Transcript Work and Energy

Work and Energy
Work is done when an external
force is used to change the
energy of the system.
Energy is the ability to create
change or do work.
• Energy and work are both measured in
Joules (J =Nm).
• Energy and work are scalar quantities.
They only have magnitude, no direction
There are many different forms
of Energy:
Kinetic Energy
The energy of motion.
Is the object moving?
1 2
K  mv
2
2
kgm
m
(kg)   2 m  Nm  J
s
s
Gravitational Potential Energy
The energy due to the height of an object.
Does the object have a height?
U g  mgh
m
 kgm 
(kg) 2 (m)   2 m  Nm  J
s 
 s 
Elastic Potential Energy
The energy stored in a stretched or
compressed spring.
Is there a loaded spring?
1 2
U s  kx
2
N 2
 m  Nm  J
m
k = The spring constant
(N/m)
x = distance stretched
or compressed (m)
Internal Energy
The energy transferred to the molecules of
the objects in the due to friction.
HEAT
Is there a force of friction acting?
Eint  fx
f = The force of friction.
∆x = The distance
traveled.
( N )( m)  Nm  J
Chemical Potential Energy
The energy released due to a chemical
reaction.
Is there a chemical reaction
occurring?
Uc  ?
ASK A CHEMISTRY TEACHER
FOR THE FORMULA
Conservation of Energy
For a closed system the sum of the
original energy (Eo) and the work (W)
done is equal to the final energy (Ef).
Eo  W  E f
Using Pie Charts to understand
Energy transfers
Example 1:
v = 0m/s
A ball is dropped from rest. (Include air friction)
A
B
Eint
A
C
B
Eint
K
Ug
=
Ug
D
=
K
C
Eint
Ug
=
K
D
h=0
Example 2:
A pendulum swings from A to E
(Neglect air resistance)
V=0m/s
E
V=0m/s
A
B
D
h =0
A
Ug
C
B
=
Ug
C
K
=
K
D
=
Ug
E
K
=
Ug
Example 3:
A spring launches a block across a horizontal table.
v=0m/s
v=0m/s
v
A
v
B
A
D
C
C
B
D
Eint
Us
=
K
=
Eint
K
=
Eint
Example 4:
A biker rides up a hill with at a constant speed.
v
D
C
8m
v
B
h=0
A
A
Ug
K
UC
C
B
=
Ug
K
=
UC
D
K
K
=
UC
Ug
UC
Let’s do some quantitative
problems:
Example 1:
A ball is dropped from a height of 15 meters. What is its
velocity just before it hits the ground?
E0  W  E f
v = 0m/s
Ug  K
1 2
mgh  mv
2
v  2 gh
m
m
v  2(10 2 )(15m)  17.3
s
s
15m
h=0
v
Example 2:
A pendulum is released from rest at point A and has a
velocity of 6 m/s at point C. Find the initial height (h) from
which the pendulum was released. (Neglect air resistance)
E0  W  E f
Ug  K
1 2
mgh  mv
2
2
v
h
2g
m 2
(6 )
s
h
 1. 8m
m
2(10 2 )
s
V=0m/s
A
h
C
v = 6m/s
Example 3:
A spring is compressed 20cm and launches a 400 gram
block across a horizontal table. The block comes to rest
after traveling 5 meters. The coefficient of friction is 0.6.
What is the spring constant (k)?
v=0m/s
v=0m/s
E0  W  E f
U s  Eint
1 2
kx  fx
2
5m
2 fx
k 2
x
2 mgx
k
2
x
f  F  mg
N
 600
m
Example 4:
A 70kg biker has a velocity of 10m/s at the bottom of a 8
meter hill. The biker does 6000J of work in climbing the hill
and 2000J is transferred to internal energy as he climbs the
v
hill. What is the final velocity of the biker?
E0  W  E f
8m
10m/s
K o  6000  U g  Eint  K f
9500  35v 2  7600
m
1 2
1 2
v  7.37
mv  6000  mv  mgh  2000
s
2
2
1
1
2
(70)(10 )  6000  (70)v 2  (70)(10)(8)  2000
2
2