Transcript The Work-Energy Theorem

Net Work
Net work (Wnet) is the sum of the work
done on an object by all forces acting
upon the object.
The Work-Energy Theorem
• Consider a force applied to an object
(ΣF ≠ 0).
• Newton’s second law tells us that this
net force will produce an acceleration.
• Since the object is accelerating, its
displacement will change, hence the
net force does work.
The Work-Energy Theorem
 FWs  mas
 F  ma
(v  v ) 2
W
W
 mmv  mvi
2
2
2
f
f
1
2
2
1i
2
 F s  W
v  v  2as
(v  v )
 as
2
2
f
2
f
2
i
2
i
Kinetic Energy
A form of mechanical energy
Energy due to motion
K = ½ m v2
– K: Kinetic Energy in Joules.
– m: mass in kg
– v: speed in m/s
The Work-Energy Theorem
 F  ma
W  mas
W  mv  mv
1
2
2
f
1
2
2
i


KE
Wnet
The Work-Energy Theorem
Wnet = KE
– When net work due to all forces acting upon
an object is positive, the kinetic energy of the
object will increase.
– When net work due to all forces acting upon
an object is negative, the kinetic energy of the
object will decrease.
– When there is no net work acting upon an
object, the kinetic energy of the object will be
unchanged.
Power
Power is the rate of which work is
done.
No matter how fast we get up the
stairs, our work is the same.
When we run upstairs, power demands
on our body are high.
When we walk upstairs, power
demands on our body are lower.
Power
The rate at which work is
done.
Pave = W / t
P = dW/dt
P = F • v
Units of Power
Watt = J/s
ft lb / s
horsepower
• 550 ft lb / s
• 746 Watts
Power Problem
Develop an expression for the
power output of an airplane cruising
at constant speed v in level flight.
Assume that the aerodynamic drag
force is given by FD = bv2. By what
factor must the power be increased
to increase airspeed by 25%?