**Unit 11: Work, Energy and
Power**

**Problem Set C**

**Overview:**

These 14 problems have very little mathematical complexity. Rather, the problems test your ability to read a description of a physical situation, extract numerical information from the description, and combine the numerical information with an conceptual understanding of kinetic energy, potential energy and work in order to solve for some unknown quantity. The emphasis will be upon reading, analyzing, conceptualizing, inferring and applying a little mathematics.

**The Theory:**

The fundamental principle behind the problem set is that the
initial amount of total mechanical energy (TME_{i}) of a
system is altered by the work which is done to it by non-conservative
(or external) forces. The final amount of total mechanical energy
(TME_{f}) possessed by the system is equivalent to the
initial amount of energy plus the work done by these non-conservative
forces.

The energy possessed by a system is the sum of the kinetic energy and the potential energy. Thus the above equation can be re-arranged to the form of

The work done to a system by non-conservative forces
(W_{nc}) can be described as either positive work or negative
work. Positive work is done on a system when the force doing the work
acts in the direction of the motion of the object. Negative work is
done when the force doing the work opposes the motion of the object.
When a positive value for work is substituted into the work-energy
equation above, the final amount of energy will be greater than the
initial amount of energy; the system is said to have *gained
mechanical energy*. When a negative value for work is substituted
into the work-energy equation above, the final amount of energy will
be less than the initial amount of energy; the system is said to have
*lost mechanical energy*. There are occasions in which the only
forces doing work are conservative forces (sometimes referred to as
internal forces). In general, such forces include gravitational
forces, elastic or spring forces, electrical forces and magnetic
forces. When the only forces doing work are conservative forces, then
the W_{nc} term in the equation above is zero. In such
instances, the system is said to have *conserved its mechanical
energy*.

**The Practice:**

In Problem Set C, you will have to carefully read the problem
description and substitute values from it into the work-energy
equation listed above. You will also have to make inferences about
certain terms based on your conceptual understanding of kinetic and
potential energy. For instance, if the object is initially on the
ground, then you can infer that its PE_{i} is 0 and that term
can be canceled from the work-energy equation. In other instances,
the height of the object is the same in the initial state as in the
final state, so the PE_{i} and the PE_{f} terms are
the same. As such, they can be mathematically canceled from each side
of the equation. In other instances, the speed is constant during the
motion, so the KE_{i} and KE_{f} terms are the same
and can thus be mathematically canceled from each side of the
equation. Finally, there are a few instances in which the KE and or
the PE terms are not stated; rather, the mass (m), speed (v), and
height (h) is given. In such instances, the KE and PE terms can be
determined using their respective equations.

KE = 0.5 • m •
v^{2} |
PE = m • g •
h |

**One Final Caution:**

This problem set is designed to train students to rely on the use of the work and energy equation listed above. It is common in many of the problems that extraneous numerical values will be stated in the problem description; such values do not need to be used in the solution. This extraneous information will only be a distraction to students who depart from the strategy described in the above paragraph. Make it your habit from the beginning to simply start with the work and energy equation, to cancel terms which are zero or unchanging, to substitute values of energy and work into the equation and to solve for the stated unknown. By so doing, you will never be tempted to use information which is unnecessary to the solution.

**Additional Readings/Study
Aids:**

The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in the understanding of the concepts and mathematics associated with these problems.

Situations Involving External Forces | Situations Involving Energy Conservation

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