Set 3 Problem number 3

• Problem

• Solution

• Generalized Solution

• Explanation in terms of Figure(s), Extension

• Figure(s)

Problem

In order to stop a moving object, the object must be caused to expend a total of 96 Joules of energy.

• This is caused by exerting a force on the moving object, which must then exert an equal and opposite opposing force and must hence do work.
• How much force must be exerted against the object if it is to be stopped within a distance of 8 meters?

Solution

The work done by the object in the 8 meter distance must be equal to the 96 Joules of energy is uses up.

• Since work equals parallel force times displacement, 96 Joules is equal to 8 meters multiplied by the force.
• This could be written as an equation

• 96 J = ( 8 m)(force).

• Solving we find that

• force = 96 J/( 8 m) = 12 Newtons.

Generalized Solution

Since work is the product of parallel force and distance, the work necessary to dissipate energy `dE over a distance `ds  by a parallel force F will be

• `dW = E = F `ds and
• F will therefore be the quotient

• F = `dW / `ds, or equivalently F = `dE / `ds.

Explanation in terms of Figure(s), Extension

The figure below shows the relationships among force, displacement and work for the case of force parallel to displacement.

• The relationship F = `dW / `ds tells us, for example, that if we wish to do a lot of work `dW over a long distance `ds we must exert only a little force.
• The relationship `ds = `dW / F tells us, for example, that if we wish to do of work `dW using a relatively large force we need only exert that force through a relatively short distance.
• The relationship `dW = F `ds tells us, for example, that the more force we exert and the greater the distance over which we exert it, the more work we do. 

Figure(s)