Set 3 Problem number 2

• Problem

• Solution

• Generalized Solution

• Explanation in terms of Figure(s), Extension

• Figure(s)

Problem

How far must an object be pushed by a force of 9 Newtons, always exerted parallel to the direction of motion, in order to gain 16 Joules of energy, if the energy gained is equal to the work done on the object?

Solution

It is assumed that there is no dissipation of energy, so the work done by the 9 Newton force must be equal to the 16 Joules of energy used up.

• Since work equals parallel force times displacement, 16 Joules is equal to 9 Newtons multiplied by the distance.
• This could be written as an equation:

• 16 J = ( 9 N)(dist).

• Solving the equation we find that

• dist = 16 J/( 9 N) = 1.777778 meters.

Generalized Solution

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

In the present problem, force and displacement are assumed to be parallel and in the same direction.

• In this case, since the work done is equal to the energy expended  we can say that `dW = F `ds.
• Solving we see that F = `ds / `dW.

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)