physics 218, lecture xv1 physics 218 lecture 15 dr. david toback

Physics 218, Lecture XV 1

Physics 218Lecture 15Dr. David Toback


Checklist for Today•Things due awhile ago:–Read Chapters 7, 8 & 9

•Things that were due Monday:–Problems from Chap 7 on WebCT

•Things that are due Yesterday in Recitation–Chapter 8–Reading for Lab


The ScheduleThis week: (3/3) • Chapter 7 due in WebCT• 5th and 6th lectures (of six) on Chapters 7, 8 & 9• Chapter 8 in recitation Next 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


Before:– Work and Energy– The Work-Energy relationship– Potential Energy– Conservation of Mechanical Energy

– Conservation of EnergyThis time:

– Summary– More Problems

Chapters 7, 8 & 9 Cont


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!


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 done 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


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

where F0 and X0 are constants. The robot picks up a block at X=0 (at rest) and throws it, releasing it at X=X0. What is the speed of the block?

2

0

2

0X x3x

1F F


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… •Next week: Spring Break•Week after Spring Break

– Homework in WebCT Monday:•Chapter 8

– Reading for Lecture: •Chaps 10 & 11: Momentum

– Recitation: •Chap 9 and Exam review


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

physics 218, lecture xv1 physics 218 lecture 15 dr. david toback

Documents

energy mechanical energy

kinetic energy total

loss of potential energy

lecture xv10 energy

lecture xv9 energy summary

lost mechanical energy

friction slide

lecture xv1 physics