You are trying to move a chair of mass 29.0 kg by pushing it horizontally along

Question

You are trying to move a chair of mass 29.0 kg by pushing it horizontally along the floor, but it is not sliding very easily. The coefficient of kinetic friction between the chair and the floor is 0.700. (a) If you push the chair with a horizontal force, what is the magnitude of the minimum force that will keep the chair moving at a constant velocity? (b) If the force on the chair is directed 30.0 degrees up from the horizontal, what is the magnitude of the minimum force that will keep the chair moving at a constant velocity? (c) What if the angle is 75.0 degrees from the horizontal?

Explanation / Answer

a ) minimum force will be equal to kinetic friction force as this is the only retarding force acting along horizontal direction
so ,f = N   

= 0.7 * 29 * 9.8 [here N = mg]

= 198.94 N

b) for moving with constant velocity: net force along horizonal direction = 0

Fcos30 - N = 0

F = N/cos30   

= 0.7 * (mg - Fsin30) /cos30 where N = mg -Fsin30

= 163.59 N

c ) when angle = 75 degree

Fcos75 - N = 0

F = N/cos75   

= 0.7 * (mg - Fsin75) /cos75 where N = mg -Fsin75

= 212 N

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