5.4 Efficiency of Energy Transformations
SPH 3U
Power – the rate at which work is done OR the rate at which electrical
potential energy is converted into other forms of energy
Power =
P=
W
t
OR
P=
OR
P=
E
t
Work is measured in __________. Time is measured in __________.
Therefore, power is measured in __________.
J
The unit of power is also called the ___________. Therefore, 1 = 1 Watt.
s
Example 1: The power rating of a light bulb is 100.0 W. Determine the
amount of electrical energy converted into light and heat energy by the
filament of the bulb in 20.0 seconds.
Example 2: Calculate the power rating of a light bulb that used 36 kilojoules
of energy in 10 minutes.
Example 3: A crane lifts a 100 kg object up in the air with a constant speed of
120 cm/s. The crane lifts the object for a total time of 12 seconds. Assume
the energy transfer is 100 % efficient (all the energy used by the crane is
converted into mechanical energy used to lift the object).
a) Calculate the force of gravity acting on the object
b) Calculate the force applied by the crane to lift the object
c) Calculate the power
d) Calculate the work done by the crane
e) Calculate the distance the object moves
Example 4: In the heart, blood flows through the aorta, as the heart applies
an average force of 4.8 N to the blood. In 0.50 seconds, the blood moves a
distance of 15 cm from the aorta. Calculate the work done by the heart, and
the power of the heart.
Automobile
When a car is driven, the only useful energy conversion is from the chemical
potential energy of the fuel to _________ energy (or moving the car). However,
sound is produced, heat is produced (exiting exhaust and the engine gets
warmer) and the ____________ is not being used for its intended purpose (to
move the car).
For example, if EK = 4 000 J and Eheat = 10 000 J and Eloss due to air
resistance = 8 000 J the Echemical potential required is ____________.
Light Bulb
For example, if Eheat = 6 000 J and Elight = 600 J, the Eelectrical is ________.
- electrical energy is converted into light energy, but heat is also produced
(this is not useful energy)
Efficiency =
useful output energy
x 100 %
input energy
Cars – only about 10% of its total input energy (from fuel) contributes to the
motion of the car.
Incandescent light bulb – only 5% of its input energy (electricity) is
converted to light energy.
NB. USEFUL OUTPUT ENERGY IS ALWAYS ________________ TOTAL
INPUT ENERGY since efficiency is always _______________.
Example 1: A 40.0 W high efficiency light bulb is turned on for 5.0 minutes.
During that time, 3.0 x 103 J of light energy is produced. Calculate
a) the total input energy for the light bulb
b) the efficiency of the light bulb
Example 2: The efficiency of a pencil sharpener is 11.0 %. The amount of
electrical energy required to sharpen a pencil is 402 J. Calculate the amount
of mechanical energy required by the sharpener.
Example 3: The mass of a car is 1500 kg. When the car is moving at 100
km/h, the efficiency of the car is 15%.
a) Calculate the kinetic energy of the car
b) Calculate the input energy of the car
c) Why does the efficiency of a car depend on the speed of the car? Why is
the efficiency of a car lower at 150 km/h than 100 km/h?
d) What is the efficiency of a car when it is stopped at a stop light/sign?
Example 4: A solar cell used in a calculator has a typical efficiency of 12 %
(12 % of the light energy is converted into electrical energy). A calculator
requires at least 1 Joule of energy every 5 seconds to function correctly.
Determine the minimum amount of light energy that the solar cell requires in
order to power the calculator.
Practice Problem:
1) A light bulb uses 15 000 J of electrical potential E and converts it into
heat and light. The amount of heat energy produced is 12 000 J. Calculate
the amount of light energy produced, and the efficiency of the bulb.
(Ans: 3 000 J, 20 %)
Supplemental Energy Questions
1. The speed of a 1500
kg object is 60 km/h.
Calculate the kinetic
energy of the object.
2. In the aorta, blood
flows at a speed of 30.0
cm/s. Every 1.00 s,
approximately 100.7 g of
blood flows out of the
aorta. Calculate the Ek of
the blood.
4. A 10 N force is applied 5. The work done by a
to an object over a
motor while lifting an
distance of 200 cm.
object 50 m is 1.2 kJ.
Calculate the work done
Calculate the force
by the force.
applied by the motor on
the object.
7. The change in Eg of an
object while being lifted
is 2000 J. The mass of
the object is 500 grams.
Calculate the increase in
the objects’ height.
10. A light bulb converts
30 kJ of electrical
energy into heat and light
energy in 8 minutes and
20 seconds. Calculate the
power rating for the light
bulb.
8. The density of blood is
1.06 grams/ml. Calculate
the change in Eg for 2.0
mL of blood as it travels
from your feet to your
heart (h = 1.1 m).
