Announcements
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Exam #1 breakdown:
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High score: 99%
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Average score: 65% (last year exam #1 → 59%)
Standard deviation 21%
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Note: lowest exam score will be dropped in computing your final grade.

Unit 8: Prelecture Feedback
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Examples similar to homework, rather than reviewing checkpoints
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Need to understand equations in more depth
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...especially springs. Parabola?
Mechanics Lecture 8, Slide 3

Today's Concepts:
Mechanics Lecture 8, Slide 4

Work-Kinetic Energy Theorem
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
Mechanics Lecture 8, Slide 5

Work-Kinetic Energy Theorem
If there are several forces acting then W is the work done by the net (total) force:
W
NET
=  K
= W
1
+ W
2
+ ...
You can just add up the work done by each force
W
NET
= W
TOT
Mechanics Lecture 8, Slide 6

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.
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Two conservative forces in this course:
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Gravity
Springs

Today's Concepts:
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
Final position
Initial position

Today's Concepts:
Mechanics Lecture 8, Slide 12

Mechanical Energy
= constant of motion, when only
conservative forces are present
Gravitational potential energy
Kinetic energy

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.

Another Conservative Force: Springs x kx 2
M
Vertical case: zero potential energy in equilibrium position with mass attached
Mechanics Lecture 8, Slide 15

Generalize mechanical energy conservation to conservative systems including springs:
Mechanical Energy
Spring P.E.
K.E.
Gravitational P.E.

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?
H
M

Homework Example
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Block slides down frictionless ramp and compresses spring.
How much?
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Apply conservation of mechanical energy.
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Does h block
change after block contacts spring?

Homework Example
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Block slides down frictionless ramp and completes “loop-theloop”. From what minimum height?
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Apply conservation of mechanical energy.

Summary: Potential energy change:
Mechanics Lecture 8, Slide 20