*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 …

**Know better? Leave your own answer in the comments!**