11. A crane lifts an
object and does 800 kJ
of work on the object.
The power rating of the
crane is 10 kW. Calculate
the time it takes for the
crane to lift the object.
3. A wrecking ball (mass
is 2000 kg) has 600 kJ of
kinetic energy. Calculate
the speed of the
wrecking ball.
6. A car slams on the
brakes. The work done
by the braking force on
the car is 10.5 kilojoules.
The braking force is 1.65
kN. Calculate the braking
distance.
9. A book (mass is 1.021
kg +/- 0.001 kg) is lifted
2 m +/- 0.1 m. Calculate
the range of the change
in gravitational potential
energy of the book.
12. An electrical motor
has a power rating of
0.50 watts. It is turned
on for 6.0 minutes.
Calculate the amount of
energy that was
converted from Eelectrical
into mechanical energy.
13. A remote control car moves at a constant velocity of 60.0 cm/s. To
maintain a constant velocity, the power of the motor is 180 mW. The car is
run for 10 seconds. Calculate
a) the energy converted from electrical energy into mechanical energy
b) the distance the car moved
c) the force of resistance the car experienced while moving at constant
velocity
Answers: 1. 208333.33 J 2. 4.532x10-3 J
N 6. 6.36 m 7. 408.16 m 8. 0.023 J
9. 18.99 J <  Eg < 21.03 J 10. 60 Watts
1.8 Joules, 6 metres, 0.3 Newtons
3. 24.49 m/s
11. 80 m
4. 20 J
5. 24
12. 180 Joules
13.
Work, Energy and Power Questions
1. In order to infiltrate a factory and having only a giant catapult with them,
the army decides to launch their troups into the factory. If the average
force acting on them is 1.0 kN and the catapult moves a total distance of
10 cm, find the work done on the army. (W = 100N)
2. The McLaren Mercedes (mass is 707.002 kg) is dominating an F1 race, when
all of the sudden, an old lady jumps onto the track. The driver immediately
slams on the brakes at the first sight of the lady and comes to a complete
stop. If the lady is initially standing 99.99 m away from the F1 car:
a) find the change in kinetic energy of JPM’s McLaren Mercedes F1 supercar
if his initial velocity is 90.0 m/s.(∆Ek = 2.86 x 106 J)
b) find the minimum braking force required if the car does not hit the lady.
(F = 2.86 x 104 J)
c) if the mass of the car was doubled, what would happen to the braking
force required to stop the car in the same distance? (double)
3. In the final minute of play, the Team Canada are up and their opponents
pull their goaltender. Captain Canada, SC87, grabs the puck (mass = 0.555
kg) from his own end and fires it along the ice towards the open net, with
an initial velocity of 25 m/s. If the force of resistance is 2.0 N, and the
initial distance the puck is from the goal is 80.0 m, do the Canadians score
the insurance goal? (Yes)
4. Rampage Jackson (mass is 90 kg) is squaring off against Brock Lesner (110
kg). Rampage lifts Lesner with a constant velocity of 0.33 m/s for 4.0 s. s
a) I) What is the force of gravity acting on Lesner? (ans: 1078 N)
II) Calculate the applied force (ans: 1078 N)
III) How the work done by Rampage while lifting Lesner? (ans: 1423 J)
IV) Calculate Jackson’s power (ans: 356 W)
b) While holding Lesner in the air, Jackson walks 2.0 m across the ring. How
much work has he done on Lesner? (0 kJ)
5. An elevator motor uses 7500 W of power and the efficiency is 15%. If the
mass of the elevator is 300 kg, how long does it take him to reach the top
floor, which is 20.0 m above from his initial position? (52 s)
6. As Mr. Belas drives to this destination, his car (1000 kg) is moving at a
constant velocity of 76 km/h. The efficiency of the car is 8%. Calculate
the input energy for the car. (ans: 2 785 493.8 J)
7. A trophy hunter decides to fly around in a helicopter to see if he could
catch a rare bird, when suddenly he spots one, and fires a net (mass is 4
kg) towards it. If the initial velocity of the net is 5 m/s [D], and the net is
initially at a height of 100 m above the ground, what is the velocity of the
net just before it hits the ground (assume conservation of mechanical
energy, no air resistance)? (ans: 44.55 m/s)
8. If a cream pie (0.500 kg) is dropped from a height of 2.50 m above the
students head, and 5.00% of the pies initial energy is lost due to air
resistance while it is falling,
a) what is the initial energy of the pie (12.2 J)
b) how much energy is lost while falling (0.6 J)
c) how much energy does the pie have before it hits the student (11.6 J)
d) what is the velocity of the pie when it hits the student (6.81 m/s [D])