A man wants to push a package of shingles of total mass 36 kg up a roof being bu

Question

A man wants to push a package of shingles of total mass 36 kg up a roof being built at an angle of 35o to the horizontal. The coefficient of kinetic friction between the package and the roofing paper already in place is 0.30. How much force does the man have to exert on the package directly along the slope of the roof to cause the package to accelerate at 0.1 m/s2? (b) What is the minimum coefficient of static friction needed so that the package will not slide when it is left at rest on the roof?

Explanation / Answer

Here , let the friction force acting is f ,

Now,

f = u * N

f = u * mg * cos(theta)

f = 0.30 * 36 * 9.8 * cos(35)

f = 86.7 N

Now, Using second law of motion ,

Fnet = m* a

F - mg* sin(theta) - f = m * a

F - 36 * 9.8 * sin(35) - 86.7 = 36 * 0.1

F = 292.7 N

the force applied on the package is 292.7 N

B)

for the package not to slip ,

f = mg * sin(theta)

u * mg * cos(theta) = mg * sin(theta)

u = tan(theta)

theta = 35 degree

u = 0.7

the minimum coefficient of static friction needed so that the package will not slide when it is left at rest on the roof is 0.7

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