What force would you have to exert on a 324-N trunk up a 21.0° inclined plane so that it would slide down the plane with a constant velocity? What would be the direction of the force? (The coefficient of friction between the plane and the trunk is 0.326.)
Thank you so much!
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For it to slide with a constant velocity means that the forces along the ramp must sum to zero.
Along the ramp you have friction (acting up)
Force of you F (acting Up)
Component of weight (m*g*sin(theta)) acting down.
Perpendicular to the ramp You have the Normal and component of weight (m*g*cos(theta))
So N= m*g*cos(theta)
The frictional force Ff = mu*N = mu*m*g*cos(theta)
So F + mu*m*g*cos(theta) - m*g*sin(theta) = 0 If F is + then we were pushing up if its negative we were pushing down
So F = m*g*(sin(theta) - mu*cos(theta)) = 324*(sin(21) - .326*cos(21)) = 17.5N
Up the ramp