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Lecture 08: Conservative Forces and Potential Energy
Physics 2210Fall Semester 2014
Announcements
● Exam #1 breakdown:● High score: 99%● Average score: 65% (last year exam #1 → 59%)● Standard deviation 21%
● Note: lowest exam score will be dropped in computing your final grade.
Unit 8: Prelecture Feedback
Mechanics Lecture 8, Slide 3
● Examples similar to homework, rather than reviewing checkpoints
● Need to understand equations in more depth
● ...especially springs. Parabola?
Today's Concepts:a) Conservative Forcesb) Potential Energyc) Mechanical Energy
Mechanics Lecture 8, Slide 4
Work-Kinetic Energy Theorem
Mechanics Lecture 8, Slide 5
The net work done on a body is equal to the change in kinetic energy of the body
Formal definition of work(“Force times distance” generalized)
Formal definition of kinetic energy
Work-Kinetic Energy Theorem
If there are several forces acting then W is the work done by the net (total) force:
Mechanics Lecture 8, Slide 6
You can just add up the work done by each force
...21 ++= WW
TOTNET WW =
WNET
= K
Example
I move an object from the surface of the Earth to a height of one Earth radius above the Earth, and to a position on the far side of the Earth from the launch position. The object is at rest with respect to the Earth before and after the move.
What is the work that I must do on the object? If the object were instead moved to “infinity” (or at
least very, very far away), what work must I do?
Conservative force: Force with the property that, the work done by the force between r
1 and r
2 is
independent of the path taken.
Consequence: The work done by a conservative force around a closed loop = 0.
● Two conservative forces in this course:● Gravity● Springs
Today's Concepts:a) Conservative Forcesb) Potential Energyc) Mechanical Energy
Mechanics Lecture 8, Slide 9
Potential Energy
Can use the properties of conservative forces to store...
“the ability to do work” ≡ “energy”
Example: Store Energy by Raising a Ball
Initial position
Final position
Today's Concepts:a) Conservative Forcesb) Potential Energyc) Mechanical Energy
Mechanics Lecture 8, Slide 12
Gravitationalpotential energy
Kinetic energy
Mechanical Energy = constant of motion, when only conservative forces are present
Example
The bob (mass = m) of a simple pendulum of length L is released from rest at a height H above the equilibrium position.
Compute the tension in the rod when the bob returns to the equilibrium position.
kx2
Another Conservative Force: Springs
Mechanics Lecture 8, Slide 15
x
M
Vertical case: zero potential energyin equilibrium position with mass attached
Generalize mechanical energy conservation to conservative systems including springs:
Spring P.E. K.E.
Gravitational P.E.
Mechanical Energy
Example
A mass M is in contact with a spring (constant k) which is compressed by an amount x
c from the
equilibrium position. After release from rest, the mass detaches from the spring, slides along the frictionless floor and then up the frictionless ramp. What is the height H to which the mass slides before reversing direction?
M
H
Homework Example
● Block slides down frictionless ramp and compresses spring. How much?
● Apply conservation of mechanical energy.
● Does hblock
change
after block contacts spring?
Homework Example
● Block slides down frictionless ramp and completes “loop-the-loop”. From what minimum height?
● Apply conservation of mechanical energy.
Summary: Potential energy change:
Mechanics Lecture 8, Slide 20