Question

A cart rolls with low friction on a track. A fan is mounted on the cart, and when the fan is turned on, there is a constant force acting on the cart. Three different experiments are performed:

(a) Fan off: The cart is originally at rest. You give it a brief push, and it coasts a long distance along the track in the +x direction, slowly coming to a stop.

(b) Fan forward: The fan is turned on, and you hold the cart stationary. You then take your hand away, and the cart moves forward, in the +x direction. After traveling a long distance along the track, you quickly stop and hold the cart.

(c) Fan backward: The fan is turned on facing the “wrong” way, and you hold the cart stationary. You give it a brief push, and the cart moves forward, in the +x direction, slowing down and then turning around, returning to the starting position, where you quickly stop and hold the cart. Figure 2.57 displays four graphs of px (numbered 1–4), the x component of momentum, 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 correct graph.

Short answer

1. The experiment showing fan off on the cart is
2. The experiment showing fan forward on the cart is
3. The experiment showing fan backwards on the cart is

Step-by-step solution

Identification of given data

• The graph will start when cart is at rest and will end when the cart is at rest.
• The cart moves in forward direction.

Concept of friction

It is friction that prevents the slide of two or more objects that have different coefficients of friction. Friction may come in several forms: When two solid surfaces come into contact, dry friction acts as a counterforce to the movement of the two surfaces relative to each other.

Evaluation of momentum-time graph

The slope of momentum-time graph will give acceleration.

In first experiment, the cart is originally at rest, a push is given to the cart, the cart moves in positive x direction and slowly it comes to rest, in this case the fan on cart is off. The second graph satisfies the condition here the graph starts with rest accelerates to a positive direction, reaches its maximum acceleration and after this point its acceleration starts to decrease slowly at slow rate and at last the cart stops.

In the second experiment, you’ve switched on the fan and are holding the cart still. When you remove your hand from the cart, it begins to travel ahead in a clockwise direction (+x). Once you've covered a significant distance, you swiftly halt and hold the cart. The fourth graph satisfies the above condition in which the cart is at still position,

reaches the maximum acceleration and then decreases slowly.

In the third experiment, you've had the fan facing the "wrong" direction and the cart isn't moving. Give it a fast push and the cart drives ahead, in the direction of the +x axis, before slowing down and finally turning around and returning towards the starting location. The first graph depicts the situation correctly here the cart starts from rest and accelerates with a positive acceleration then goes to rest and again takes the initial position.

Thus, the graphs are identified according to the situations given in the experiment.