Question

Consider the three experiments described in Problem 30. Figure 2.58 displays four graphs of F_{net, x}, the x component of the net force acting on the cart, vs. time. The graphs start when the cart is at rest, and end when the cart is again at rest. Match the experiment with the graph

Short answer

• The graph when the fan is off 6.

• The graph when the fan is moving forward 7.
• The graph when the fan is moving backward 5.

Step-by-step solution

Identification of given data

• The graph starts when the cart is at rest and ends when the cart is again at rest

Concept of change of momentum

The difference between final and beginning momentum levels is called the change in momentum.The change in momentum is equal to the impulse.

The change of momentum can be given as,

$F_{net=∆p∆t}$

Evaluation of graph between force and time

The area under force and time gives the change in momentum.

The first experiment is the initial state of the cart. Give it a little nudge, and it coasts for a long time in the +x direction down the track, eventually stopping.This situation can be depicted using graph 6.

In the second experiment the fan is turned on but the cart is held stationary and in some while when the hold is removed the cart starts to move in the +x direction the cart is stopped suddenly and it eventually comes to rest. This situation can be depicted using graph 7.

In the third experiment,the fan is facing the wrong direction initially the cart was held at rest. A brief push was given and it starts moving in +x direction, it slows down and returns to the starting position where the cart is held and stopped. The situation can be depicted using graph 5.

Thus, the graphsare being identified according to the experiment.