• Potential energy

• Conservative and non-conservative forces

• CONSERVATION OF ENERGY

Chapter 8: Potential Energy and Conservation of Energy

Reading assignment: Chapter 8.5-8.6

Homework : due Friday, September 30, 2005

Problems: 40, 47, 65, 67, 73, 74

Review Important energy formulas:Work:

22

2

1ifs xxkW

zzyyxx dFdFdF

dF

dFW

cos

2

2

1vmK

f

i

x

x

dxxFW

Work done by spring:

Kinetic Energy:

dfK k

Potential energy U:

- Can be thought of as _________ energy that can either do work or be converted to kinetic energy.

- When work gets done _____ an object, its potential and/or kinetic energy ______________.

- There are different types of potential energy:

1. Gravitational energy

2. Elastic potential energy (energy in an stretched spring)

3. Others (magnetic, electric, chemical, …)

Gravitational potential energy:

ygmU g -Potential energy only depends on y (height) and not on x (lateral distance)

-MUST pick a point where potential energy is considered zero!

)( ififg yymgUUU

You are 1.80 m tall.

A 0.1 kg apple, which is hanging 1 m above your head, drops on you.

What is the difference in gravitational potential energy when it hangs and when it hits you?

1 m

Black board example 8.1

2)(2

1eqxxkU

Elastic potential energy stored in a spring:

Elastic potential energy:

Elastic potential energy depends on the distance from equilibrium

Conservation of mechanical energyIf we deal only with conservative forces and

If we deal with an isolated system (no energy added or removed):

The total mechanical energy of a system remains constant!!!!

UKE The final and initial energy of a system remain the same: Ei = Ef

E… total energy

K… Kinetic energy

U… potential energy

Thus: ffii UKUK

Remember: 2

2

1vmK

Conservative and non-conservative forces

Conservative forces:

Work is independent of the _________ taken.

Work depends _______ on the final and initial point.

Work done is zero if the path is a __________ loop (same beginning and ending points.)

We can associate a potential energy with conservative forces.

Work done by a conservative force:

Examples of conservative forces:

_____________________________________________

UUUW fic

Non-conservative forces:A force is non-conservative if it causes a ______________ in mechanical energy; mechanical energy is the sum of _________ and ____________ energy.

Example: Frictional force.

- This energy cannot be converted back into other forms of energy (irreversible).

- Work does depend on path.

Conservative and non-conservative forces

Sliding a book on a table

A child decides to go go down these 4 meter high (about 13 feet) slides right after an ice storm. The presence of ice on the slide makes the friction between the child and slide negligible. Which slide permits the child to have the greatest change in potential energy?

1 2 3

1

23

4- None of the above

A frictionless roller coaster with an initial speed of vi = 10.00 m/s, at the initial height h = 100.0 m, has a mass m = 1000.0 kg

(a) What is the speed at point A?

(b) What is the speed at point B

(c) How high will it move up on the last hill?

Black board example 8.4

Work done by non-conservative forces

2. Situations involving kinetic friction.(Friction is not a conservative force).

Kinetic friction is an example of a __________________ force. If an object moves over a surface through a distance d, and it experiences a kinetic frictional force of fk it is losing kinetic energy

dfWK kfrictionfriction

Thus, the mechanical energy (E = U + K) of the system is ________________ by this amount.

Black board example 8.7

A spring with a spring constant of 640 N/m is compressed 0.5 m. The compressed spring accelerates a 3.5 kg block. After leaving the spring at the spring’s relaxed length, the block travels over a horizontal surface with a frictional coefficient k = 0.25.

(a) Where does the block have maximum potential energy?

(b) Where does the block have maximum kinetic energy?

(c) How far along the rough horizontal surface does the block travel until stopping?