Work and Kinetic Energy

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Work and Kinetic Energy

• Work by a variable force
• Kinetic Energy and the Work-Energy Theorem
• Power

Serway Jewett 7.3, 7.4
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Determine the work done by a force as the
particle moves from x0 to x6m
F(N)
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x(m)
0 1 2 3 4 5 6
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Kinetic Energy
Definition for a particle moving with speed v,
the kinetic energy is
K ½ mv2
(a SCALAR)
Then the Work-Energy Theorem says
The total work done by all external forces acting
on a particle is equal to the increase in its
kinetic energy.
Proof from Newtons Second Law, and the
definition of Work.
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• Kinetic Energy is measured in joules (1J1Nm).
• Kinetic energy is a scalar the work-energy
  theorem is a scalar relation.
• This theorem is equivalent to Newtons Second
  Law. In principle, either method can be used for
  any problem in particle dynamics.
• The energy approach works most easily with
  forces and velocities as functions of position,
  rather than time.

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Example
A block of mass 1kg moving with vi2m/s gets a
push of 10N over a distance of 4m. What is the
new velocity ?
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Example
A bartender slides a 1-kg glass 3 m along the
bar to a customer. The glass is moving at 4 m/s
when the bartender lets go, and at 2 m/s when the
customer catches it. Find the work done by
friction, and calculate the force of friction.
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Quiz
A spring is hanging vertically. A student
attaches a 0.100-kg mass to the end, and releases
it from rest. The mass falls 50 cm, stretching
the spring, before stopping and bouncing
back. During the 50-cm descent, the total work
done on the mass was

1. zero
2. 0.49 J
3. -0.49 J
4. none of the above

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Power
Power is the rate at which work is done
units 1 J/s 1 watt (W)
Average power Work/Time
Instantaneous power infinitesimal time dt,
displacement dr work dW F.dr, and power is
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Example

• A 100kg block is pulled at a constant speed of
  5.0m/s across a horizontal floor by force of 122N
  directed 37º above the horizontal.
• What is the power supplied by the force?
• Where does the energy go?

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122N
a) Free body diagram. b) The table
(friction) does negative work on the block. The
frictional work transfers energy to the random
thermal motion of atoms of the block, table
air.
n
37º
v5.0 m/s
mg
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Concept Quiz
A 2000-kg elevator starts from rest and moves
upwards with a constant acceleration of 1.0 m/s2.
The power required from the motor

1. Increases with time, starting from zero
2. Is large as soon as the elevator starts, then
   decreases with time
3. Is constant after the elevator starts to move.

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Quiz

• A 100-kg sprinter accelerates from rest to 10 m/s
  in 4 seconds. His average power output is about
• 2.5 W
• 1.25 kW
• 50 kW
• It depends on whether accleration is constant

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Quiz
The resistance to the motion of a racing bicycle
on a smooth level road is mostly due to air
resistance. The force of air resistance is
proportional to the square of the speed (Fair
v2). A cyclist uses 500 W of power to ride at 50
km/h. What power does he need to ride at 30 km/h
?

1. 300 W
2. 180 W
3. 108 W

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Summary

• Work
• To stretch an ideal spring W ½ kx2
• Kinetic Energy K ½ mv2
• Work-energy theorem The total work is equal to
  the change in kinetic energy.