Set 3 Problem number 6

• Problem

• Solution

• Generalized Solution

Problem

Assuming that 864.0001 Joules of kinetic energy are dissipated in the process, how much kinetic energy increase should be expected as a result of a 20 Newton force being exerted over a distance of 80 meters?

Solution

The work done is ( 20 meters)( 80 Newtons) = 1600 Joules.

• After dissipating 864.0001 Joules, there are 735.9999 Joules left.
• This is the increase in kinetic energy.

Generalized Solution

The increase in KE is equal to the work `dW done on the object by the 'pushing' or 'pulling' force, less that dissipated by other forces.

• In this case, friction dissipates energy `dE<sub>frict</sub>.
• The KE increase is therefore `dW - `dE_frict.

The pushing force is in the direction of motion, the frictional force opposite to the direction of motion.

• The object's equal and opposite response to the pushing force is opposite to its direction of motion so the object does negative work with this force, thereby tending to increase its KE.
• The object must also exert a force opposite to the frictional force, and therefore in its direction of motion.  So the object does positive work with this force, thereby tending to decrease its KE.