Download Power - Year 11 Physics Motion

Year 11 T1 Wk 8
Power Energy Bits and Pieces
Falling objects
If there is no significant air
resistance then conservation
of energy results in
gravitational potential energy
being converted into kinetic
energy as an object falls.
gain in KE = loss of GPE
m
gpe = mgh
ke = 0
h
v1
gpe = ke
gpe = ½ mgh
ke = ½ mv12
v2
gpe = 0
ke = ½ mv22
ke = mgh
½h
Conservation of Energy
Example
Graphs of GPE and KE
TOTAL ENERGY
= GPE + KE
GPE
Energy
KE
0
object
dropped
0
Time
object reaches
lowest point
Question
A child of mass 40kg climbs a
wall of height 3m and then
steps off. Calculate the speed
at which the child reaches the
bottom of the wall.
Child’s initial gravitational
potential energy:
GPE = m x g x h
= 40kg x 10N/kg x 3m
GPE = 1 200 J
If air resistance is insignificant
then all of this GPE is converted
into kinetic energy
KE = ½ x m x v2
1200 J = ½ x 40kg x (speed)2
1 200 = 20 x (speed)2
1 200 ÷ 20 = (speed)2
60 = (speed)2
speed = 60
speed = 7.75 m/s
Choose appropriate words to fill in the gaps below:
potential energy is the energy stored when an
Gravitational ________
upwards This energy is released when the
object is lifted ________.
falls back to its initial position.
object _____
Kinetic energy is the energy possessed by an object due to its
speed and mass. If the mass of an object is ________
doubled its
_______
kinetic energy doubles. If the speed is doubled the kinetic
four
energy will increase by ______
times.
raised
When a __________
object is released gravitational potential
kinetic
energy is converted into _________
energy.
WORD SELECTION:
falls
speed four kinetic potential upwards
doubled raised
Power (P)
Power is a measurement of how quickly work is done.
power = work done
time taken
P= W
t
power, P is measured in watts (W)
work done, W is measured in joules (J)
time, t is measured in seconds (s)
One watt is the same as one joule per second.
Power is also equal to how quickly
energy is transformed from one form to
another.
power = energy change
time
P=E
t
Power
• The work done every second
• The rate at which work is done or the rate
at which E is consumed
•
• Power = Force × Velocity
Question 1
Calculate the power of a motor that exerts a force
of 40N over a distance of 2m for 10seconds.
W=Fs
= 40 N x 2 m
work done = 80 J
P=W/t
= 80J / 10 s
power = 8.0 W
Question 2
Calculate the power of an
electric motor that lifts a
mass of 50 kg upwards by
3.0 m in 20 seconds.
gain in GPE = m g h
= 50 kg x 10 N/kg x 3 m
= 1500 J
g = 10 N/kg
P=E/t
= 1500 J / 20 s
power = 75 W
Power Example 3
• A student (50kg) climbs stairs of vertical
height 7m in 9s.
• Lifting force = weight: =mg=50x10=500N
• Work done: Fxd = 500 x 7 = 3500J
• PE gained = mgh = 50x10x7=3500J
• Power = E/t = 3500/9 = 389 W
Power Example 4
Power Example 5
• Crane lifts a load of 1200kg onto a building
of height 12m. The carrier of the load has
a mass of 300kg. What minimum power
must the motor of the crane develop to lift
the load in 15s?
• Work done =PE gained (g=10N/kg)
• mgh= 1500x10x12=180 000
• Power = work done/time
• 180 000/15 = 12000w or 12kW
Example 6
Example 7
Measuring a person’s power
1. Measure the weight, W of
person using weighing scales.
s
total stairs
height, h
stairs
of n
steps
person of
weight, W
=nxs
2. Measure the time taken for
the person to run up a flight of
stairs of height, h
3. Work done
= weight x height
=Wxh
=Wxnxs
4. Power of the person
= work done / time taken
= (W x n x s) / t
Example calculation
Weight of person, W = 800N
Time taken, t = 3.0 seconds
s
total stairs
height, h
stairs
of n
steps
person of
weight, W
=nxs
Stairs:
number of steps, n = 12
height of step = 0.20m
total stair height, h
= 12 x 0.20m = 2.4m
Work done
= weight x height
= 800N x 2.4m = 1920J
Power = 1920J / 3.0s
= 640W