Question

A baseball pitcher in good form can throw a baseball that attains a speed of 97.0 mi/h in a distance of 1.30 m. Assume that the ball starts from rest and its mass is 0.150 kg. (a) Determine the magnitude of the average force exerted on the ball. (b) How would the pitcher need to alter the required force to reach the same speed if the mass of the ball is decreased. The pitcher would need to increase the force. The pitcher would need to decrease the force. The pitcher would not need to change the force.

Answer 1

(a) 108.47 N

(b) increased

Step-by-step explanation:

u = 0

v = 97 mi/h = 43.36 m/s

s = 1.30 m

m = 0.150 kg

(a) let a be the acceleration

Us third equation of motion

v^2 = u^2 + 2 a s

43.36 x 43.36 = 0 + 2 x a x 1.30

a = 723.11 m/s^2

Force = mass x acceleration = 0.150 x 723.11 = 108.47 N

Thus, the force exerted on the ball is 108.47 N.

(b) as the mass is decreased and speed be same so force should be increased.

Answer 2

Step-by-step explanation:

It is given that,

Initial velocity of the baseball, u = 0

Final velocity of the baseball, v = 97 mi/h = 43.36 m/s

Mass of baseball, m = 0.15 kg

Distance, s = 1.3 m

(a) Let a be the acceleration of the baseball. Use third equation of motion as :

`v^2-u^2=2as`

`a=(v^2)/(2s)`

`a=(43.36^2)/(2* 1.3)`

`a=723.11\ m/s^2`

Force is given by :

F = m a

`F=0.15* 723.11=108.46\ N`

So, 108.46 N force is exerted on the ball.

(b) The pitcher would need to increase the force so as to alter the required force to reach the same speed if the mass of the ball is decreased.