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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 鈥渨rong鈥 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鈥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

Expert verified
  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

01

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.
02

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.

03

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鈥檝e 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.

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Most popular questions from this chapter

You observe three carts moving to the left. Cart A moves to the left at nearly constant speed. Cart B moves to the left, gradually speeding up. Cart C moves to the left, gradually slowing down. Which cart or carts, if any, experience a net force to the left?

You observe three carts moving to the left. Cart A moves to the left at nearly constant speed. Cart B moves to the left, gradually speeding up. Cart C moves to the left, gradually slowing down. Which cart or carts, if any, experience a net force to the left?

A playground ride consists of a disk of mass M=43kgand radius R=1.7mmounted on a low-friction axle (Figure 11.94). A child of mass m=25kgruns at speed v=2.3m/son a line tangential to the disk and jumps onto the outer edge of the disk.

(a.) If the disk was initially at rest, now how fast is it rotating? (b) What is the change in the kinetic energy of the child plus the disk? (c) where has most of this kinetic energy gone? (d) Calculate the change in linear momentum of the system consisting of the child plus the disk (but not including the axle), from just before to just after impact. What caused this change in the linear momentum? (e) The child on the disk walks inward on the disk and ends up standing at a new location a distance from the axle. Now what is the angular speed? (f) What is the change in the kinetic energy of the child plus the disk, from the beginning to the end of the walk on the disk? (g) What was the source of this increased kinetic energy?

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 鈥渨rong鈥 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鈥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.

For each graph of vx vs. t numbered 1-6 in Figure, choose the letter (a-i) corresponding to the appropriate description of motion of a fan cart moving along a track. Not all descriptions will be used. Assume the usual coordinate system (+x to the right, +y up. +z out of the page).

(a) A cart moves to the left, gradually slowing down.

(b) A cart moves to the right, gradually speeding up.

(c) A cart moves to the left at a constant speed.

(d) A cart moves to the left, gradually slowing down, stops, and moves to the right, speeding up.

(e) A cart remains stationary and does not move.

(f) A cart moves to the right, gradually slowing down,

(g) A cart moves to the right. gradually slowing down, stops, and moves to the left, speeding up.

(h) A cart moves to the left, gradually speeding up.

(i) A cart moves to the right at a constant speed.

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