Atension force of 165 n inclined at 35.0° above the horizontal is used to pull a 31.0 kg storage crate a distance of 5.60 m on a rough surface. if the crate moves at a constant speed, find (a) the work done by the tension force and (b) the coefficient of kinetic friction between the crate and surface. hint (a) the work done by the tension force (in j) j (b) the coefficient of kinetic friction between the crate and surface

(a) 756.9 J

The work done by a force when moving an object is given by:

where

F is the magnitude of the force

d is the displacement of the object

is the angle between the direction of the force and of the displacement

In this situation,

F = 165 N

d = 5.60 m

so the work done by the tension is

(b) 0.646

The crate is moving at constant speed: this means that the acceleration of the crate is zero, so the net force on the crate is also zero.

There are only two forces acting on the crate along the horizontal direction:

- The horizontal component of the tension, , forward

- The frictional force, , backward, with being the coefficient of kinetic friction, N being the normal reaction of the surface on the crate

The normal reaction is the sum of the weight of the crate + the vertical component of the tension, so

Since the net force is zero, we have

where

T = 165.0 N

N = 209.2 N

Solving for , we find the coefficient of friction:

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