A block of mass m begins at rest at the top of a ramp at elevation h with whatev

Question

A block of mass m begins at rest at the top of a ramp at elevation h with whatever PE is associated with that height.

The block slides down the ramp over a distance d until it reaches the bottom of the ramp. How much of its original total energy (in J) survives as KE when it reaches the ground?

(In other words, the acceleration is not zero like it was in lab and friction does not remove 100% of the original PE. How much of that original energy is left over after the friction does work to remove some?)

m = 1.8 kg
h = 1.6 m
d = 5 m
= 0.3
= 36.87°

I know the answer is 7.06, but I'm not sure how to solve the problem. I worked it out and got 49.

Explanation / Answer

given,

m = 1.8 kg
h = 1.6 m
d = 5 m
= 0.3
= 36.87°

frictional force = mg * cos()

frictional force = 0.3 * 1.8 * g * cos(36.87)

work done by the friction = frictional force * distance

work done by the friction = 0.3 * 1.8 * g * cos(36.87) * 5

initial potential energy = mgh

initial potential energy = 1.8 * 9.8 * 1.6

original energy left = initial potential energy - work done by the friction

original energy left = 1.8 * 9.8 * 1.6 - 0.3 * 1.8 * g * cos(36.87) * 5

original energy left = 7.056 J

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