In a grocery store, you push a 12.3 kg shopping cart with a force of 10.1 N. If

Question

In a grocery store, you push a 12.3 kg shopping cart with a force of 10.1 N. If the cart starts at rest, how far does it move in 2.50 s? A 0.53 kg billiard ball initially at rest is given a speed of 12 m/s during a time interval of 4.0 ms. What average force acted on the ball during that time interval? In baseball, a pitcher can accelerate a 0.15 kg ball from rest to 98 mph in a distance of 1.7 m. What is the average force exerted on the ball during the pitch? If the mass of the ball in increased, does the force required of the pitcher increased, decreased or unchanged? Explain.

Explanation / Answer

1.

acceleration a = F/m = 10.1/12.3 = 0.82 m/s^2

from s = ut + 1/2 * a *t^2

s = 0 + 1/2 * 0.82 * 2.5^2

s = 2.56 m

2.

from impulse momentum theorem

F * t = m (v2 - v1)

F * 0.004 = 0.53 * 12

F = 1590 N

3.

u = 0

v = 98 mph = 43.81 m/s

s = 1.7 m

from v^2 - u^2 = 2*a*s

43.81^2 = 2 * a * 1.7

a = 564.5 m/s^2

a) F = m * a = 0.15 * 564.5 = 84.67 N

b) if mass increases then force also increases because

because F = m*a

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