Physics 218, Lecture XIII1 Physics 218 Lecture 13 Dr. David Toback.

Physics 218, Lecture XIII 1

Physics 218Lecture 13Dr. David Toback


Checklist for Today•Things due for Last Thursday:–Read Chapters 7, 8 & 9

•Things that were due Last Monday:–Chap 5&6 turned in on WebCT

•Things that were due for Wednesday’s Recitation:–Problems from Chap 7

•Things due for this coming Monday:–Problems from Chap 7 on WebCT–Chaps 5&6 if you haven’t done them already


The ScheduleThis week: (2/25) • HW on Chaps 5&6 on WebCT• 3rd and 4th lectures (of six) on Chapters 7, 8 & 9• Chapter 7 in recitationNext week: (3/3) • Chapter 7 due in WebCT• 5th and 6th lectures (of six) on Chapters 7, 8 & 9• Chapter 8 in recitation Following week: (3/10) Spring Break!!!Following Week: (3/17)• Chapter 8 due in WebCT• Reading for Chapters 10 & 11• Lecture on Chapters 10 & 11• Chapter 9 and Exam 2 Review in recitation Following Week: (3/24)• Chapter 9 due in WebCT• Exam 2 on Tuesday• Recitation on Chapters 10 & 11• Reading for Chapters 12 & 13 for Thursday• Lecture 12 & 13 on Thursday


Last time:– Work and Energy– The Work-Energy relationship

This time and next time:– Potential Energy– Conservation of Mechanical Energy

– Conservation of Energy– Lots of problems

Chapters 7, 8 & 9 Cont



Different Style Than the Textbook

I like teaching this material using a different style than the textbook

1.Teach you the concepts2.Give you the important

equations3.Then we’ll do lots of

problems


Potential Energy

•Things with potential: COULD do work– “This woman has great potential as an engineer!”

•Here we kinda mean the same thing

•E.g. Gravitation potential energy:

– If you lift up a brick it has the potential to do damage


Example: Gravity & Potential Energy

You lift up a brick (at rest) from the ground and then hold it at a height Z

•How much work has been done on the brick?

•How much work did you do?•If you let it go, how much work will be done by gravity by the time it hits the ground?

We say it has potential energy: U=mgZ

–Gravitational potential energy


Other Potential Energies: Springs

Last week we calculated that it took ½kx2 of work to compress a spring by a distance xHow much potential energy does it now how have?U(x) = ½kx2


Force and Potential EnergyIf we know the potential energy, U,

we can find the force

This makes sense… For example, the force of gravity points down, but the potential increases as you go up

dxdU

xF


Force and Potential Energy

Draw some examples…

–Gravity–Spring


Mechanical Energy

•We define the total mechanical energy in a system to be the kinetic energy plus the potential energy

•Define E≡K+U


Conservation of Mechanical Energy

• For some types of problems, Mechanical Energy is conserved (more on this next week)

• E.g. Mechanical energy before you drop a brick is equal to the mechanical energy after you drop the brick

K2+U2 = K1+U1

Conservation of Mechanical EnergyE2=E1


Problem Solving• What are the types of examples

we’ll encounter?– Gravity– Things falling– Springs

• Converting their potential energy into kinetic energy and back again

E = K + U = ½mv2 + mgy


Problem Solving

For Conservation of Energy problems:

BEFORE and AFTER diagrams


Conservation of Energy Problems

Before…


After


Quick Problem

We drop a ball from a height D above the ground

Using Conservation of Energy, what is the speed just before it hits the ground?


Potential EnergyA brick held 6 feet in the air has potential energy

•Subtlety: Gravitational potential energy is relative to somewhere!

Example: What is the potential energy of a book 6 feet above a 4 foot high table? 10 feet above the floor?

• U = U2-U1 = Wext = mg (h2-h1)•Write U = mgh•U=mgh + Const

Only change in potential energy is really meaningful


Z Z

Before After

C

Falling onto a Spring

We want to measure the spring constant of a certain spring. We drop a ball of known mass m from a known height Z above the uncompressed spring. Observe it compresses a distance C.

What is the spring constant?


Quick Problem

A refrigerator with mass M and speed V0 is sliding on a dirty floor with coefficient of friction .

Is mechanical energy conserved?


Non-Conservative Forces•We’ve talked about three different types of forces:

1.Gravity: Conserves mechanical energy

2.Normal Force: Conserves mechanical energy (doesn’t do work)

3.Friction: Doesn’t conserve mechanical energy

•Since Friction causes us to lose mechanical energy (doesn’t conserve mechanical energy) it is a Non-Conservative force!


Law of Conservation of Energy

• Mechanical Energy NOT always conserved

• If you’ve ever watched a roller coaster, you see that the friction turns the energy into heating the rails, sparks, noise, wind etc.

• Energy = Kinetic Energy + Potential Energy + Heat + Others…

–Total Energy is what is conserved!


