Question

We can compare these two interactions on the basis of impulse (see above), but sometimes, we are more interested in the forces (human body can withstand very large amount of impulse, if it's delivered over a long time with small forces, but we cannot withstand very large forces lasting over more than a few milliseconds, delivering relatively small impulse). In order to estimate average force from impulse, we need the duration of interaction. Suppose that the contact of the bat with the baseball in (b) lasts for 0.7 milliseconds. What is the magnitude of the average force that the bat exerts on the baseball, for the duration of contact

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

 $I = 476 \ N \cdot s$

b

 $I_1 = 14.21 \ N\cdot s$

c

    $F = 20300 \ N$

Explanation:

Considering the first question

From the question we are told that

   The force produced is $F = 3400 \ N$

   The duration of the punch is  $t = 0.14 \ s$

Generally the impulse delivered is mathematically represented as

    $I = F * t$

=>    $I = 3400 * 0.14$

=>    $I = 476 \ N \cdot s$

Considering the second  question

   The approaching velocity of the ball is  $v_b = 45 \ m/s$

    The leaving  velocity of the ball is  $v_l = -53 \ m/s$

     The mass of the ball is  $m_b = 0.145 \ kg$

Generally the magnitude of the impulse delivered is mathematically represented as

     $I_1 = m* v_b - m * v_l$

=>     $I_1 = [0.145 * 45] - [0.145 * -53]$

=>     $I_1 = 14.21 \ N\cdot s$

Considering the third  question

     The  duration of the impact of the bat is  $t _1 = 0.7 \ ms = 0.7 *10^{-3} \ s$

      Generally the average force exerted by the bat is mathematically represented as  

       $F = \frac{I_1}{t_1}$

=>     $F = \frac{14.21 }{0.7 *10^{-3}}$

=>       $F = 20300 \ N$