The answer to the question will be 108.76 N.
CALCULATION:
The mass of the ball is given as m = 0.17 kg.
The initial speed of the ball [ u ] = 37.9 m/s.
The momentum of a body is defined as the product of its mass with velocity.
Mathematically momentum P = m × v.
Here, v is the velocity of the body.
Hence, the initial momentum of the ball is calculated as -
P = m × u
= 0.17 kg × 37.9 m/s
= 6.443 kg m/s
The ball returns after striking the bat with a speed of 20.0 m/s.
Hence, the final velocity of the ball [ v ] = 20.0 m/s
The final momentum of the ball is calculated as -
P' = m × v
= 0.17 kg × (-20.0 m/s)
= -3.4 kg m/s.
Here, the negative sign used in the velocity is due to the fact that final velocity is opposite to the initial velocity.
Hence, the change in momentum dP = P' - P
= -3.4 - 6.443 kg m /s
= -9.843 kg m/s
The time of contact of the bat with ball [ dt ] = 90.5 milliseconds.
= [tex]90.5\times 10^-3\ seconds[/tex]
From Newton's second law of motion, we know that rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.
Mathematically [tex]F\ =\ \frac{dP}{dt}[/tex]
[tex]=\ \frac{-9.843}{90.5\times 10^-3}\ N[/tex]
[tex]=\ -0.10876\times 10^3\ N[/tex]
[tex]=\ -108.76\ N[/tex]
Taking only magnitude of the force, the force applied by the bat to the ball is 105.78 N.
