physics 218, lecture xiv1 physics 218 lecture 14 dr. david toback
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Physics 218, Lecture XIV 2
Checklist for Today•Things due awhile ago:–Read Chapters 7, 8 & 9
•Things that were due Yesterday:–Problems from Chap 7 on WebCT
•Things that are due Tomorrow in Recitation–Chapter 8–Reading for Lab
Physics 218, Lecture XIV 3
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
Physics 218, Lecture XIV 4
Before:– Work and Energy– The Work-Energy relationship– Potential Energy– Conservation of Mechanical Energy
This time and next time:– Conservation of Energy– Lots of problems
Chapters 7, 8 & 9 Cont
Physics 218, Lecture XIV 6
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
Physics 218, Lecture XIV 7
Mechanical Energy
•We define the total mechanical energy in a system to be the kinetic energy plus the potential energy
•Define E≡K+U
Physics 218, Lecture XIV 8
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
Physics 218, Lecture XIV 9
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
Physics 218, Lecture XIV 10
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?
Physics 218, Lecture XIV 11
Quick Problem
A refrigerator with mass M and speed V0 is sliding on a dirty floor with coefficient of friction .
Is mechanical energy conserved?
Physics 218, Lecture XIV 12
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!
Physics 218, Lecture XIV 13
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!
Physics 218, Lecture XIV 14
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)
Physics 218, Lecture XIV 15
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
Physics 218, Lecture XIV 16
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?
Physics 218, Lecture XIV 17
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
Physics 218, Lecture XIV 18
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
Physics 218, Lecture XIV 19
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
Physics 218, Lecture XIV 20
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?
Physics 218, Lecture XIV 21
Coming up… •Lectures:
– Last lectures on Chaps 7, 8 and 9•Chapter 7 was due in WebCT on Monday
•For Recitation– Chap 8 problems due – Lab reading
•Reading for Lecture next week– Chaps 10 & 11: Momentum
Physics 218, Lecture XIV 23
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
Physics 218, Lecture XIV 24
Energy•Potential Energy & Conservation of Energy problems
•The relationship between potential energy and Force
•Energy diagrams and Equilibrium
Physics 218, Lecture XIV 25
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
Physics 218, Lecture XIV 26
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
Physics 218, Lecture XIV 27
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
Physics 218, Lecture XIV 28
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?
Physics 218, Lecture XIV 29
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).
Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path?
Physics 218, Lecture XIV 30
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 we don’t know anything about the friction or the path, how much work is done by friction on this path?
Assuming that the magnitude and angle of the force of friction, F, between the car and the track is constant, find |F|.
Physics 218, Lecture XIV 31
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
Physics 218, Lecture XIV 32
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