AL-Ma’rifa . Int . School
Physics Am – G12
Unit 11/ ( ENERGY and its Conservation ) .
Section1: the many forms of energy
Objectives :
 To know how is a system’s motion related to its kinetic energy
 To write the rotational kinetic energy formula
 To obtain what is the gravitational potential energy
 To define the reference level .
Kinetic energy :
Translational kinetic energy : 𝑲𝑬𝒕𝒓𝒂𝒏𝒔 =
Rotational kinetic energy : 𝑲𝑬𝒓𝒐𝒕 =
Total kinetic energy : 𝑲𝑬𝑻𝒐𝒕 =
𝟏
𝟐
𝟏
𝟐
𝟐
𝑰𝝎
𝒎𝝑 +
𝟏
𝟐
𝟐
𝟏
𝟐
𝒎𝝑𝟐
𝑰𝝎𝟐
Q1: A 52kg skater moves at 2.5m/s and glides to a stop over a distance
Of 24m. find the skater’s initial kinetic energy . how much of her kinetic
Energy is transformed into other forms of energy by friction as she stop?
How much work must she do to speed up to 2.5m/s again?
Q2 : A 875kg car speeds up from 22m/s to 44m/s . what are the initial and final kinetic
energies of the car? How much work is done on the car to increase the speed?
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Q3: A comet with a mass of 7.85x1011kg strikes earth at a speed of 25km/s .find the kinetic
energy of the comet in joules , and compare the work that is done by earth in stopping the
comet to the 4.2x1015J of energy that was released by the largest nuclear weapon ever
exploded .
Q4: A 2kg wheel rolls down the road with linear speed of 15m/s. find its translational and
rotational kinetic energies ( Hint: 𝑰 = 𝒎𝒓𝟐 ) .
Potential energy:
Is an energy stored due to interactions between objects in a system.
In physics , potential energy divides into three parts :
1. Gravitational potential energy : 𝑷𝑬𝒈 = 𝒎𝒈𝒉
2. Elastic potential energy ( in springs ) : 𝑷𝑬𝒔 =
𝟏
𝟐
𝒌𝒙𝟐
3. Electric potential energy : 𝑷𝑬𝒆𝒍 = −𝒒∆𝑽
Gravitational potential energy ( GPE ) :
Reference level : the position where GPE is defined to be zero.
𝑮𝑷𝑬 = 𝒎𝒈𝒉
Work done by gravity ( Wg ) :
 Upward : 𝑾𝒈 = −𝒎𝒈𝒉
 Downward : 𝑾𝒈 = +𝒎𝒈𝒉
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A diagram representation between KE and GPE under gravity :
Q5:
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Q6: if you slowly lower a 20kg bag of sand 1.2m from the truck of a car to the driveway .
how much work do you do?
Q7: A boy lifts a 2.2kg book from the desk , which is 0.8m high to a bookshelf that is 2.1m
high. What is the potential energy of the book – earth system relative to the desk when the
book on the shelf?
Q8: If a 1.8kg brick falls to the ground from a chimney that is 6.7m high . what is the change
in the potential energy of the brick-earth system?
Elastic potential energy ( EPE ) :
Is an energy stored due to pulled or compressed strings .
Mass :
Albert Einstein recognized yet another form of potential
Energy that is proportional to the object’s mass .
He demonstrated that mass represents a form of energy .
The energy is called the rest energy ( Eο ) and can be calculated using the following formula :
𝑬° = 𝒎𝑪𝟐
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Q9: A 25kg shell is shot from a cannon at earth’s surface . the reference level is earth’s
surface.
1. What is the shell- earth system’s gravitational potential energy when the shell’s
height is 425m?
2. What is the change in the system’s potential energy when the shell fails to a height of
225m?
Q10: A 90kg rock climber climbs 45m upward , then descends a 85m . the initial height is the
reference level . find the potential energy of the climber – earth system at the top and at the
bottom . draw bar graphs for both situations.
Other forms of energy :
 Chemical energy : released from the burning of fossil fuels and during digestion.
 Nuclear energy : released with the structure of an atom’s nucleus changes.
 Thermal energy : the sum of the kinetic energy and potential energy of the particles
in a system.
 Radiant energy : carried by electromagnetic waves.
 Electrical energy : associated with charged particles.
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Section2: Conservation of energy.
The law conservation of energy states that :
( in a closed , isolated system energy can neither be created nor
Destroyed , rather energy is conserved ).
That’s mean energy can change its forms , but remains a constant in
All total energy system’s forms.
Mechanical energy :
Its an energy comes from the motion and the interactions between
Objects.
Mechanical energy equal to the sum of all shapes of kinetic and
Potential energies.
But here we will study only the translational KE and GPE .
𝑴𝑬 = 𝑲𝑬 + 𝑮𝑷𝑬
Assume that a 10 N system of a bowling ball falls to the earth , in this case you can find the
( ME =20J ) as shown in the figure below .
Important point :
If the friction does not work on the ball the final
Kinetic energy is equal to the initial GPE regardless
of which the path it follows. ( show the figure ) .
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Conservation of mechanical energy :
The sum of the kinetic energy and potential energy before event is equal to the sum of the
kinetic energy and potential energy after event.
𝑴𝑬𝒊 = 𝑴𝑬𝒇
𝑲𝑬𝒊 + 𝑮𝑷𝑬𝒊 = 𝑲𝑬𝒇 + 𝑮𝑷𝑬𝒇
Conservation and other forms of energy :
1. Roller-coaster : if a hill farther along the
Track were higher than the first one , the
Car – coaster would not be able to climb the
Higher hill because the energy required to do
So would be greater than the total mechanical
Energy of the system.
2. Skiing : when you ski down a steep slope you begin
from rest at the top of the slope and ( ME=GPE ) .
Once you start skiing downhill this
GPE transformed to( KE ) . as you ski down the slope
Your speed increases as more GPE is transformed to ( KE ).
3. Pendulums : we can choose the lowest point of the bob
Bob is the reference level , where GPE = 0 .
At the instant the bob is released from point A
Where ME=GPE transformed to KE at point C
Where GPE = 0 .
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Q11:
Q12: A bike rider approaches a hill at a speed of 8.5m/s. the combined mass of the bike and
the rider is 85 kg . choose a suitable system .
1. Find the initial kinetic energy of the system.
2. If the rider coasts up the hill , assuming the friction is negligible . at what height will
the bike come to rest?
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Q13: A skier starts from rest at the top of 45m – high hill . skis down a 30ο incline into a
valley , and continues up a 40m – high hill . the heights of both hills are measured from the
valley floor. Assume that friction is negligible and ignore the affect of the ski poles .
1. How fast is the skier moving at the bottom of the valley?
2. What is the skier’s speed at the top of the second hill?
3. Do the angles of the hills affect your answers?
Q14: the spring in a pinball machine exerts an average force of 2N on a 0.08kg pinball over
5cm. as a result the ball has both translational and rotational kinetic energy . if the ball is a
uniform sphere ( 𝑰 =
table’s tilts ).
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𝟓
𝟐
𝒎𝒓𝟐 ) . what is the linear speed after leaving the spring? ( ignore the
Analyze Collisions :
Perfectly elastic collision
Normal elastic collision
Momentum is Conserved
Momentum is Conserved
Perfectly inelastic collision
Momentum is Conserved




