WORK AND ENERGY

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WORK AND ENERGY
Work done by a constant force
Kinetic Energy
Gravitational Potential Energy
Simple Machines
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WORK
x
W Fx
SI unit of work Newton-meter Joule
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EXAMPLE
Accelerating a crate on a truck
f ma (150)(2) 300N
If the truck accelerates for x 50 m, the work
done on the crate is
W (f)x 300(50) 15000 J
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KINETIC ENERGY

• The work done on the crate is W max
• Use x 1/2at2
• W 1/2m(at)2 1/2mv2
• Kinetic Energy KE 1/2mv2
• SI unit of kinetic energy Joule
• Work-Energy Theorem W KEf - KEi

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Crate Example Backwards
W 15000J. What is v?
1/2mv2 15000, so v2 30000/m 30000/150
200(m/s)2 v 14.1 m/s
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Example Space Ship

• m 50000kg, v0 10,000 m/s
• Engine force 500,000 N, x 3,000,000m. What is
  final speed?
• W (5105N)(3106m) 1.51012 J
• KEf KEi W 2.51012 1.51012 41012 J
• vf (2KEf/m)1/2 12,600 m/s

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Gravitational Potential Energy

• The gravity force can do positive or negative
  work on an object.
• W mg(h0 - h)
• All that counts is the vertical height change.
• PE mgh

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EXAMPLE PILE DRIVER
Mass is dropped on a nail from a height h. Wg
mgh 1/2mv2
It exerts force F on nail, pushing it into the
wood a distance d, and coming to a stop.
Wn -Fd -1/2mv2
F mg(h/d)
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THE LEVER
Work done on one end work done by the other
end.
fd FD
f/F D/d L/l
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WORK-ENERGY THEOREM GRAVITY DOING THE WORK
W 1/2mvf2 - 1/2mvi2 DKE - DPE
W -?PE
DKE DPE 0
Mechanical Energy E KE PE CONSTANT
When friction can be ignored
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Principle of Conservation of Mechanical Energy

• E remains constant as an object moves provided
  that no work is done on it by external friction
  forces.

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EXAMPLE PENDULUM
Forces Gravity
Tension (does no work)
E KE PE remains constant as
pendulum swings
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BOUNCING BALL
E PE mgh
E KE 1/2mv2
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DOUBLE BALL BOUNCE
A problem in relative motion
Just after big ball hits floor, vbB -2v
Just after little ball hits big ball, vbB 2v
and vbf vbB vBf 3v. How high will it rise?
h vbf2/2g 9v2/2g 9h0
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Using the Conservation of Mechanical Energy

• Identify important forces. Friction forces must
  be absent or small.
• Choose height where gravitational PE is zero.
• Set initial and final KE PE equal to each other

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Roller Coaster

• After a vertical drop of 60 m, how fast are the
  riders going?
• Neglecting friction, mechanical energy will be
  conserved.
• Ei mgh Ef 1/2mv2
• v (29.860)1/2 34.3 m/s (76 mph)

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Roller Coaster Again

• If the final speed is 32m/s, how much work was
  done by friction on a 60 kg rider?
• Wnc Ef - Ei 1/2mv2 - mgh
• 1/260(32)2 - 609.860
• 30700 - 35300 - 4600 J

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Power

• P Work/Time W/t
• SI unit J/s watt (W)
• 1 horsepower (hp) 746 W
• If a force F is needed to move an object with
  average speed vav, then the power required is Pav
  Fvav

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Accelerating a Car

• A 1500 kg car accelerates with a 5m/s2 for 6
  s. What power is needed?
• F ma 7500 N
• vf at 30 m/s so vav 15m/s
• Pav Fvav 1.1105 W (151 hp)

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Car at constant speed

• Car going 60 mph (27 m/s) requires F 200 N to
  overcome friction.
• What power is required from the engine?
• P Fv 20027 5400 W 7.2 hp

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TOUR DE FRANCE
What power does cyclist need?
Air friction force f kv2
P fv kv3
P 1 kW for v 25 mph
What power does Superman need to go 50 mph?
P 1 kW(v2/v1)3 8 kW
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Principle of Energy Conservation

• Energy can be neither created nor destroyed, but
  only converted from one form to another.