A 0.16 kg baseball moving at +21.20 m/s is slowed to a stop by a catcher who exerts a constant force of -355 N.

Question

a.) How long does it take this force to stop the ball?

b.) How far does the ball travel before stopping?

Answer 1

The Impulse-Momentum Theorem says that Impulse is equal to the change in momentum:

I = P₂ - P₁

Also Impulse equals force multiplied by time:

I = Ft therefore:

Ft = P₂ - P₁ or t = (P₂ - P₁)/F

P₂ = mv₂ = 0.16(0) = 0

P₁ = mv₁ = 0.16(21,20) = 3.392 so:

t = (P₂ - P₁)/F

t = (0 - 3.392)/(-355) = 0.0096 seconds

All the kinetic energy (E_k) that the ball had was lost to work in the catchers mitt.

E_k1 = E_k2 + W or W = E_k1 - E_k2

E_k1 = (1/2)mv₁² = (1/2)(0.16)(21.20)² = 35.9552 j

E_k1 = (1/2)mv₁² = (1/2)(0.16)(0)² = 0 j

So W = 35.9552 - 0 = 35.9552 j

And W = Fd so d = W/F = 35.9552/355 = 0.101 meters