A box of mass 40 kg is dragged along the floor by a rope inclined at 60° to the horizontal. The frictional force between the box and the floor is 100N and the tension on the rope is 300N. How much work is done in dragging the box through a distance of 4m?

Physics
A box of mass 40 kg is dragged along the floor by a rope inclined at 60° to the horizontal. The frictional force between the box and the floor is 100N and the tension on the rope is 300N. How much work is done in dragging the box through a distance of 4m?

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Answer

600\ J

Step 1: Identify the work done by the tension force.
The work done by a force is given by
W=Fdcos⁡θW = F d \cos \theta
where FF is the magnitude of the force, dd is the displacement, and θ\theta is the angle between the force and the displacement.

Step 2: Substitute the given values.
Here, F=300 NF = 300\ \mathrm{N}, d=4 md = 4\ \mathrm{m}, and θ=60∘\theta = 60^\circ.
cos⁡60∘=0.5\cos 60^\circ = 0.5
W=(300 N)(4 m)(0.5)W = (300\ N)(4\ m)(0.5)

Step 3: Calculate the work.
W=300×4×0.5=600 JW = 300 \times 4 \times 0.5 = 600\ \mathrm{J}

The work done is 600 J\boxed{600\ J}.

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Identify the work done by the tension force. The work done by a force is given by W = F d where F is the magnitude of the force, d is the displacement, and is the angle between the force and the displacement.

A box of mass 40 kg is dragged along the floor by a rope inclined at 60° to the horizontal. The frictional force between the box and the floor is 100N and the tension on the rope is 300N. How much work is done in dragging the box through a distance of 4m?
Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

ScanSolve AI Answer
Step 1: Identify the work done by the tension force. The work done by a force is given by W = F d where F is the magnitude of the force, d is the displacement, and is the angle between the force and the displacement. Step 2: Substitute the given values. Here, F = 300\ N, d = 4\ m, and = 60^. 60^ = 0.5 W = (300\ N)(4\ m)(0.5) Step 3: Calculate the work. W = 300 × 4 × 0.5 = 600\ J The work done is 600\ J.