 m11i  m22i  m11 f  m22 f




 m11i  m22i  m11 f  m22 f
Objects still separate after
Collision .
Kinetic energy is Conserved
 KE i   KE f
Objects still separate after
Objects join together after
Collision .
Collision .
Kinetic energy is not Conserved
Kinetic energy is not Conserved
 KE i   KE f
 KE i   KE f
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


 m11i  m22i  (m1  m2 ) f
Q15:
Q16: An 8g bullet is fired horizontally into a 9kg block of wood on an air table and is
embedded in it. After the collision , the block and bullet slide along the frictionless surface
together with a speed of 10cm/s. what was the initial speed of the bullet?
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Q17: A 91kg hockey player is skating on ice at 5.5m/s . another hockey player of equal mass
moving at 8.1m/s in the same direction hits him from behind , they slide off together .
1. What are the total mechanical energy and momentum of the system before the
collision?
2. What is the velocity of the two hockey players after the collision?
3. How much was the system’s kinetic energy decreased in the collision?
Q18: As shown in the beside figure a child slides down a playground slide. At the bottom of
the slide she is moving at 3m/s . how much energy was transformed by friction as she slid
down the slide?
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Q19: the driver of the car in figure suddenly applies the brakes , and the car slides to a stop.
The average force between the tires and the road is 7100N . how far will the car slide after
the brakes are applied?
Q20: A rock sits on the edge of a cliff as shown in figure .
1. What potential energy does the rock – earth system
Possess relative to the base of the cliff?
2. The rock falls without rolling from the cliff .
What is its kinetic energy just before it strikes the ground?
3. What is the rock’s speed as it hits the ground?
GOOD LUCK
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