Energy loss and inclined planes

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SUMMARY

The discussion centers on the energy loss experienced when pushing a 20kg trolley up a 35-meter inclined plane, which reaches a height of 10 meters. A force of 100N is applied parallel to the incline, resulting in 3500J of work done, while the potential energy gained is only 1960J. The discrepancy of 44% energy loss is attributed to the gravitational component acting against the trolley's motion, despite the absence of friction. Understanding the relationship between work, potential energy, and opposing forces is crucial in analyzing this scenario.

PREREQUISITES
  • Basic understanding of Newton's laws of motion
  • Familiarity with the concepts of work and energy
  • Knowledge of gravitational potential energy calculations
  • Understanding of inclined plane mechanics
NEXT STEPS
  • Study the principles of work-energy theorem in physics
  • Learn about the components of forces on inclined planes
  • Explore the concept of gravitational potential energy in different contexts
  • Investigate the effects of friction and resistance on energy loss
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone interested in understanding energy dynamics in inclined planes.

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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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