The graph in the figure shows the x component F of the net force that acts for 10 s on a 100-kg crate.What is the change in the momentum of the crate during the 10 s that this force acts?
A)-100 kg ∙ m/s
B)-25 kg ∙ m/s
C)75 kg ∙ m/s
D)-75 kg ∙ m/s
E)25 kg ∙ m/s

Question

The graph in the figure shows the x component F of the net force that acts for 10 s on a 100-kg crate.What is the change in the momentum of the crate during the 10 s that this force acts? 
A)-100 kg ∙ m/s 
B)-25 kg ∙ m/s 
C)75 kg ∙ m/s 
D)-75 kg ∙ m/s 
E)25 kg ∙ m/s

Quizplus · Accepted Answer

The change in momentum of an object is given by the formula:

Δp = FΔt

where F is the net force acting on the object and Δt is the time interval for which the force acts. In this case, we are given the x-component of the net force for 10 s. The area under the force vs. time curve gives us the impulse of the force, and therefore the change in momentum of the crate.

The area under the curve is negative, which means that the force is in the negative x-direction (to the left). Therefore, the change in momentum is also negative (to the left).

The area of the shaded region is:

A = (-1000 N)(10 s) = -10000 N·s

Since the mass of the crate is 100 kg, we can convert the area to a change in momentum:

Δp = A = -(10000 N·s) = -10000 kg·m/s

But since the change is in the negative x-direction, the answer is:

Answer: D
 The change in momentum is -7500 N·s, which is equivalent to -7500 kg·m/s in the negative x-direction.

The Graph in the Figure Shows the X Component F