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22:34:49 11-14-2005 22:34:49 ** When force is parallel to displacement, work is force * distance, so the proportionality with distance follows immediately.
The force comes from the gravitational interaction of the masses of the washers with the Earth's gravitational field. More washers imply more force, and the force is proportional to the number of washers. **......!!!!!!!!...................................
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22:35:18 11-14-2005 22:35:18 Why is this consistent with the idea that the work done on a given cart on an incline is proportional to the vertical distance through which the cart is raised?
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22:36:17 11-14-2005 22:36:17 ** The steeper the incline the more washers are required to pull the cart up the incline. In fact for small inclines and correcting for friction the number of washer is proportional to the slope of the incline. The vertical distance, being the rise through which the cart is raised, is also proportional to the slope of the incline.
So for a given cart the number of washers is proportional to the incline. Since work is proportional to the number of washers we conclude the work is proportional to the vertical distance through which the cart is raised. **......!!!!!!!!...................................
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22:37:06 11-14-2005 22:37:06 How does the work done against friction of the cart-incline-pulley-washer system compare with the work done by gravity on the washers and the work done to raise the cart?
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22:38:01 11-14-2005 22:38:01 ** The work against friction plus the work done to raise the cart are all provided by the gravitational force acting on the descending weight. **
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22:38:15 11-14-2005 22:38:15 How do we establish, using a cart-pulley-washer system on a constant-velocity incline, that the acceleration of cart is proportional to the net force on the cart?
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22:39:13 11-14-2005 22:39:13 ** STUDENT ANSWER: In order to keep the velocity constant the amount of force should be constant but it must overcome the effects of gravity and therefore it must increase at a constant rate . The increase in the ramp slope will correspond to the increase in the force.
INSTRUCTOR RESPONSE: Good start. This is half of it. This indicates how the force on the cart is proportional to acceleration. The other half is that the acceleration of the cart is proportional to the effective slope. Since the force and the acceleration of the cart are both proportional to the effective slope, they are proportional to each other. **......!!!!!!!!...................................
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