To pull a 50 kg crate across a horizontal frictionless floor, a worker applies a force of 210 N, directed 20° above the horizontal. As the crate moves 3.0 m, what work is done on the crate by (a) the worker's force, (b) the gravitational force on the crate, and (c) the normal force on the crate from the floor? (d) What is the total work done on the crate?

The work done on the crate by the worker's force is 592 J.

Given that,

Mass of the crate, m = 50kg

Force applied by the worker, F = 210N

Angle to the horizontal, θ = 20°,

Distance moved by crate, d=3m

A force causes an object with mass to change its velocity, therefore, the acceleration. acceleration caused by a force is always in the direction of force applied.

Also, we know that work done is always given as the product of force and displacement in the direction of the force.

(a.) work done on the crate by the worker's force,

As the force is been applied at an angle directed 20° above the horizontal.

Therefore, the force is causing the crate to move in the horizontal direction, thus, only the horizontal component of the force is taken.

(b) work done on the crate by the gravitational force,

As the gravitational force is always applied perpendicular to the horizontal.

Therefore, the gravitational force is not causing the crate to displace anywhere, thus, the displacement is zero.

Hence, work done on the crate by the gravitational force is 0 J.

(c.) work done on the crate by the normal,

Normal is the contact force that is perpendicular to the surface with which the object has contact.

As the normal force did not cause the crate to displace upward by any distance.

(d.) The total work done on the crate,

As discussed above the only work done on the crate is by the worker.

Therefore, The total work done on the crate is 592 J.

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Explanation:

Given that,

A crate of mass M = 50kg

The crate is pulled along an horizontal floor by a string at an angle

Force pulling the crate

F = 210N

Angle θ = 20° to the horizontal

Distance moved by crate d=3m

A. Work done by force

W = FdCosθ

W = 210 × 3 × Cos20

W = 592J

B. Work done by Gravitational force?

Work is define as the dot product of force and displacement in the direction of the force.

Since the gravitational force does not cause the crate to move any distance downward

Then,

W(gravity) = mg×d

distance d=0

W(gravity) = 0 J

C. Work done by normal?

Since, the normal force did not cause the crate to move upward by any distance

Then,

W(normal) = 0J

D. The total workdone?

The only workdone on the crate is by the person

Then, the total workdone is the workdone by the person

W = 592 J

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