A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the net work done on the block is 247 J. What angle does the rope make with the horizontal?

The rope makes an angle of 28° with the horizontal.

Work is the product of force and displacement. It is given by:

Work = Force along direction of displacement * displacement

If the force is acting at an angle, the work done is:

Work (W) = (Fcosθ) * s

F is the force, s is the displacement and θ is the angle of force.

Given that W = 247J, F = 40N, s = 7 m, hence:

247 = 40cosθ * 7

cosθ = 0.88

θ = 28°

The rope makes an angle of 28° with the horizontal.

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Explanation:

ΣF = ma

Also, work done is given by

W=F.d

Then, applying scalar product

W=FdCos θ

Given that W=247J, d=7m, and F=T=40N

Then,

W=FdCos θ

247=40×7Cos θ

Then,

Cos θ=0.8821

θ=arccos(0.8821 )

θ=28.1°

The angle the rope make with the horizontal is 28.1°

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