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    A Cart on an Inclined Plane

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    A cart is on an inclined plane. If it is given a push up the ramp and released, then it moves up, reverses direction, and comes back down again. How will the kinetic energy change? How will the gravitational potential energy change? How will the mechanical energy change?

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    Solution Preview

    Hi there, and thank you for posting your question to Branmass.

    Let's differentiate between three different points along the path.
    1. Initial position: The cart is given a push.
    2. Intermediate position: The car stops moving momentarily and starts sliding down the incline.
    3. Final position, the car is back at the initial position.

    First of all, the law of conservation of energy requires that the total mechanical energy of the system remains constant throughout the process, unless some external forces are applied (gravity does not count - the work of this force is the potential energy).
    Only a type of energy can change. In this case, it can either be kinetic or potential or a combination of both. The sum of all the types of ...

    Solution Summary

    The solution answers how a cart on an inclined plane has a change in its kinetic energy, mechanical energy and gravitational potential energy. Initial and final velocities are obtained to establish maximal height as a function of initial velocity, in order to obtain these changes.