ChemPhys 173/273

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 (TMEi) 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 (TMEf) possessed by the system is equivalent to the initial amount of energy plus the work done by these non-conservative forces.

TMEi + Wnc = TMEf

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

KEi + PEi + Wnc = KEf + PEf

The work done to a system by non-conservative forces (Wnc) 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 Wnc 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 PEi 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 PEi and the PEf 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 KEi and KEf 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 • v2
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.

Work | Sample Work Calculations | Potential Energy | Kinetic Energy | Mechanical Energy

Situations Involving External Forces | Situations Involving Energy Conservation

 

View Sample Problem Set.

 

Problem

Description

Audio Link
1

Calculation of the amount of work done on a braking car on a level highway using the work-energy relationship.

2

Calculation of the amount of work done on a skiier descending a hill.

3

Calculation of the amount of work done on a volleyball being hit downward from an elevated position.

4

Calculation of the initial KE of a baseball based on the PE and KE at a given location in the trajectory.

5

Calculation of the KE of a pendulum ball as it swinges to one-fourth its original height.

6

Calculation of the final KE of a root beer mug which is pushed across a level countertop.

7

Calculation of the final KE of a ski jumper from the initial PE and KE and work done on her.

8

Calculation of the mass of a car given the work required to move it vertically to a given height.

9

Calculation of the final speed of a baseball based on the KE and PE value at a given location in the trajectory.

10

Calculation of the final KE of a roller coaster car based on the initial KE, PE and work done upon it.

11

Calculation of the final KE of a cart based upon the initial height and the percent energy lossed while descending a hill.

12

Calculation of the final PE of a ball rolling up an incline based on the initial speed of the ball as it rolls into the incline.

13

Calculation of the final speed of a ski jumper based upon the initial PE and KE and work done on her.

14

Calculation of the final KE of a roller coaster car at the bottom of a loop based on the speed and the height at the top of a loop.

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