How does the position of a cart  affect the acccleration as it travels down the ramp?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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As a cart moves down a ramp, its acceleration is not altered by its position.

If the coefficient of friction C between the cart and the ramp is the same throughout, and the angle of elevation of the ramp is A, there is an acceleration due to gravity acting in the vertically downwards direction of 9.8 m/s^2. This can be divided into two components, one that is parallel to the ramp equal to 9.8*cos A and the other perpendicular to the ramp equal to 9.8*sin A. The net acceleration of the cart is 9.8*cos A - C*9.8*sin A along the ramp.

The difference between the height of cart at the top of the ramp and at the bottom is so small that the change in acceleration due to gravity is negligible and as a result it is safe to assume that the acceleration is not dependent on the position.

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