A 9.00 meter long ramp is inclined at an angle of 6 degrees above horizontal. A
ID: 1410342 • Letter: A
Question
A 9.00 meter long ramp is inclined at an angle of 6 degrees above horizontal. A 7 kg box is given an intial push at the bottom of the ramp so that when it gets to the top it stops. The coefficient of kinetic friction between the box and the ramp is .230 a) what is the initial speed of the box just as it is pushed b) Suppose the box slides back down the ramp, what is the maximum value of its coefficient of static friction? Does that value make sense? Why or why not? (according to my professor, the answer to part A is 7.68 m/s) Please provide clear and complete solution and diagram to receive a rate. Thank you.
Explanation / Answer
A) friction force, f = uk N = uk m g cos6
Using Work-energy theorem,
Work done by gravity + work done by friction = change in KE
- m g L sin6 - uk m g L cos6 = 0 - m v^2 / 2
v^2 = (2 x 9.8 x 9 x sin6) + (2 x 0.230 x 9.8 x 9 x cos6)
v = 7.67 m/s .........And
b) for block to coming down,
net force along the incline,
Fnet = mgsin@ - f = mgsin@ - us mg cos@
Fnet = mg(sin@ - uscos@) = 0
us = tan@ = tan6 = 0.105
us should greater than kinetic friction coefficient(uk).
so this value does not make sense.
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