## Module 8 Class Activities

## Work and Energy

Energy is never created nor destroyed; it just transforms from one kind to another, and from one object to another. This tutorial introduces you to energy conservation and its connection to the concept of work.

### I. Introduction to work, kinetic energy, and potential energy

Here are some basic definitions, phrased informally:

*Kinetic energy*= The energy something has because of its motion. The heavier or faster something is, the more kinetic energy it has.*Gravitational potential energy*= The energy “stored” in an object because it’s been lifted. The energy is “potential” because it has the potential to turn into kinetic energy—for instance, if the object gets dropped. The heavier or higher an object is, the more potential energy is stored up.

A. A child pushes a loaded wagon up a hill, starting slowly but gradually getting faster and faster. Is the wagon gaining kinetic energy, gravitational potential energy, both, or neither? Explain.

B. Suppose the wagon gains a total of 50 joules of energy. (A joule, like a calorie, is a unit of energy.) According to energy conservation, energy is never created nor destroyed. But the wagon just gained 50 joules! Does this scenario contradict conservation of energy? Explain why or why not.

C. When you say something like “the jogger just burned 100 calories” of energy, what does that mean? Where exactly do those 100 calories come from? In other words, what form of energy is depleted by 100 calories? Hint: This is as much a biology or chemistry question as it is a physics question.

D. Roughly speaking, *work* is the mechanical energy—the kinetic and potential energy—given to an object by exerting a force on it. How much work did the child do on the wagon?

### II. Lifting a book

In this problem, you’ll use the formal definition of *work* to figure out some stuff. Work is done when a force ** F** acts on the object over a distance ∆

**. When the force points in the same direction that the object moves, the work is given by**

*x**W*=

*F*∆

*x*. (In lecture, you’ll deal with “misaligned” forces and displacements.)

A. A student holds a book of mass *m* in her hand and raises the book vertically at constant speed. Sketch a free-body diagram for the book. As the book rises at steady speed, is the force exerted by the student on the book greater than, less than, or equal to *mg? * Explain briefly.

B. Suppose the student does 25 joules of work lifting the book.

- Does the book lifted at constant speed gain potential energy, kinetic energy, or both? Explain.
- Is the potential energy gained by the book greater than, less than, or equal to 25 joules? Explain.

C. Now we’ll repeat the reasoning of part B in terms of symbols rather than numbers.

- Use the definition of work to determine the amount of work the student does in raising the book through a height
*h.*Express your answer in terms of*m*,*g*, and*h*. - So, how much potential energy did the book gain, in terms of
*m*,*g*, and*h*?

D. In this class or a previous class, you may have seen the equation *U* = *mgh* for gravitational potential energy. For people who already knew that formula, what’s the point of parts B and C above?

*Consult an LA before you proceed.*

### III. Pushing on a wall

In this section we’ll clarify the meaning of *work*.

A. A student pushes hard enough on a wall that she breaks a sweat. The wall, however, does not move; and you can neglect the tiny amount it compresses. Does the student do any work on the wall? Answer using:

- your intuition.
- the physics definition of work.

B. Apparently, some reconciliation is needed. We’ll lead you through it.

- In this scenario, does the student
*give the wall any kinetic or potential energy*? - Does the student
*expend energy*, i.e., use up chemical energy stored in her body? - If the energy “spent” by the student doesn’t go into the wall’s mechanical energy, where does it go? Is it just gone, or is it transformed into something else? Hint: How do you feel when you’ve expended lots of energy?

C. Intuitively, when you push on a wall, are you doing *useful* work or are you “wasting energy”?

D. A student says,

“In everyday life, ‘doing work’ means the same thing as ‘expending energy.’ But in physics,

workcorresponds more closely to the intuitive idea of useful work, work that accomplishes something, as opposed to just wasting energy. That’s why it’s possible to expend energy without doingworkin the physics sense.”

In what ways do you agree or disagree with the student’s analysis?

### IV. Supplemental problem: Practice using work and energy conservation

A small, homemade rocket of mass 5.0 kg takes off from the ground and goes straight up. During the first 100 meters of its ascent, the engine exerts a 70 newton upward force on the rocket.

A. How much work does the engine do on the rocket during those first 100 meters?

B. Based on the given information, how much kinetic energy would you expect the rocket to have when it’s at a height of 100 meters? (*Hint:* Don’t use a formula for kinetic energy. Instead, think about the relationship between work, kinetic energy, and potential energy. To keep the math less messy, approximate *g* as 10 m/s^{2}.)