Physics Questions on ENERGY? Please help?

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oceanblue

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A horizontal spring with spring constant 100N/m is compressed 20cm and used to launch a 2.5 kg box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. Use work and energy to find how far the box slides across the rough surface before stopping.

An 8.0kg crate is pulled 5.0 m up a 30 degrees incline by a rope, angled 18 degrees above the incline. The tension in the rope is 120N and the crate's coefficient of kinetic friction on the incline is .25.
A) how much work is done by tension, by gravity, and by the normal force
B) what is the increase in thermal energy of the crate and incline?
 
Energy imparted to the box by the spring when the box is released
= (1/2) kx^2
= (1/2) 100 * (0.2)^2
= 2 J.
If d = distance traveled by the box before stopping, energy of the box is utilized in doing work against the frictional force
=> F * d = 2
=> μmg * d = 2
=> d
= 2/μmg
= 2 / [(0.15) * (2.5) * (9.8)]
= 0.544 m
= 54.4 cm.
 
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