Using a mallet, you strike a ball of mass 0.50 kg that is initially at rest. The force F on the ball as a function of time is plotted in the figure. At t = 2.0 ms, the speed of the ball is
A) 10 m/s
B) 8.0 m/s
C) 6.0 m/s
D) 4.0 m/s
E) 2.0 m/s

Question

Using a mallet, you strike a ball of mass 0.50 kg that is initially at rest. The force F on the ball as a function of time is plotted in the figure. At t = 2.0 ms, the speed of the ball is
A) 10 m/s 
B) 8.0 m/s 
C) 6.0 m/s 
D) 4.0 m/s 
E) 2.0 m/s

Quizplus · Accepted Answer

From the force-time graph, we can see that the time interval during which the force is being applied is from 0 ms to 2 ms. During this time, the impulse (change in momentum) of the ball is given by the area under the force-time graph:

Impulse = force x time = (0.20 N) x (2.0 × 10^-3 s) = 4.0 × 10^-4 Ns

By the impulse-momentum theorem, this impulse is equal to the change in the ball's momentum:

p = mv

Δp = p - p0 = mv - 0

Δp = mv

Δp = 4.0 × 10^-4 Ns

Therefore, the final velocity of the ball is:

v = Δp/m

v = (4.0 × 10^-4 Ns)/(0.50 kg)

v = 0.8 m/s

Thus, the speed of the ball at t = 2.0 ms is 0.8 m/s, which is closest to 4.0 m/s (choice D).

Using a Mallet, You Strike a Ball of Mass 0