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