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An illustration of the path independence of gravitational work.
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Drop
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Consider three ways to get a block from height hi down to height hf = 0: dropping the block straight down through the air (freefall), sliding the block down a frictionless ramp, or sliding the block along a frictionless track. The options are illustrated above.
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Assuming that the block starts from rest, what is the final speed of the block as it reaches the ground in each case?
Solution
We begin by solving all three problems using mechanical energy. We will then re-solve the first two cases using the equations of kinematics and dynamics to illustrate the agreement between the methods.
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Method 1
Method 1
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Block as plus the earth as a rigid body with infinite mass.
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In each case, there is a conservative gravitational interaction between the block and the earth which will provide a gravitational potential energy. In the final two cases (the ramp and the track) the block is also subject to a non-conservativenormal force from the surface upon which it travels. In each case, however, the normal force does no work, since it is always perpendicular to the direction of the block's travel (the block is always moving parallel to the surface and the normal force is, by definition, perpendicular to the surface). Thus, in all three cases, the non-conservative work is zero.
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Model:
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External influences from the earth (gravity) and for the block on the ramp, the ramp provides a normal force.
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One-Dimensional Motion with Constant Acceleration and .
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External influences from the earth (gravity) and for the block on the ramp, the ramp provides a normal force.
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One-Dimensional Kinematics with Constant Acceleration.
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Wiki Markup
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