A marble with a mass of .002 kg and a velocity of 2m/s hits
another stationary marble of equal mass. After the elastic
collision, they have equal forward velocities and exactly opposite
0.5 m/s sideways speeds.
What is the forward velocity component after the collision?
What is their overall velocity?
Choose either:
A person pushes a 1000 kg car sideways
along flat ground with a force of 4000
N for a distance of 100 m. Then,
without being pushed, the car rolls up a
hill. How high up the hill does it get
before coming to a stop?
Simplify:
2x -2*(3-x)=0
5x^2 + 2y = z
where x=4, y=-1
solve for z
3/x + 2 = -3
Answers: 40 meters, x=3/2, z=78, x=-3/5
Opening Activity
1) An engine piston moves forwards 1 m with a force of 100N . Then it
moves backwards 1 m with a force of 25 N. How much work is done per
cycle? If the engine is moving at 1500 rpm (rotations per minute), how
many Watts is it producing?
2) An engine does 15,000 J of work on a motorcycle, which has a mass of
150 kg. Assuming it started at 0 m/s, how fast is the motorcycle now
moving?
Energy, Work, and Power
Wednesday, November 9th, 2011
Energy is the ability to cause change, and is measured in Joules (J).
Law of Conservation of Energy - Energy can be transferred from object to
object, and can change form, but never just disappears.
Kinetic Energy – Large-scale motion. (Joules)
KE = ½ m v2
Potential Energy – Based on position and a force. (Joules)
PE = m g h
Work – A transfer of one kind of energy to another. (Joules)
W=Fd
Power – How quickly the work is done. (Watts)
P = W/t
W=F*d
Work is the application of force over a distance.
What work is not:
Pushing on something stationary.
Pushing on something in a direction perpendicular to the direction it
is moving.
Work is measured in Joules (J), just like energy. An object which does
work loses energy. An object which has work done to it gains energy.
You need to consider whether the change in energy is positive or
negative.
Example:
A car engine does 1000J of work on a car. The car has gained 1000J of
kinetic energy. The engine has lost 1000J of heat energy. Overall
energy is conserved.
A weight lifter exerts a force on the weights over some distance, doing
work to it. The weights have been lifted up, gaining potential energy.
The weight lifter has burnt some calories (also a unit of energy, by the
way) losing chemical energy.
1.
2.
3.
4.
5.
6.
92%
100 W
1000 W
10 W
100 J
1000 J
10 J
8%
0%
1
0%
2
3
4
0%
0%
5
6
1.
2.
3.
4.
5.
2500000 J
2.5 J
1500 N
3500 J
None of the above
75%
17%
8%
0%
1
2
3
0%
4
5
P=W/t
Power is a measure of how quickly work is done.
It’s units are Watts, which are made of Joules/second. You’ve already heard
light-bulbs described in Watts. A bigger number means it uses up more
energy every second (and is usually correspondingly brighter).
When we say something is more powerful, we mean that it can do more
work in the same amount of time than something else.
1.
2.
3.
4.
360000 s
100 s
1000 s
Cannot be
determined
5. None of the above
67%
33%
0%
1
2
3
0%
0%
4
5
1.
2.
3.
4.
5.
20,000 W
1250 W
5004 W
4996 W
None of the above
91%
9%
0%
1
0%
2
3
0%
4
5
Definition: Energy based on the
location of mass within a force
field.
Equation: PE = m * g * h
PE is Potential Energy
m is mass
g is gravity*
h is height*
*Most of our problems will deal
with gravity, and the height above
the floor.
•Compression (springs)
•Tension (elastic bands)
•Torsion (twisted ropes)
•Electrons ‘above’ protons
More general equation: PE = m * a * d
(See how………………. PE = m * g * h
is the same, but more specific?)
1.
2.
3.
4.
5.
7,500,000N
750,000N
1,000J
1333J
None of the above
89%
5%
5%
0%
1
2
3
0%
4
5
6) An elevator is connected to a counterbalancing mass. When the elevator goes
up, the counterbalance goes down. The
elevator by itself has a mass of 200 kg, and
the people who get inside have a mass of 150
kg. The elevator goes up 30 m, while the
counterbalance, which has a mass of 300 kg
goes down 45 m. What is the total amount
of energy input into the system?
Definition: The energy of a mass
in motion.
Equation: KE = ½ m * v2
KE is Kinetic Energy
m is mass
v is velocity
The bigger it is, and the faster it is, the more ability to cause change it has.
7) A football player has a mass of 100 kg and is
moving at 5 m/s. He accidentally runs into
a goal post and comes to a complete stop.
How much energy is transferred to the goal
post?
The total energy before equals the total energy after.
If it seems like some energy went missing, check for Thermal Energy (heat
generation).
1.
2.
3.
4.
5.
200,000J
20J
200 m/s
40,000 m/s
None of the above
53%
18%
12%
12%
6%
1
2
3
4
5
1.
2.
3.
4.
5.
0.4 m
0.8 m
40 m
80 m
None of the above
75%
25%
0%
1
0%
2
3
0%
4
5
1) A football player runs 50 m across the field exerting a downward force of
600 N and a sideways force of 25 N, over 5 seconds. A cheerleader jumps
into the air, exerting a downward force of 600 N across a distance of 1 m
in .2 seconds. How much power is exerted in each case?
2) A motorboat continually accelerates at 2 m/s2. It has a mass of 1000 kg. It
does this for 5 seconds. If its power is 40,000 watts, then across what
distance did it do this?
(You’ll need F = m * a, W = F * d, and P = W/t and lots of rearranging to
solve this, OR you’ll need to use dimensional analysis to figure it out as
you go.)
P = power
W = work
F = Force
p = momentum
∆p = impulse
m = mass
a = acceleration
v = velocity
d = distance
Watts (W)
Joules (J)
Newtons (N)
kg*m/s or N*s
kg*m/s or N*s
kilograms (kg)
meters/second2 (m/s2)
meters/second (m/s)
meters (m)
P = W/t
W = f*d
F = m*a
p = m*v
∆p = F*t
vf = vi +a*t
df = di +vi*t + ½ a t2