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

**Problem Set E**

**Overview:**

Problem Set E contains 17 problems which test your ability to use the work-energy relationship to analyze a physical situation and solve for some unknown quantity. Most problems are complex, demanding both strong algebra skills and the ability to accurately read and interpret a verbal description of a physical situation. The set represents a classic case in which you will have to blend a sturdy conceptual understanding with strong math skills to be successful.

**The Theory:**

The fundamental principle behind this 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.

If a term does not cancel out of the work-energy equation, then
you will have to use given values to calculate the term. In such
instances, the KE, PE and W_{nc} terms can be determined
using their respective equations.

KE = 0.5 • m •
v^{2} |
PE = m • g •
h |
W_{nc} = F • d
• cos() |

In some of the more difficult problems, stated values will have to be treated to convert to standard units. In other cases, the force will have to be calculated using Newton's laws or an inclined plane analysis.

To be successful on this problem set, you will need to be able to:

- give attention to the units of stated quantities and peform proper conversions.
- determine the value of a friction force as
mu•F
_{norm}. - determine the perpendicular component of gravity on an
inclined plane (in order to determine the friction force on an
incline): F
_{perp}= m•g•cos(). - use trigonometry to relate the distance traveled along the length of an inclined plane to the inclined angle and the height of the plane at a given point.
- determine the power of a machine using P = F•v where v is either the average or the constant velocity.
- calculate kinetic and potential energies and work values.
- calculate percentages.
- use the work-energy equation.

**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

Resolving Fgrav on an Inclined Plane

View Sample Problem Set.

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