A block with mass m is being pushed by a constant force F that makes an angle of $\theta$ with the horizontal as shown below.The block is moving with constant velocity on a level surface.The coefficient of kinetic friction between the block and the surface is µ_k.Which one of the following equations is correct for the magnitude of F?

Question

Quizplus · Accepted Answer

Since the block is moving with constant velocity, we know that the net force on the block is zero. We can resolve the force F into its x and y components, and write the equations of force balance in each direction. 
In the x-direction, we have: 
Fcosθ = f 
where f is the force of kinetic friction, given by f = μkN = μkmg, where N=mg is the normal force. 
In the y-direction, we have: 
Fsinθ = N = mg 
Solving for F from these two equations, we get: 
F = mg/(sinθ + μkcosθ) 
which matches option B.

A Block with Mass M Is Being Pushed by a Constant