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Force: Mption on an incline with friction.

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Problem: The incline is 30 degrees with a kinetic friction coefficient of 0.20. Initially the system is not moving. It is given a push uphill at 1m/s and there is a total distance of 1.5m from initial point to the end of the incline.
a. Minimum coefficient of friction to keep the system from moving initially
b. When the system I set into motion, what is the magnitude.
c. How long will it take the block to reach the end of the incline
d. What is the acceleration of the block if pushed downhill at 5m/sec
e. How far would it slide until coming to rest given details from question (d).

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Motion of a block on an incline with friction is discussed and the related parts are solved.

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Problem: The incline is 30 degrees with a kinetic friction coefficient of 0.20. Initially the system is not moving. It is given a push uphill at 1m/s and there is a total distance of 1.5m from initial point to the end of the incline.
a. Minimum coefficient of friction to keep the system from moving initially

Let the mass of the system be m then its weight is mg. Component of the weight perpendicular to the incline will be mg cos  and parallel to the incline will be mg sin .
The normal force of the incline on the system is given by
N = mg cos 
The limiting friction force on the system will be
Ff = N =  mg cos 
If the system is just not moving the friction force on it is balancing the component of the weight and ...

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