finding magnitude of the frictional force

Question

A block of mass m is pulled by force F (originating from the top left corner of the block) in an upward direction with *angle θ above the horizontal, across a rough surface (coefficient kinetic friction is μ_k) at a constant velocity. The magnitude of the frictional force is:

 

* angle θ formed by force vector and (for visualizing's sake) a horizontal line that is a continuation of the top of the block.

 

Thank you

Answer 1

 

Horizontal direction:

 

f = magnitude of friction

N = normal force

 

No acceleration in horizontal direction ⇒

 

Fcosθ = f = μ_kN

 

No acceleration in vertical direction ⇒

 

Fsinθ + N = mg

 

N = mg - Fsinθ

 

Based on the wording of this problem, f must satisfy both of these equations:

 

f = μ_k(mg - Fsinθ)

f = Fcosθ