, a batter approaches the plate wearing rollerblades. Why is he wearing rollerblades you might ask? Simple, because we have not begun our discussion of friction! As such, assume the rollerblades can roll on the field without friction. The pitcher hurtles the ball in the direction of the batter at a speed of 85 miles per hour. The batter swings and makes contact with the ball. The kinetic energy of the ball-batter system is increased by 50%. It is important to know that the regulation weight of a baseball is 5oz. Our batter weighs in at 1951bs, including his bat. Even though we know he is going to swing the bat, assume the initial velocity of the batter is 0. (a)[4 pt(s)____]What is the kinetic energy of the ball-batter system before the collision? (b)[2 pt(s)_____]What is the momentum of the system in the center of mass frame? (c)[6 pt(s)_______]What is the relative velocity of the system immediately after the collision? (d)[4 pt(s)____]What are the velocities of the ball and batter immediately after the collision?

Explanation / Answer

mass of ball m1=5oz

mass of batter m2=195lbs=3120 oz

velocity of ball u1=85 miles per hour

velocity of batter=0

(a) before colllision kinetic energy of system= 1/2(m1u12 + m2u22) =18062.5 oz(miles perhour)2

(b) momentum =m1u1 + m2u2 =425oz miles/hour

(c) relative velocity

ke is increased by 50% so final kinetic energy =27093 oz(miles perhour)2

relative velocity= 1/2 (m1 +m2) v2=27093

=4.16 miles/ hour

(d) velocity of ball and batter immediately after collision=(m1-em2)u1 + (m2 +em2)u2/ m1 +m2 where e= coeficient of restitution=0.55

=-0.54 mph

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