● Depends on:
1) Force
2)
Distance/Displacement force is applied
for
● Question: If we apply a force to an object
and it doesn’t move, how much work has
been done?
None, the force did not cause displacement
● Equation:
W = Fd
Units – N*m = Joule (J)
scalar quantity(____________)
no direction
● Work is a ______
● Example: A 50 kg crate is pulled 40 m across a
horizontal surface in 120 s by a force of 150 N.
Find the work done.
force due to gravity (weight) of object that is being
● Use the ___________________
moved to find the amount of work done in lifting the object
● How much work is done lifting a 3 kg backpack a distance of
1.25 m?
● How many calories is this? (1 cal = 4184 J)
0.00896 cal
rate of doing ________
work
● Definition: _________
(how quickly work is done)
● By doing work on an object, you transfer
________
energy from one object to another.
● Equations (see Reference Tables):
Units:
● Example: An electric motor lifts an elevator
that weighs 1.20 x 10 4 N a distance of 9 m in
15 s. What is the power of the motor?
● Example: A person applies a force of 25 N to
a toy car and it moves at an average velocity of
10 m/s. What is the power developed by the
car?
● Definition: “Energy of motion”
● Equation (see ref. tabs.)
KE = ½ mv2
Units:
Joule (J)
KE
v
● Example: A 75 kg skydiver is falling through the air
at 60 m/s. What is the kinetic energy of the
skydiver?
● Definition: Stored energy (based on position)
● Definition: stored energy due to position in
gravitational field
● Equation (see ref. tabs.)
PE = mgh
PE (J)
Units: Joule (J)
Slope = mg
(weight)
h (m)
● Reference Point: Position where gravitational
energy equals zero
Example: What is the gravitational PE of a 100 kg
skydiver that is in a plane 1000 m above the ground?
● Restoring Force: force required to return
spring to its original position
● Spring Constant: (k) (Phet Sim)
“stiffness” of spring
Larger the spring constant, larger the force
● Hooke’s Law (see ref. tabs)
Fs = k x
x = displacement (m)
Fs (N)
Slope = k
k = spring constant (N/m)
x (m)
● Factors that affect how much elastic PE an
object has:
1) Displacement of spring
2) Spring constant
● Equation (see ref. tables)
PEs = ½ k x2
Units: Joules (J)
PEs (J)
x (m)
• Example: A 0.0500 kg mass is hung from a spring
causing it to stretch 0.150 m.
A) What is the spring constant?
B) What is the PE stored in the spring?
• Energy cannot be created nor destroyed
• Therefore, total energy before = total
energy after
• Equation:
Larger Pendulum Version Video
MEbefore = MEafter (Mechanical E = KE + PE)
KEi + PEi = KEf + PEf
More conservation of Energy Animations
More conservation of Energy Animations
∙ Example:
A
B
40 m
C
10 m
If the cart starts from rest, has a mass of 100 kg
and assuming no friction, find the following:
A) The amount of KE and speed at position B.
B) The amount of KE and speed at position C.
∙ Example:
If the cart has a mass of 100 kg and assuming
no friction, find the following:
A) The amount of KE and speed at
position B.
∙ Example:
If the cart has a mass of 100 kg and assuming
no friction, find the following:
B) The amount of KE and speed at
position C.
A. What does the work on a pendulum?
• Gravity (does not take away from total ME)
• Energy is conserved
h = max
PE = max
v=0
KE = 0
ME = PE
h
h
h = 0 v = max
PE = 0 KE = max
ME = KE
h = max
PE = max
v=0
KE = 0
ME = PE
• Energy vs. Horizontal Position Graph
Energy
Horizontal Position