Question

which is the reason why the equation is reached: dU = FcosΘds to describe the work done by a force.

Include descriptive schemes.

Write when the work is positive, negative or null depending on the angle between the force component and the displacement.

What is the unit of measurement of labor (U) in the international system and in the imperial system?

Answer 1

DEFINITION OF WORK DONE:

The work done is the change in measure of energy or the change in energy when a body displaced upon the action of force.

The work done is the product of Force and Displacement,Work Done=Force*Displacement

Consider a block which is placed on a horizontal frictionless surface.The block is acted upon by the Constant Force (F) which causes it to displace to a certain distance (d) in the direction of the force,hence the work done W=F*d

Now if the force acts on the block is at some angle (θ) to the displacement (d),The force gets resolved into two components Fsinθ and Fcosθ,The component of the force which results in the displacement is Fcosθ (As it acts in the direction of the force).

Therefore,the work done by the force in displacing the block through the displacement (d) is given as,

W=Fcosθ *d

Therefore the change in work done can be written as,

dU=Fcosθ *ds

1. POSITIVE WORK DONE

When the force is acting in the direction of displacement,the component of force acting in the direction of the displacement Fcosθ (θ=0) will be F.

Therefore the work done will be,W= F*d

2. NEGATIVE WORK DONE

When the force is acting in the opposite direction of the displacement,the component of force acting in the direction

of the displacement Fcosθ (θ=180) will be -F

Therefore the work done will be,W= -F*d

3.ZERO/NULL WORK DONE

When the direction of force is perpendicular to that of displacement it is called as zero work done ,Since the angle between the force and the displacement is (θ=90),Therefore the work done will be W= Fcos(90) *d

Hence,W=0 (As cos(90)=0)

The unit of measurement of labor (U) is ,

In International System (SI System)=Nm or Joule(J)

In Imperial System=Pound Foot (lbf ft)

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