Set 3 Problem number 1

• Problem

• Solution

• Generalized Solution

• Explanation in terms of Figure(s), Extension

• Figure(s)

Problem

When force and direction of motion are parallel, work is the product of force and displacement.

• Work is in Joules when force is in Newtons and displacement in meters.

How many Joules of work are done on an object when a force of 7 Newtons acts on it through a displacement of 13 meters?

Solution

The precise definition of the work done by a force is the product of the force component  parallel to motion and the displacement through which the force acts.

• In the present problem,  force and displacement are assumed to be parallel.
• In this case we can say that `dW = F `ds.
• We  say that in order to perform this work `dW, we must expend energy `dW:

• The work done and  the energy required to do the work are equivalent.

• Usually in the process of doing work `dW, the process is not 100% efficient and energy in excess of `dW is required.  In no case can the energy required by less than `dW.

In this problem we see that the force is 7 Newtons, acting in the same direction as the displacement of 13 meters.

• The work done is therefore

• `dW = 7 Newtons * 13 meters = 91 Newton meters = 91 Joules.

Explanation in terms of Figure(s), Extension

The figure below depicts a force F acting on a moving object along a straight-line path from  point A to point B.

• The force is considered uniform in the direction from A to B.
• The work  done by the force is `dW = F `ds. 

Figure(s)