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Distance the block slide up inclined ramp before it comes to rest

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A block of mass 2.0 kg resting on a horizontal frictionless surface is initially held against a spring of constant 5200 N/m that is compressed by 13 cm from its normal length. After the block is released, it slides along the frictionless surface until it encounters a ramp that makes an angle 22 degrees to the horizontal. The coefficient of kinetic friction between the block and the ramp is 0.15 .

a. What distance will the block slide up the ramp before it comes to rest?
b. What is the potential energy of the block when it comes to rest on the incline?

Please refer to the attachment for layout of ramp, block and spring.

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Solution Summary

The distance the block slides up inclined ramp before it comes to rest is determined.

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(a) To do this problem, we have to consider the conservation of energy, where

Estart - Elost = Efinal

Consider the start energy, the only energy at this point is the energy in the spring, that is given by the formula

Estart=1/2kx^2 where k is the spring constant and x is the distance of which it's compressed.
In this problem, k = 5200 N/m and x = 13 cm = 0.13 m

Now, consider the final energy. When we release the block, it travels at a frictionless surface until the incline. During this period, no energy is lost because there is no friction on the ...

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