PHY131H1F - Class 11

Today: • Conservative and Nonconservative Forces • Potential Energy • Conservation of Energy

Clicker Question

A cart rolls up a frictionless incline. It starts

with speed vi, but stops near the top. As it rolls up the ramp, its kinetic energy is transformed to A. stopping energy. B. gravitational potential energy. C. energy of motion. D. internal thermal energy. E. energy of rest.

1 Class 11 Preclass Quiz on MasteringPhysics . This was due this morning at 8:00am . 72% of students got the first true/false question. . A nonconservative force permits a two-way conversion between kinetic and potential energies. FALSE . A potential energy function can be specified for a nonconservative force. FALSE . A conservative force permits a two-way conversion between kinetic and potential energies. TRUE . The work done by a nonconservative force depends on the path taken. TRUE . The work done by a conservative force depends on the path taken. FALSE . A potential energy function can be specified for a conservative force. TRUE

Class 11 Preclass Quiz on MasteringPhysics . This was due this morning at 8:00am . 67% of students got the second true/false question. . The total mechanical energy of a system, at any one instant, is either all kinetic or all potential energy. FALSE (although it could be) . The total mechanical energy of a system is constant only if conservative forces act. TRUE . The total mechanical energy of a system is equally divided between kinetic and potential energy. FALSE (although it could be) . Mechanical energy can be dissipated to nonmechanical forms of energy. TRUE . The total mechanical energy of a system is constant only if nonconservative forces act. FALSE (always false)

2 Class 11 Preclass Quiz Student Comments . “FYI, the answer to the last question is posted online on yahoo since two years ago. https://ca.answers.yahoo.com/question/index?qid=20131003 213113AAT6UcS”

Yahoo! Answers can help you get this part of your mark. …but it’s not going to help you with this part!

Class 11 Preclass Quiz Student Comments

. “I say that Could you please differentiate between what conservative and non-conservative forces are? Some examples would be helpful perhaps :)” . Harlow answer: Yes will do! . “Do you believe in me?” . Harlow answer: Yes I do! You can do this! . (at 2:42 am) “I have a CHM138 midterm in about, let's see, 15 hours. Please wish me luck.” . Harlow answer: Good luck!

3 Class 11 Preclass Quiz Student Comments

. “i trust in physics, but i'd never tie a bowling ball to the end of a string and let it go to see if it would hit me in an attempt to test a theorem, just sayin'. my mom paid a lot of money for my teeth”

Conservative and Nonconservative Forces

• A conservative force stores any work done against it, and can “give back” the stored work as kinetic energy. • For a conservative force, the work done in moving between two points is independent of the path.

4 Conservative and Nonconservative Forces

• Because the work done by a conservative force is path independent, the work done in going around any closed path is zero: 퐹 ∙ 푑푟 = 0

Conservative and Nonconservative Forces

• A nonconservative force does not store work done against it, the work done may depend on path, and the work done going around a closed path need not be zero.

5 Conservative and Nonconservative Forces

• Examples of conservative forces include: • Gravity • The electric force • The force of an ideal spring

• Nonconservative forces include: • Kinetic Friction • Pushing force of a human or animal • Automobile engine

Potential Energy

. Consider two particles A and B that interact with each other and nothing else. . There are two ways to define a system. . System 1 consists only of the two particles, the forces are external, and the work done by the two forces change the system’s kinetic energy.

6 Potential Energy

. System 2 includes the interaction within the system.

. Since Wext = 0, we must define an energy associated with the interaction, called the potential energy, U. . When internal forces in the system do work, this changes the potential energy.

Potential Energy

• The change in potential energy is defined as the negative of the work done by a conservative force acting over any path between two points: B U   F  dr AB A – Potential energy change is independent of path. – Only changes in potential energy matter. – We’re free to set the zero of potential energy at any convenient point.

7 Gravitational Potential Energy

Gravitational Potential Energy • Gravitational potential energy stores the work done against gravity: U  mg y

– Gravitational potential energy increases linearly with height y. – This reflects the constant gravitational force near Earth’s surface.

8 Last class at the end I asked:

• Which has more energy, a desk on the top floor of a building, or a desk on the ground floor? • Technically, neither (a desk is a desk)!! • But, if you count the gravitational interaction between the Earth and the desk, then the system of the Earth+desk on top floor has more energy than the system of the Earth+desk on bottom floor. • Potential energy is the interaction energy of at least two things!

Clicker Question

A car starts with speed vi, but the driver puts on the brakes and the car slows to a stop. As the car is slowing down, its kinetic energy is transformed to A. stopping energy. B. gravitational potential energy. C. energy of motion. D. internal thermal energy. E. energy of rest.

9 Kinetic Energy: The energy of motion

1 퐾 = 푚푣2 2

Potential Energy: The energy of position

푈 = 푚푔푦

10 Internal Energy: The energy of microscopic thermal vibrations

퐸푖푛푡 ∝ 푇

Mechanical Energy

• Mechanical Energy is defined as the sum of the kinetic plus potential energy:

Emech = K + U

• When the only forces doing work on an object are all conservative, then the mechanical energy is conserved.

Ef = Ei

11 Another way of looking at freefall:

v f

QUESTION: I hold a ball at a distance of 5 m above the ground and release it from rest. How fast is it going just before it hits the ground?

12 A small child slides down the four frictionless slides A–D. Each has the same height, and the child always starts from rest. Rank in order, from largest to smallest, her

speeds vA to vD at the bottom.

A. vC > vA = vB > vD

B. vC > vB > vA > vD

C. vD > vA > vB > vC

D. vA = vB = vC = vD

E. vD > vA = vB > vC

NOTE: The Zero of Potential Energy . You can place the origin of your coordinate system, and thus the “zero of potential energy,” wherever you choose and be assured of getting the correct answer to a problem.

. The reason is that only ΔU has physical significance, not Ug itself.

13 QUESTION: Zainab runs forward with her sled at 2.0 m/s. She hops at the top of a very slippery slope. The slope is 7.0° below the horizontal, and extends down a total vertical distance of 5.0 m. What is her speed at the bottom?

A child is sliding down a playground slide at constant speed. While sliding, the energy transformation is

A. U → K

B. U → Eint C. K → U

D. K → Eint E. There is no transformation because energy is conserved.

14 Elastic Potential Energy . Consider a before-and-after situation in which a spring launches a ball . The compressed spring has −푥i “stored energy,” which is then transferred to the kinetic energy of the ball .We define the elastic potential energy U of a spring to be: 푥f = 0 U  1 kx2 2

A spring-loaded gun shoots a plastic ball with a speed of 4 m/s. If the spring is compressed twice as far, the ball’s speed will be A. 1 m/s. B. 2 m/s. C. 4 m/s. D. 8 m/s. E.16 m/s.

15 Before Class 12 on Monday • Please finish reading Wolfson Chapter 7 • Something to think about: • A red marble is balanced on the top of a smooth hill. A blue marble sits at the bottom of a smooth valley. Which marble is in equilibrium? What is the difference between these two situations?