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Day 9 – May 27 – WBL 5.1- 5.2 Chapter 5 Work and Energy PC141 Intersession 2013 Slide 1 Every branch of science is concerned with energy. That being the case, you would think that we could come up with a good definition of exactly what energy is. However, the best we can do for now is this: energy is the capacity to do work. In this chapter, we will define work and its relation to force. Then, we will introduce kinetic energy and potential energy, and relate them to work. Finally, we will draw a connection between energy and power. except math. math is weird.

Chapter 5 Work and Energy

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Chapter 5 Work and Energy. Every † branch of science is concerned with energy. That being the case, you would think that we could come up with a good definition of exactly what energy is. However, the best we can do for now is this: energy is the capacity to do work. - PowerPoint PPT Presentation

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Page 1: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

Chapter 5Work and Energy

PC141 Intersession 2013 Slide 1

Every† branch of science is concerned with energy. That being the case, you would think that we could come up with a good definition of exactly what energy is. However, the best we can do for now is this: energy is the capacity to do work.In this chapter, we will define work and its relation to force. Then, we will introduce kinetic energy and potential energy, and relate them to work. Finally, we will draw a connection between energy and power.

†except math. math is weird.

Page 2: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

Work describes what is accomplished by a force when it moves an object through a particular displacement. Its mathematical definition is as follows:The work done by a constant force is equal to the product of the magnitudes of the displacement and the component of the force that is parallel to the displacement.

That’s a rather confusing sentence. The situations depicted on the next two slides will clarify it.

The symbol for work is W (it’s capitalized, so as to not confuse it with the magnitude of weight, w).

5.1 Work Done by a Constant Force

PC141 Intersession 2013 Slide 2

Page 3: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

In part (a), there is a force F acting on the crate, but it does not move. Since there is no displacement, no work is done.In part (b), there is a force F acting on the waterskier, and this force is in the same direction as his displacement d. In this case, .

5.1 Work Done by a Constant Force

PC141 Intersession 2013 Slide 3

Page 4: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

In part (c), there is a force F and a displacement d, but they are not in the same direction. Instead, the force acts at an angle to the displacement. From chapter 3, we know that the component of F along the direction of d is (the subscript “∥” indicates the “parallel component”). Here, the work is

5.1 Work Done by a Constant Force

PC141 Intersession 2013 Slide 4

Don’t be fooled into thinking that there are three different equations for work. The one above works in every case…for the waterskier, , and (since ), the equation reduces to . Do note however that this equation is only valid for constant forces.

Page 5: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

To complete the case in part (c), we note that the perpendicular component of force, , does no work, since there is no displacement in this direction. This fact will end up being incredibly useful in simplifying problems later on in this chapter.

5.1 Work Done by a Constant Force

PC141 Intersession 2013 Slide 5

Since work is the product of a force and a distance, it should be clear that it has SI units of N·m (“Newton-meters”). One N·m is also called a “Joule” (J). Although force and displacement are both vectors, the formula for work only involves their magnitudes and the cosine of their relative directions. Therefore, work is a scalar quantity. It may have a negative value, however.

Page 6: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

In chapter 2, we learned about graphical methods to calculate changes in velocity (position) based on the area under a curve of acceleration (velocity) vs. time.Work can be analyzed graphically as well. If an object moves a distance x while it is acted upon by a constant x-directed force F, a plot of F vs. x is shown below. The area under the curve is Fx, which is equal to the work done on the object.

5.1 Work Done by a Constant Force

PC141 Intersession 2013 Slide 6

This is a trivial example, of course…we’re all capable of multiplying two numbers together. However, it will become important in the next section, when we study the work done by a non-constant force.

Page 7: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

When there are several forces acting on an object as it moves through a displacement d, it is possible for many of them (or many of their parallel components) to do work on the object. Their sum is called the net work. When calculating net work, you have two options:1. Calculate the net force (the vector sum of each individual force)

and then find the work done by this net force; or2. Calculate the work done by each individual force, and then

perform a scalar sum of these to find the net work.

