Question

A worker with spikes on his shoes pulls on rope that is attached to a box that is resting on a flat, frictionless frozen lake. The box has mass m, and the worker pulls with a constant tension T at an angle θ = 40 ∘ above the horizontal. There is a strong headwind on the lake, which produces a horizontal force Fw that is pointed in the opposite direction than the box is being pulled. Draw a free-body diagram for this system. Assume that the worker pulls the box to the right. If the wind force has a magnitude of 30 N, with what tension must the worker pull in order to move the box at a constant velocity?

Answer 1

a

The free body diagram is shown on the first uploaded image

b

The tension on the rope is
`T=39.16 \ N`

Step-by-step explanation:

From the question we are told that

The mass of the box is m

The tension on the box is T

The angle at which it is pulled is
`\theta = 40^o`

The force produced by the strong head wind is
`Fw = 30 \ N`

At equilibrium the net force acting on the block along the horizontal axis is zero i.e

`Tcos \theta -F_w = 0`

substituting values

`Tcos (40) -30 = 0`

`Tcos (40) = 30`

`T(0.76604)) = 30`

`T=39.16 \ N`