Last Thoughts on Work Work can be done by friction

Friction always opposes motion so the work it does is usually negative. (exceptions are like conveyor belt.)

Friction is a “dissipative force.” Turns Mech. Energy into another form:

often useless heat.Sometimes called non-conservative force, since it doesn't conserve mechanical energy.

Kinetic EnergyEnergy associated with the motion of an object

Scalar quantity with the same units as work

Work is related to kinetic energy

2mv2

1KE

K.E. Is not momentum p = momentum

p = mv p is a vector p is always conserved in a closed system. Always. Always. Always.

K.E. = 1/2mv2

K.E. Is a scalar

K.E. Is not always conserved. It can turn into any other form of energy.

Work-Kinetic Energy Theorem When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy

Speed will increase if work is positive

Speed will decrease if work is negative

net fiW KE KE KE

Work and Kinetic Energy An object’s kinetic energy can also be thought of as the amount of work the moving object could do in coming to rest The moving hammer has kinetic energy.

The hammer will be doing work on the nail.

Types of Forces

There are two general kinds of forcesConservative

Work and energy associated with the force can be recovered.

(Usually means all the energy stays as some form of mechanical energy. Put ME in to the system and get ALL the ME out.)

NonconservativeThe forces are generally dissipative and work done against it cannot easily be recovered

More About Conservative ForcesExamples of conservative forces include:Gravity (Roller Coaster, lift a brick)

Spring force (Pull a spring)Electromagnetic forces (Magnetic crane at junk yard lifting a car)

Potential energy is another way of looking at the work done by conservative forces

Conservative Forces A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the pointsThe work depends only upon the initial and final positions of the object

Any conservative force can have a specific potential energy for each point in space.

(move brick straight up 2 feet. 2nd. Spin around in circles and move brick up 2 feet.)

Nonconservative ForcesA force is nonconservative if:

The work it does is path dependent.

Examples of nonconservative forcesKinetic friction, air drag.

Friction Depends on the Path

Which path loses more energy to friction?

Red or Blue?

Friction Depends on the Path

Which path loses more energy to friction?

Red or Blue?

Red, because the path is longer.

Pushing the book backwards across the table won't give you the energy back.

Potential EnergyPotential energy is associated with the position of the object within some systemPotential energy is a property of the system, not the object.

Assuming no friction, ME of the system is constant. It can transfer from one object to another in the system.

Work and Potential EnergyFor every conservative force, a potential energy is associated with each position.

Think about a projectile. When the object falls, it “gets the energy back” that went into elevating it.

(Royals hitting a foul ball up into top deck vs ball falling back down to 1st row.)

Reference Levels for Gravitational Potential Energy A location where the gravitational potential energy is zero must be chosen for each problemThe choice is arbitrary since the change in the potential energy is the important quantity

Choose a convenient location for the zero reference heightOften the Earth’s surfaceMay be some other point suggested by the problem

Once the position is chosen, it must remain fixed for the entire problem.

(Go back to Royals picture. Where does problem suggest as Frame of Ref? 3 good choices, bat height, top of flight, ground, but could do anything such as center of the earth.)

Reference Levels At location A, the desk may be the convenient reference level

At location B, the floor could be used

At location C, the ground would be the most logical reference level

The choice is arbitrary, though,

it must remain fixed for the entire problem.

Conservation of Energy, cont.

Total mechanical energy is the sum of the kinetic and potential energies in the system.

ME = KE + PE of any point in the system.

Equation: ME = KE + PE = constantThis is only valid in the absence of friction!

ffii

fi

PEKEPEKE

EE

Additional Questions: 1.) Above KE everywhere, add v =2.) Above v = everywhere, add ME=3.) What is mass?

Below the Line write:1.) Equation for ME.2.) Equation for KE.3.) Equation for PE.MEMORIZE these for the test.

Problem solving strategy:

1)“Where did the energy start out?”

2)“How much of it was changed?”--(work)

3)“Where did the energy end up?”4)Did the path matter?

Discuss:Where is work positive and negative and relate it to velocity of skier.

The Work-Energy Theorem and Kinetic Energy

Example 4 Deep Space 1

The mass of the space probe is 474-kg and its initial velocityis 275 m/s. If the 56.0-mN force acts on the probe through adisplacement of 2.42×109m, what is its final speed?

The Work-Energy Theorem and Kinetic Energy

2212

f21W omvmv

sF cosW

6.2 The Work-Energy Theorem and Kinetic Energy

2

212

f2192- sm275kg 474kg 474m1042.20cosN105.60 v

2212

f21cosF omvmvs

sm805fv

The gymnast leaves the trampoline at an initial height of 1.20 mand reaches a maximum height of 4.80 m before falling back down. What was the initial speed of the gymnast?

Gravitational Potential Energy

2212

f21W omvmv

fo hhmgW gravity

221

ofo mvhhmg

foo hhgv 2

sm40.8m 80.4m 20.1sm80.92 2 ov

Example 11 Fireworks

A bottle rocket is set off. It flies upwards 29 m from it’s original height, and the propellant supplies 425 J, what is the final speedof the rocket. Ignore air resistance. Mass = .2kg

Nonconservative Forces and the Work-Energy Theorem

2212

21

ofofnc mvmvmghmghW

2

21

2

kg 20.0

m 0.29sm80.9kg 20.0J 425

fv

221

fofnc mvhhmgW

sm61fv