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Question:

A block of mass m is pulled along a horizontal surface by applying a force at an angle θ with the horizontal. If the block travels with a uniform velocity and has a displacement d and the coefficient of friction is μ, then the work done by the applied force is:

μmgd sinθ cosθ + μsinθ

μmgd cosθ cosθ - μsinθ

μmgd cosθ + μsinθ

μmgd cosθ cosθ + μsinθ

Solution:

Let the force applied on the block be F,
The surface applies a frictional force on the block in the backward direction.
Vertical direction : N + Fsinθ = mg
N = mg - Fsinθ (1)
Horizontal direction: As the block moves with a constant velocity, so Fcosθ is balanced by f
∴ Fcosθ = f
Fcosθ = μN
Fcosθ = μ(mg - Fsinθ)
⇒ F = μmgcosθ + μsinθ
Work done by the applied force
WF = →F.→S
WF = Fdcosθ
⇒ WF = μmgd cosθ cosθ + μsinθ