An incline makes an angle of 25.7 o with the horizontal. A 6.81 kg block is give

Question

An incline makes an angle of 25.7o with the horizontal. A 6.81 kg block is given a push up this incline and released. It starts at the bottom with initial speed 6.56 m/s, travels up the incline, stops, and slides back to the bottom at final speed 4.77 m/s. Using energy considerations, find:

a) the energy used to overcome friction traveling up and down the incline.
1 ?J

b) the distance the block traveled up along the incline before coming momentarily to rest.
2 ?m

c) The coefficient of kinetic friction between the block and the incline.
3???????

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Explanation / Answer

energy used to overcome friction = change in k.e

= 1/2*6.81* (6.56^2 -4.77^2)

= 69.05 J

b. work by friction in going upward = 69.05/2

= 34.53 J

by energy conservation,

34.53 + mgsin25.7*s = 1/2*6.81*6.56^2

s = 3.869 m

c. work done by friction in going up = mgcos25.7 *3.869

34.53 = mgcos25.7 *3.869

= 0.148

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