Lecture 8

Chapter 7 Kinetic Energy Mechanical Energy Conservation of Mechanical Energy Non-Conservative Forces Simple Machines 11-Sep-10

Physics 101

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. 11-Sep-10

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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

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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 11-Sep-10

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Question 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? a) 0.50 v

b) 0.707 v

c) v

d) 1.414 v

e) 2.00 v

Physics 101

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Conservation of Mechanical Energy Definition of mechanical energy E: E = KE + PE If the only work done in going from the initial to the final position is done by gravity or springs:

When only gravity or spring forces act Or equivalently:

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Sample Problem

6 kg

What is the speed of the ball just as it hits the ground?

20 m

What is the kinetic energy of a 6kg bowling ball, falling from a height of 20 meters, just as it reaches the ground?

20 m/s

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Physics 101

Conservation of E on Different Paths PE = 1200 J, KE = 0 J

Energy is the “currency” of motion PE = 600 J, KE = 600 J

20 m

10 m

6 kg

PE = 0 J, KE = 1200 J 11-Sep-10

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Conservation of Mechanical Energy (Potential Energy) + (Kinetic Energy) stays constant during motion if the only forces doing work are gravity and spring forces. Energy “bookkeeping” makes motion simple.

Physics 101

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Pendulum Energy exchange from PE to KE and back.

Maximum Height

Maximum Speed

Can predict speed from height since PE+KE constant 11-Sep-10

Maximum Height, again

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Demo: Ball Races Can predict ball speeds along the tracks.

Ball on track B goes the same speed as ball on track A whenever the two balls are at the same height 11-Sep-10

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What is the Final Speed?

v=0

v=4 m/s

v = 1 m/s, 2 m/s, or 3 m/s?

v=5 m/s

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Conservative and Nonconservative Forces Conservative force: the work it does is stored in

the form of energy that can be released as mechanical energy at a later time

Conservative forces: gravity, spring force , electric force, magnetic force

Nonconservative forces: friction, air resistance, motors, “person force”

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Physics 101

Nonconservative Forces In the presence of nonconservative forces, the total mechanical energy is not conserved. The work done by non-conservative forces equals the change in mechanical energy.

∆E = ∆PE + ∆PE = WNC

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Example: Friction Work = ∆E • You (mass 50 kg) are skiing at 10 m/s on a flat frictionless surface. What is your KE? KE = ½mv2 = ½ (50 kg)(10 m/s)2 = 2500 J • You dig your poles into the snow, causing a friction force of 100 N. What distance will you travel before stopping?

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∆E from Friction • ∆E =∆KE = Wfriction = Ffriction d d = ∆KE / Ffriction = 2500J / 100N = 25 m

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Check Yourself Compared with going 30 mph, a car going 60 mph has ____ times the kinetic energy. Four times the KE means ____ times the work required to stop the car. Four times the work means ____ times the distance (same friction force on brakes).

Physics 101

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Stopping & Braking Distance 55’

35’

30 mph

90’ Reaction Distance Braking Distance Stopping Distance

45 mph

70’

60 mph

220’

290’

At twice the speed, braking distance is four times longer 11-Sep-10

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Work & Energy Change When non-conserving forces do work on an object, the work done equals the change in mechanical energy. (small force) X (LONG DISTANCE) (BIG FORCE) X (short distance)

Here two persons do the same work in different ways. You can choose to use less force over a longer distance. 11-Sep-10

Physics 101

Simple Machines The ramp on the previous slide is an example of a “simple machine.” Simple Machine • Device for changing the amount of force used and the distance moved when doing an amount of work. • No work for free, but can use less force over greater distance or more force over shorter distance. 11-Sep-10

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Simple Machines Principle of a simple machine • Conservation of energy (for 100% efficiency): Work input = work output • Input force × input distance = Output force × output distance • (Force × distance)input = (force × distance)output Physics 101

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Simple Machine Example Simplest machine • Lever – rotates on a point of support called the fulcrum – allows small force over a large distance and large force over a short distance

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Simple Machine - Pulley System • “Multiplies” the force you exert

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Machines CHECK Question In an ideal pulley system, a woman lifts a 100-N crate by pulling a rope downward with a force of 25 N. For every 1-meter length of rope she pulls downward, the crate rises A. B. C. D.

50 centimeters. 45 centimeters. 25 centimeters. None of the above.

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Other Simple Machines • Ramp • Gears (Bicycle gears, car transmission)

Engines and Motors • Convert other types of energy (chemical, electrical) to mechanical energy (do mechanical work) • Usually produce some heat energy as well Physics 101

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Efficiency Efficiency • Percentage of work put into a machine that is converted into useful work output • In equation form: Efficiency =

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useful energy output total energy input

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Key Points of Lecture 8 • Kinetic Energy • Mechanical Energy • Conservation of Mechanical Energy • Non-conservative forces -- changing mechanical energy • Simple Machines • Efficiency of Machines z Before next lecture, read Hewitt through Chap. 7 z Homework Assignment #5 is due before 11:00 PM on Thursday, Sept. 16.

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