physics 218 lecture 13 - texas a&m...
TRANSCRIPT
Physics 218, Lecture XIII 1
Physics 218Lecture 13Dr. David Toback
Physics 218, Lecture XIII 2
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
Physics 218, Lecture XIII 3
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
Physics 218, Lecture XIII 4
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
Physics 218, Lecture XIII 5
Physics 218, Lecture XIII 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 XIII 7
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
Physics 218, Lecture XIII 8
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
Physics 218, Lecture XIII 9
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
Physics 218, Lecture XIII 10
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
x −=
Physics 218, Lecture XIII 11
Force and Potential Energy
Draw some examples…–Gravity–Spring
Physics 218, Lecture XIII 12
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 XIII 13
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+U1Conservation of Mechanical Energy
E2=E1
Physics 218, Lecture XIII 14
Problem Solving• What are the types of examples we’ll encounter?– Gravity– Things falling– Springs
• Converting their potential energy into kinetic energy and back againE = K + U = ½mv2 + mgy
Physics 218, Lecture XIII 15
Problem Solving
For Conservation of Energy problems:
BEFORE and AFTER diagrams
Physics 218, Lecture XIII 16
Conservation of Energy Problems
Before…
Physics 218, Lecture XIII 17
After
Physics 218, Lecture XIII 18
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?
Physics 218, Lecture XIII 19
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?
• ΔU = U2-U1 = Wext = mg (h2-h1)•Write U = mgh•U=mgh + ConstOnly change in potential energy is really meaningful
Physics 218, Lecture XIII 20
Z Z
Before After
C
Falling onto a SpringWe want to measure the spring constant of a certain spring. We drop a ball of known mass mfrom a known height Zabove the uncompressed spring. Observe it compresses a distance C.
What is the spring constant?
Physics 218, Lecture XIII 31
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