Transcript Work Energy Theory - McMaster Physics and Astronomy

Work and Kinetic Energy
•
•
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Work by a variable force
Kinetic Energy and the Work-Energy Theorem
Power
Serway & Jewett 7.3, 7.4
Physics 1D03
Determine the work done by a force as the
particle moves from x=0 to x=6m:
F(N)
5
x(m)
0 1
2
3 4 5 6
Physics 1D03
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 Newton’s Second Law, and the definition of Work.
Physics 1D03
• Kinetic Energy is measured in joules (1J=1Nm).
• Kinetic energy is a scalar; the work-energy theorem is a
scalar relation.
• This theorem is equivalent to Newton’s 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.
Physics 1D03
Example
A block of mass 1kg moving with vi=2m/s gets a push of 10N over a
distance of 4m. What is the new speed?
Physics 1D03
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.
Physics 1D03
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:
a)
b)
c)
d)
zero
0.49 J
-0.49 J
none of the above
Physics 1D03
Power
Power is the rate at which work is done:
Average power = Work/Time
units: 1 J/s =1 watt (W)
Instantaneous power: infinitesimal time dt,
displacement dr; work dW = F.dr, and power is
dW
dr
P
 F  Fv
dt
dt
Physics 1D03
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.
a) What is the power supplied by the force?
b) Where does the energy go?
Physics 1D03
a) Free body diagram.
 
P  F v
 (122N)(cos 37)(5.0 m s )
 487 Watt
n
37º
mg
v=5.0 m/s
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.
Physics 1D03
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
a) Increases with time, starting from zero
b) Is large as soon as the elevator starts, then
decreases with time
c) Is constant after the elevator starts to move.
Physics 1D03
Answer: a) Increases with time.
The force required from the motor is constant: 21.6 kN
(19.6 kN to support the weight, plus 2 kN to accelerate
a 2000-kg mass).
The power = force x velocity (F and v are parallel).
Force is constant, but velocity increases linearly with
time, starting from zero, therefore the work increases.
Physics 1D03
Quiz
A 100-kg sprinter accelerates from rest to 10 m/s in
4 seconds. His average power output is about:
a)
b)
c)
d)
2.5 W
1.25 kW
50 kW
It depends on whether accleration is constant
Physics 1D03
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 ?
a) 300 W
b) 180 W
c) 108 W
Physics 1D03
Summary
• Work: W   F dx
• 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.
Physics 1D03