A 4.0kg object slides down a ramp of length 3.0m. The ramp is inclined 30º above

Question

A 4.0kg object slides down a ramp of length 3.0m. The ramp is inclined 30º above
horizontal and has a coefficient of kinetic friction 1 = 0.20. At the bottom of the
ramp, the object slides across a rough surface with 2 = 0.30 until it comes to rest.

a) What is the work done by friction while the object slides down the ramp?

b) What is the work done by gravity force while
the object slides down the ramp?

c) What is the kinetic energy of the object at the
bottom of the ramp?

d) What is the work done by friction across the
rough surface?
e) How far does the object slide along the rough
surface?

Explanation / Answer

a) work done by friction along ramp = mgcos(s) = 0.20(4)(9.8)cos 30 ( 3) =- 20.37 J apprx

b) height of ramp = 3sin30 = 2m

work done by gravity = mgh = 4(9.8)( 2) = 78.4 J

c) kinetic energy at bottom of ramp = 78.4 - 20.37 = 58.03 J

d) work don e bt=y friction on rough surface= 0 - 58.03 = -58.03 J

e) velocity of object before it encounters the rough surface= 0.5mv^2 = 58.03

v^2= 29.015

retardation = g = 0.30(9.8) = 2.94 m/s^2

using the kinematic equation,

v^2 - u^2 = 2as

0 - 29.015 = 2(2.94)S

s= 4.934 m apoprx

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