ChemPhys 173/273

Unit 11: Work, Energy and Power

Problem Set D

Overview:

Problem Set D targets your ability to use the work and energy equation and the expressions for potential energy and kinetic energy in order to analyze physical situations. The power of the work and energy concept is that it allows a person to make predictions about how fast (speed) and how far (distance) an object moves if given some initial known parameters about the object.

In Problem Set C (the previous problem set), the goal was to learn to use the work-energy equation to analyze a physical situation. The equation which was used with great regularity was

KEi + PEi + Wnc = KEf + PEf

Problem Set D is an extension of Problem Set C in that the same equation becomes used with regularity. However, there is an extra dimension to Set D which makes it one degree more complex than Set C. In Set C, actual values of KE, PE, and Wnc were frequently given and the problem commonly involved finding an unknown energy or work value. In Set D, values of mass, speed and height are commonly stated and energy values will have to be calculated using the following formulas:

 KE = 0.5 • m • v2 PE = m • g • h W = F • d cos

Detailed information about the use of these three equations is provided at The Physics Classroom as assessed by using the links above.

If the expressions for kinetic energy, potential energy and work are substituted into the work-energy equation shown above, then the equation can be re-written as follows.

0.5 • m • vi2 + m • g • h i + F • d • cos = 0.5 • m • vf2 + m • g • h f

This new form of the work-energy equation will be the dominant equation for the remainder of the unit.

While Set D includes this added complexity, there is one simplification. Each problem in Set D involves a situation in which there are no non-conservative forces doing work. When only conservative forces are doing work, the F•d•cos() term in the above equation drops out of the equation, leaving

0.5 • m • vi2 + m • g • h i = 0.5 • m • vf2 + m • g • h f

The left side of this equation represents the total mechanical energy of the system initially; the right side of this equation represents the final mechanical energy. The equation states that the initial amount of total mechanical energy is equal to the final amount of total mechanical energy. This is sometimes referred to as the energy conservation equation. Set D will rely upon the use of this equation.

Elastic Potential Energy:

For the first time in this unit, the concept of spring energy is seen with more than a passing reference. Spring energy or elastic potential energy is the energy stored in an object due to its stretching or compressing an attached spring. The amount of energy stored in the object/spring system is dependent upon the nature of the spring (mainly its spring constant, k) and the amount of stretch or compression which the spring experiences. This quantified by the equation

PEspring = 0.5• k • x2

where k is the spring constant of the spring (with standard metric units of Newton/meter) and x is the amount of stretch or compression of the spring (with standard metric units of meter) relative to the rest or equilibrium position.

Being one more form of potential energy, this spring energy term must be included in any energy analysis when present. Thus, our energy conservation equation becomes

0.5 • m • vi2 + m • g • h i + 0.5• k • xi2 = 0.5 • m • vf2 + m • g • h f + 0.5• k • xf2

Analyzing a Physical Situation:

A good deal of time and effort is spent in class analyzing physical situations in terms of work and energy. A conceptual tool which is commonly used in such analyses is the work-energy bar chart. A work-energy bar chart illustrates in a conceptual manner the forms of energy possessed by an object and how those forms change as the object moves from its initial state to its final state. The construction of a work-energy bar chart requires that a student understand the concepts of work and energy and the variables which effect these quantities. This conceptual understanding is crucial to the completion of Problem Set D. As you procede through a problem, you will have to be proficient at identifying which energy terms are present in a given situation and which terms are zero or unchanging. Examples and detailed discussions of work-energy bar charts are provided online at The Physics Classroom.

You will be successful in Set D if you practice the following habits:

1. Read the problem carefully and construct a diagram to assist in visualizing the physical situation.
2. Extract and label explicitly stated numerical information from the problem description, giving attention to units and making proper conversions when necessary.
3. Rely on a strong conceptual understanding to make correct inferences about terms in the work-energy equation which can be neglected because they are either 0 or unchanging.
4. Identify the unknown quantity to be solved for.
5. Make proper substitutions of known numerical values into the work-energy equation.
6. Perform proper algebraic manipulations of the work-energy equation to solve for the unknown quantity.

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

View Sample Problem Set.

 Problem Description Audio Link 1 Calculation of the final speed of a baseball dropped from a known initial height. 2 Determination of the height of a hill from the knowledge of the speed of a sledder at the bottom of thi hill. 3 Calculation of the peak height of a high jumper who leaps with a stated take-off speed. 4 Calculation of the final speed of the ball at the halfway pointto the peak of its trajectory. 5 Calculation of the speed of Tarzan at the lowest point while swinging from a vine of known length and known angle of initial deflection from the vertical. 6 Determination of the initial speed of a textbook to achieve a stated landing speed. 7 Determination of the final speed of a bead moving along a curved wire from an initial height to a final height. 8 Calculation of the final speed of a man who has jumped out of a window of known height. 9 Determination of the height to which Tarzan rises as he swings from a vine; the initial angle of deflection of the vine (expressed relative to the horizontal) is given. 10 Calculation of the take-off speed of a flea from the height to which it rises. 11 Calculation of the elastic potential energy stored in an object based on the spring constant and the compresson distance of the spring. 12 Calculation of the height to which an object rises if launched by a compressed spring upward into the air.

Audio Help for Problem: 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 ||

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