Energy loss and inclined planes

AI Thread Summary
Energy loss occurs when pushing the trolley up the inclined plane due to the work done against the gravitational component acting down the slope. Despite the absence of friction, the weight of the trolley has a component that opposes the upward motion, requiring additional force to overcome it. The applied force of 100N results in a work output of 3500J, while the potential energy gained is only 1960J, indicating that not all the work contributes to potential energy. The difference represents energy lost, which can be attributed to the gravitational force component acting along the incline. Understanding these energy dynamics is crucial for analyzing inclined plane mechanics.
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Homework Statement



A trolley is of mass 20kg is pushed 35 metres up an inclined plane (to a height of 10m above ground level). The inclined plane is at arcsin(2/7) to the horizontal. A 100N force pushes the trolley to the top of the plane, the force being parallel to the inclined plane. The work done by the force in pushing the trolley to this point is 3500J and the potential energy 35m up the slope is 1960J. No friction is present, hence the slope is smooth. Why is energy lost in pushing the trolley up the incline?

Homework Equations


Ok, well obviously 44% of the energy is wasted, but I'm truly stuck as to why it is if there is no resistance force acting? Would it be the component of the weight which opposes the motion? Or that too much force is applied to move it? Any advice here would be much appreciated, I just simply don't know mathematically how to prove this loss and why? Thanks
 
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