A pitcher throws a fastball to the right with a speed of 45 m/s towards home pla

Question

A pitcher throws a fastball to the right with a speed of 45 m/s towards home plate. The batter swings his bat (m_bat = 0.94 kg) with a speed of 47 m/s (to the left) and hits the ball (m_ball = 0.145 kg) to the left with a speed of 50 m/s. The time of contact between the bat and the ball is 0.7 milliseconds (0.0007s). (See the Impulse Example Problem videos for the method to use on this problem what is the change in momentum of the ball in kg^*m/s? What is the average force in N exerted on the ball by the bat? What is the acceleration of the ball in m/s^2? What is the velocity in m/s of the bat immediately after the collision? What is the direction of the velocity of the bat immediately after the Collision? How many times larger or smaller is the acceleration of the ball than the gravitational acceleration, g? What is the kinetic energy of the system immediately before the bat hits the ball? What is the kinetic energy of the system immediately after the bat hits the ball? Was kinetic energy conserved in the collision? Is this an elastic or inelastic collision?

Explanation / Answer

Given

initially, Ball

mass m = 0.145 kg, velocity to the right u1 = + 45 m/s

bat

mass m = 0.94 kg, speed u2 = - 47 m/s to the left

finally the ball moving with velocity to left v1 = - 50 m/s

time in which the ball and bar are in contact is t = 0.7*10^-3 s

6A

   change in momentum of the ball is P = m(v1-u1) = 0.145(-50-45)= - 13.775 kg m/s

6B

  
   Average force by bat on ball is F*t = change in momentum

                   F = chagne in momentum /t

                   = 13.775 /0.0007 N

                   = 19678.5715 N

6C
   Accelerationof the ball is a = F/m = 19678.5715/0.145 m/s2 = 135714.29 m/s2

6D
   velocity of the bat immediately after the collition is , newton's third law for every action and force there is equal and oppisite reaction

   so the forceis -19678.5715 N

6E
   the dierection is to the right

6F
acceleration of ball is a = 135714.29 m/s2 , g = 9.8 m/s2 ==> a = 13848.4*g6G

6G kinetic energy of system before collision is

   k.e = 0.5(0.145*45^2+0.94(-47)^2) J = 1185.0425 J
  
     
  

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