Physics problem: energy conservation to find to find distance a block slides?

Question by A77Y: Physics problem: energy conservation to find to find distance a block slides?
An 8.78-kg block slides with an initial speed of 1.80m/s down a ramp inclined at an angle of 28.0° with the horizontal. The coefficient of kinetic friction between the block and the ramp is 0.77. Use energy conservation to find the distance the block slides before coming to rest.

Best answer:

Answer by jeffrey
Take zero gravitational potential energy GPE = 0 at the initial position …
… initial energy E₀ = ½ m v₀ ² … final energy E = – m g L sin 28° … where
L is the distance traveled along the ramp … but due to friction, energy is
removed … work done by friction W = – μ ( m g cos 28° ) L … negative
since friction is always opposite to the displacement … by conservation
of energy … E₀ = E + | W | … ½ m v₀ ² = – m g L sin 28° + μ ( m g cos 28° ) L
… ½ v₀ ² = – g L sin 28° + μ ( g cos 28° ) L …
… v₀ ² = [ μ cos 28° ‒ sin 28° ] g L
… L = v₀ ² / { g [ μ cos 28° ‒ sin 28° ] } …
Just substitute the given values to get the final answer …

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