Derivation of Work-Energy Theorem

AI Thread Summary
The discussion focuses on applying the Work-Energy Theorem to determine the stopping distance of an object on a rough surface. The equation derived is d = vo^2/(2μKg), where vo is the initial velocity, μ is the coefficient of friction, and Kg is the gravitational acceleration. Participants express confusion about how to begin the problem and suggest calculating the friction force as a starting point. It is emphasized that the work done by friction will equal the initial kinetic energy lost by the object. The conversation highlights the relationship between work, force, and energy in the context of motion on a rough surface.
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Homework Statement


Use the Work-Energy Theorem to show that an object with initial velocity vo will travel a distance d across a rough horizontal surface before stopping, where d = vo2/(2muKg).

Homework Equations


W = delta KE = mV^2/2


The Attempt at a Solution


To be honest, I have absolutely no idea where to even start. Any suggestions on how to start would be greatly appreciated.
 
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Can you compute what the friction force is?

The work done by this force is force * distance (if the force is always in the same direction as the movement, but that is the case here)

The object will lose all the kinetic energy is has at the start while it slows to a stop.
 
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