lecture 7 chapter 7 work energy potential energy kinetic...

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9-Sep-10 Physics 101

Chapter 7Work

Energy Potential EnergyKinetic Energy Energy -- The “money” of physics

Lecture 7


Demo: Elastic CollisionsObjects of equal mass exchange momentum in

elastic collisions.

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Demo: Blaster Balls

When masses unequal, momentum change can be large.

Pingpongball

Golfball

Speed ofping-pong ball

is 3x larger(Slingshot effect)


Demo: Inelastic CollisionsObjects stick together after colliding.

A

A

A

B

B

B

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Check Yourself

Large (4 kg) fish swims at 3 m/s towards a small (2 kg) fish (at rest) and swallows it for lunch.

Total momentum before lunch?

Total momentum after lunch?

Velocity of the large fish (with small fish inside)?


Recoil

Momentum conservation also explains recoil

(MASS) x (velocity) (mass) x (VELOCITY)

Recoil effect is like an inelastic collision in reverse.

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WorkDefine work W done on an object by a force F as

(Work) = (Force) X (Distance traveled)W = F•d

SI Unit of Work: Joule (J)

d is distance along force directionForce acting in direction of motion: Positive work.Force acting in opposite direction: Negative work.Force perpendicular to motion: Zero work


Check YourselfSlaves pull a heavy load.Work done by slaves is

positive, negative, or zero?

Work done by friction force?

Work done by the ground?LOAD

SupportPullFriction

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Work Against & By GravityIn lifting an object of weight mg by a height h, the person doing the lifting does an amount of work W = mgh.If the object is subsequently allowed to fall a distance h, gravity does work W = mgh on the object.


Example: Loading Ship3,000 kg truck is loaded onto a ship by crane that exerts upward force of 31 kN on truck. This force is applied over a distance of 2.0 m.(a) Find work done on truck by crane.(b) Find work done on truck by gravity.(c) Find net work done on the truck.

app app (31 kN)(2.0 m) 62 kJyW F y= ∆ = =

2g (3000 kg)( 9.81 m/s )(2.0 m) 58.9 kJyW mg y= ∆ = − =−

net app g (62.0 kJ) ( 58.9 kJ) 3.1 kJW W W= + = + − =

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Power (P)Power (P)Power is a measure of the rate at which work

is done. If work W done during time t:

SI power unit: 1 J/s = 1 watt = 1 W

Also: 1 horsepower = 1 hp = 746 W


Human Basal Metabolism 80W

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Example: Power of a MotorA small motor operates a lift that raises a load of bricks weighing 500 N to height of 10 m in 20 s at constant speed. Lift weighs 300 N.

What is the power output of the motor?

W = F d = (800N)(10m) = 8000J

P = W/t = 8000J / 20s = 400 W

(400 W = 0.54 hp)


EnergyThe ability to do work.

• Forms of energy:– Mechanical

• Kinetic, Potential; focus for now– Thermal– Chemical– Electromagnetic– Nuclear

• Energy can be transformed from one form to another

• Can be used in place of Newton’s laws to solve certain problems more simply

• Energy units: SI Unit - Joule (J); Calorie (food calorie) = 4.2 kJ; Kilowatt-hour = 3.6 MJ

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Primitive EconomicsDo your job Get paid


Modern Economics

Using money simplifies economics and accounting.

Do your jobGet paid

Buy stuff

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Why Energy HelpsMotion, in general, is hard to calculate.

Using forces, momentum, acceleration, etc. gets complicated because they are all vectors (have magnitude & direction).

Energy is not a vector; it’s just a number.

Can predict motion by figuring out how much energy that motion will “cost.”


Potential Energy (PE)Potential Energy (PE)•Energy an object has because of its position.

•Two kinds of PE in mechanics

• Gravitational

• Spring

• SI Unit of Potential Energy: Joule (J)

• PE can be positive or negative -- depends on choice of where we take PE = 0

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Gravitational Potential EnergyGravitational potential energy of an object is

(Potential Energy) = (Weight) x (Height)PE = m• g• h = mgh

where m is mass of object in kg, h is height of object in m, and g = 9.8 N/kg = 9.8 m/s2

Choose h = 0 to be at a convenient place


Reference Level for Reference Level for PEPEgravgravA location where the A location where the

gravitational potential gravitational potential energy is zero must be energy is zero must be chosen for each problemchosen for each problem

The choice is arbitrary; The choice is arbitrary; the changethe change in potential in potential energy is what mattersenergy is what matters

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Example: Bottle on ShelfA 0.350 kg bottle is on a shelf that is 1.75 m above floor.Find the gravitational potential energy of bottle-Earth system when bottle is on shelf. Take potential energy = 0 when bottle on floor.

PE = mgh = (0.35 kg)(9.8 N/kg)(1.75 m)

= 6.0 J


Sample ProblemWhat is the gravitational potential energy of a

6kg bowling ball at a height of 20 meters above the floor? (Take h = 0 at floor.)

What is gravitational potential energy at zero height?

20 m

6 kg

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Example: Candy Bar EnergyCandy bar has energy content of 212 Cal = 212 kcal = 8.87 x 105 J.If 81.0 kg mountain climber eats the bar, how much altitude ∆y should she be able to gain? (Assume her body is 100% efficient engine)

f iU mgy mgy mg y∆ = − = ∆5

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(8.87 10 J) 1,120 m(81.0 kg)(9.81 m/s )

Uymg∆ ×

∆ = = =

∆PE

∆PE


Kinetic Energy (KE)Energy associated with motion.

Kinetic energy of an object is(Kinetic Energy) = ½ x (Mass) x (Speed)2

KE = ½ m • v2

where m is mass of object in kg and v is speed in m/s.

A stationary object has zero kinetic energy.Kinetic energy is never negative.

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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 and can do work on the nail


KE Example• What is the kinetic energy of a 4.0 kg hammer

moving at 3.0 m/s?• KE = ½mv2

= ½(4.0 kg)(3.0 m)2

= 18 J• How much work could the hammer do on the

nail?• If the force needed to drive the nail is 1800N,

how far would one hammer hit drive the nail?• Which more effective -- double mass of hammer

or double speed of hammer

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Question

b) 0.707 va) 0.50 v e) 2.00 vd) 1.414 vc) v

Car 1 has twice the mass of Car 2, but they both have the same kinetic energy. If the speed of Car 2 is v, approximately what is the speed of Car 1?


Conservation of Mechanical EnergyConservation of Mechanical EnergyDefinition of mechanical energy E:

If the only work done in going from the initial to the final position is done by gravity or springs:

Or equivalently:

When only gravity or spring forces act

E = KE + PE

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Sample ProblemWhat is the kinetic energy of a 6kg

bowling ball, falling from a height of 20 meters, just as it reaches the ground?

20 m

6 kg

20 m/s


Key Points of Lecture 7Key Points of Lecture 7

Before next lecture, read Hewitt through 1st half Chap.7

Homework Assignment #4 is due before 11:00 PM on Sunday, Sept. 12.

Homework Assignment #5 is due before 11:00 PM on Tuesday, Sept. 14.

• Conservation of momentum• Collisions• Work• Power• Energy

• Potential Energy• Kinetic Energy

• Mechanical Energy

lecture 7 chapter 7 work energy potential energy kinetic...

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