CONSERVATION OF ENERGY
CONSERVATION OF ENERGY
For an isolated system, energy can be
transformed to different forms, but cannot
be created or destroyed.
INTERESTING IDEA
https://www.youtube.com/watch?v=PplaBASQ_3M
ISOLATED SYSTEM
A system of objects from which no energy can
escape and there are no outside influences
What is the biggest isolated system?
How can we change energy in an isolated system?
WORK-ENERGY THEOREM
The total work done on an object equals the change in
kinetic energy, if there is no other change in any other
form of energy.
𝑊 = ∆𝐸
ANALYZING WORK-ENERGY THEOREM
What types of energy can we calculate?
DERIVE 𝐸𝑘 =
Start from Work
1
2
𝑚𝑣
2
KINETIC ENERGY
Energy is caused by the movement of an
object
𝐸𝑘 =
1
2
𝑚𝑣
2
Ek – Kinetic energy (J)
m – mass (kg)
v – speed (m/s)
DERIVE 𝐸𝑔 = 𝑚𝑔ℎ
Start from Work
GRAVITATIONAL POTENTIAL ENERGY
Energy is apparent due to an object’s position in a
gravitational field
𝐸𝑔 = 𝑚𝑔ℎ
Eg – Gravitational potential energy (J)
m – mass (kg)
g – gravitational field strength (N/kg)
h – Height above a reference level (m)
EXAMPLE # 1
A basketball player shoots a ball at a speed of 10.0m/s.
The ball leaves the player’s hand at a height of 1.98 m
and goes through a 10.0 foot high hoop. Calculate the
speed of the ball as it goes through the hoop if air friction
is neglect able. Note: 1 inch = 2.54 cm (Use energy)
EXAMPLE # 2
A physics student slides down a hill on a sled. The mass of
the sled and the physics student is 70.0 kg. The student
has a speed of 10.0 m/s at the bottom of the hill and
slides a horizontal distance of 34.0 m from the bottom of
the hill. Calculate the coefficient of friction between the
snow and the sled.
SPRING MOTION
When a spring is stretched and let go, the force that is produced is a function of the
stretch of the spring
We call this a Restorative Force
Fspring  kx
k – spring constant (N/m)
x – displacement (m)
Why would the negative sign be present?
DETERMINE THE SPRING CONSTANT
DERIVE 𝐸𝑒 =
Start from Work
1
2
𝑘𝑥
2
EXAMPLE
A spring (k=20N/m) is compressed 30cm by a
ball (m= 100g) and fired upwards. How fast
will the object be moving after it has a vertical
displacement of 20cm after it leaves the
spring?
26. A 0.20 kg mass is hung from a vertical spring
of force constant 55N/m. When the spring is
released from its unstretched equilibrium position,
the mass is allowed to fall. Use the conservation of
energy to determine:
a) the speed of the mass after it falls 1.5cm.
b) the distance the mass will fall before reversing
direction
EXAMPLE
A 35kg child is bouncing on a pogo stick, if the spring constant is 4945N/m and it is
compressed by 25cm, how high will the child bounce?