I don’t usually use class time to discuss examples that are worked out in the text. However, Example 5.3 (pages 146-147) is too good to pass up…

5.1 Work Done by a Constant Force

PC141 Intersession 2013 Slide 7

Page 8: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

A 0.75-kg block slides with a uniform velocity down a 20° incline. a) How much work is done by

the frictional force?b) What is the net work done

on the block?

5.1 Work Done by a Constant Force – Example 5.3

PC141 Intersession 2013 Slide 8

Page 9: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

Problem #1: Catching a Baseball

PC141 Intersession 2013 Slide 9

A pitcher throws a fastball. When the catcher catches it…

A …positive work is done

B …negative work is done

C …the net work is zero

WBL LP 5.3

Page 10: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

Problem #2: Work Done by Gravity

PC141 Intersession 2013 Slide 10

A ball is thrown vertically upward. Unsurprisingly, it eventually reaches a maximum height, then returns to the point at which it was thrown. What can we say about the work Wg done by the force of gravity on the ball?

A Wg is positive

B Wg is negative

C Wg = 0

Page 11: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

Problem #3: Sliding Down a Ramp

PC141 Intersession 2013 Slide 11

WBL Ex 5.4/5.5

A 3.00-kg block slides down a frictionless plane inclined 20 to the horizontal. If the length of the plane’s surface is 1.50 m, how much work is done on the block, and by what force?

Then, suppose that there is kinetic friction between the block and the plane, with In this case, what is the work done on the block?

Solution: In class

Page 12: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

Problem #4: Pushing a Desk

PC141 Intersession 2013 Slide 12

WBL Ex 5.15

A man pushes horizontally on a desk that rests on a rough wooden floor. The coefficient of static friction between the desk and floor is 0.750 and the coefficient of kinetic friction between the desk and floor is 0.600. The desk’s mass is 100 kg. The man pushes just hard enough to get the desk moving and continues pushing with that force for 5.00 s. How much work does he do on the desk?

Solution: In class

Page 13: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

Recall that the entire discussion in section 5.1 assumed that the force was constant. This is a bit of a restrictive condition, since many forces vary with time and/or position.One example of a variable force is a spring. If an applied force Fa stretches or compresses the spring, it is countered by an oppositely-directed “spring force” Fs.

5.2 Work Done by a Variable Force

PC141 Intersession 2013 Slide 13

Page 14: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

For “well-behaved” springs, the spring force is proportional to the change in length of the spring from its equilibrium position x0, and opposite in direction. This gives Hooke’s Law,

Often, we set x0 = 0, in which case

Here, we see that the spring force is a function of position. That is, it is variable, rather than constant.

5.2 Work Done by a Variable Force

PC141 Intersession 2013 Slide 14

Page 15: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

The in the previous equations is called the spring constant or force constant, and it has SI units of N/m. A high value of indicates a stiff spring, while a low indicates that the spring is very compliant. Hooke’s law – that the spring force varies linearly with x – is only valid for ideal springs. Real springs follow this law for reasonably small values of |x|, but past their elastic limit, the linear relation no longer applies.

5.2 Work Done by a Variable Force

PC141 Intersession 2013 Slide 15

Page 16: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

Calculating the work done by an arbitrary variable force – that is, for an arbitrary function F(x) – usually requires techniques of calculus. However, for a linear force, it’s actually quite easy using the graphical method of the last section.Recalling that the area of a triangle is ½ (base)(height), we see that

5.2 Work Done by a Variable Force

PC141 Intersession 2013 Slide 16

Page 17: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

Problem #5: Compressing a Spring

PC141 Intersession 2013 Slide 17

WBL CQ 5.7

If a spring is compressed 2.0 cm from its equilibrium position and then compressed an additional 2.0 cm, how much more work is done in the second compression than in the first?

Solution: In class

Page 18: Chapter  5 Work and Energy

Day 9 – May 27 – WBL 5.1-5.2

Problem #6: Overstretched Spring

PC141 Intersession 2013 Slide 18

WBL Ex 5.27

In stretching a spring in an experiment, a student inadvertently stretches it past its elastic limit; the force-vs-stretch graph is shown below. Basically, after it reaches its limit, the spring acts as if it were considerably stiffer. How much work was done on the spring?

Assume that each tick mark on the force axis is 10 N and every tick mark on the distance axis is 10 cm.

Solution: In class