Conservative ForcesIf there are only conservative forces in the

problem, then there is conservation of mechanical energy

• Conservative: Can go back and forth along any path and the potential energy and kinetic energy keep turning into one another– Good examples: Gravity and Springs

• Non-Conservative: As you move along a path, the potential energy or kinetic energy is turned into heat, light, sound etc… Mechanical energy is lost.– Good example: Friction (like on Roller

Coasters)


Law of Conservation of Energy

•Even if there is friction, Energy is conserved

•Friction does work– Can turn the energy into heat– Changes the kinetic energy

•Total Energy = Kinetic Energy + Potential Energy + Heat + Others…

– This is what is conserved•Can use “lost” mechanical energy to estimate things about friction


Roller Coaster with FrictionA roller coaster of mass m starts at rest at height y1 and falls down the path with friction, then back up until it hits height y2 (y1 > y2).

Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path?


Energy SummaryIf there is net work on an object, it

changes the kinetic energy of the object (Gravity forces a ball falling from height h to speed up Work done.)

Wnet = KIf there is a change in the potential

energy, some one had to do some work: (Ball falling from height h speeds up→ work done → loss of potential energy. I raise a ball up, I do work which turns into potential energy for the ball)

UTotal = WPerson =-WGravity


Energy Summary

If work is done by a non-conservative force it does negative work (slows something down), and we get heat, light, sound etc.

EHeat+Light+Sound.. = -WNC

If work is done by a non-conservative force, take this into account in the total energy. (Friction causes mechanical energy to be lost)

K1+U1 = K2+U2+EHeat…

K1+U1 = K2+U2-WNC


Friction and SpringsA block of mass m is traveling on a rough surface. It reaches a spring (spring constant k) with speed Vo and compresses it a total distance D. Determine


l

l

Bungee JumpYou are standing on a

platform high in the air with a bungee cord (spring constant k) strapped to your leg. You have mass m and jump off the platform.

1.How far does the cord stretch, l in the picture?

2.What is the equilibrium point around which you will bounce?


Coming up… •Lectures:

– Last lectures on Chaps 7, 8 and 9•HW due in WebCT on Monday

– Chapter 7•Reading for Lecture next week

– Chaps 10 & 11: Momentum•Recitation next week

– Chapter 8



Roller CoasterYou are in a roller coaster car of mass

M that starts at the top, height Z, with an initial speed V0=0. Assume no friction.

a)What is the speed at the bottom?b)How high will it go again?

c)Would it go as high if there were friction?

Z


Energy•Potential Energy & Conservation of Energy problems

•The relationship between potential energy and Force

•Energy diagrams and Equilibrium


Energy Review

If there is net work on an object, it changes the kinetic energy of the object (Gravity forces a ball falling from height h to speed up Work done.)

Wnet = KIf there is a change in the potential energy, some one had to do some work: (Ball falling from height h speeds up→ work done → loss of potential energy. I raise a ball up, I do work which turns into potential energy for the ball)

UTotal = WPerson =-WGravity


Energy Review

If work is done by a non-conservative force it is negative work (slows something down), and we get heat, light, sound etc.

EHeat+Light+Sound.. = -WNC

If work is done by a non-conservative force, take this into account in the total energy. (Friction causes mechanical energy to be lost)

K1+U1 = K2+U2+EHeat…

K1+U1 = K2+U2-WNC


Potential Energy Diagrams• For Conservative

forces can draw energy diagrams

• Equilibrium points

– Motion will move “around” the equilibrium

– If placed there with no energy, will just stay (no force) 0F dx

dUx


Stable vs. Unstable Equilibrium Points

The force is zero at both maxima and minima but…

– If I put a ball with no velocity there would it stay?

– What if it had a little bit of velocity?


Roller Coaster with FrictionA roller coaster car of mass m starts at rest

at height y1 and falls down the path with friction, then back up until it hits height y2 (y1 > y2).



Roller Coaster with FrictionA roller coaster car of mass m starts at rest

at height y1 and falls down the path with friction, then back up until it hits height y2 (y1 > y2). An odometer tells us that the total scalar distance traveled is d.


Assuming that the magnitude and angle of the force of friction, F, between the car and the track is constant, find |F|.


Bungee JumpA jumper of mass m

sits on a platform attached to a bungee cord with spring constant k. The cord has length l (it doesn’t stretch until it has reached this length).

How far does the cord stretch y?

l


A football is thrownA 145g football starts at rest and is

thrown with a speed of 25m/s.

1. What is the final kinetic energy?2. How much work was done to reach

this velocity?

We don’t know the forces exerted by the arm as a function of time, but this allows us to sum them all up to calculate the work


Robot ArmA robot arm has a funny Force equation in 1-dimension

where F0 and X0 are constants.What is the work done to move a block from position X1 to position X2?

2

0

2

0 x3x

1F F(x)

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Physics 218, Lecture XIII1 Physics 218 Lecture 13 Dr. David Toback.

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