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

**Problem Set A**

**Overview:**

Problem Set A targets your ability to use equations related to work and power in order to solve 1-, 2- and 3-step problems. There are three equations of importance in the completion of this set.

**Work Equation**Work is defined as a force acting upon an object to cause a displacement (or a motion) or in some instances, to hinder a motion. Three variables are of importance in this definition - force, displacement, and the extent to which the force

*causes*the displacement. Each of these three variables find their way into the equation for work. That equation is:**Work = Force • Displacement • Cosine(theta)****W = F • d • co()**Since the standard metric unit of force is the Newton and the standard meteric unit of displacement is the meter, then the standard metric unit of work is a Newton•meter, defined as a

**Joule**and abbreviated with a**J**.The most complicated part of the work equation and work calculations is the meaning of the angle theta in the above equation. The angle is not jut any ol' stated angle in the problem; it is the angle between F and d. In solving work problems, one must always be aware of this definition - theta is the angle between the force and the displacement which it causes. If the force is in the same direction as the displacement, then the angle is 0 degrees. If the force is in the opposite direction as the displacement, then the angle is 180 degrees. If the force is up and the displacement is to the right, then the angle is 90 degrees. This is summarized in the graphic below.

**Power Equation**Power is defined as the rate at which work is done upon an object. Like all rate quantities, power is a time-based quantity. Power is related to how fast a job is done. An identical job or task can be done slowly or quickly; the work is the same in each case (since it is an identical job) but the power is different. The equation for power shows the importance of time:

**Power = Work / time****P = W / t**The unit for standard metric work is the Joule and the standard metric unit for time is the second, so the standard metric unit for power is a Joule / second, defined as a

**Watt**and abbreviated**W**.**Derived Power Equation**Combining the equations for power and work can lead to a second equation for power. Power is W/t and work is F•d•cos(). Substituting the expression for work into the power equation yields P = F•d•cos()/t. If this equation is re-written as

one notices a simplification which could be made. The

**d/t**ratio is the speed value for a constant speed motion or the average speed for an accelerated motion. Thus, the equation can be re-written as**P = F • v • cos()**where

**v**is the constant speed or the average speed value. Several problems in the set will utilize this derived equation for power.

To be successful on this problem set, you will have to master the use of the above equations. Additionally, you will need to be able to:

- convert units from non-standard metric form to standard metric form.
- utilize the equation for the force of gravity in situations in which an object is being lifted at constant speed.
- utilize Newton's laws and a free-body diagram to determine the value of an individual force in situations involving an accelerated motion (such as in problems #11, #14 and #15).
- use the sine function to calculate the force parallel to an inclined plane for a constant speed motion along an incline (such as in problem #10).
- practice the habits of a good problem-solver.

**One Final Caution:**

This problem set only test your conceptual understandings in addition to you mathematical abilities. 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 be a distraction primarily to students who treat physics problems as mere exercises in mathematics. Without an understanding of the above relationships, you will be tempted to force such information into your calculations. Physics is about conceptual ideas and relationships; and problem sets test your conceptual understanding of these relationships. If you treat this problem set as a mere exercise in the algebraic manipulation of physics equations, then you are likely to become frustrated quickly. As you proceed through this problem set, be concepts-minded. Do not strip physics of its conceptual meaning.

**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.

Resolving Fgrav on an Inclined Plane

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