work, energy, power chapter 7 in a nutshell work is force times distance. the change in kinetic...
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Work, Energy, Power
Chapter 7 in a nutshell
Work is Force times Distance.The change in Kinetic Energy is equal to the work.
Power is Work per unit time.
TWP
KW
dFW
/
New Concept:Kinetic Energy
K = ½ m V2
Work causes a change in kinetic energy, so the units are the same.
Units of Kinetic energy: Joule
But, from the definition of kinetic energy, the units are also,
1 Joule = 1 Kg-m2/s2
Table 7-1Typical Values of Work
Annual U.S. energy use 8 x 1019
Mt. St. Helens eruption 1018
Burning one gallon of gas 108
Human food intake/day
Melting an ice cube
107
104
Lighting a 100-W bulb for 1 minute 6000
Heartbeat 0.5
Turning page of a book 10–3
Hop of a flea 10–7
Breaking a bond in DNA 10–20
Activity Equivalent work (J)
Work is force times distance…but!
Only the force component in the direction of motion counts!
Units of work: Joule
I’ve got work to do….
F = Mg
F = Mg
y
W=F*y=MgH
This is the work done by the person lifting the box.
How about the reverse?….
F = Mg
F = Mg
H
W=F*y = - MgH
Work can be positive or negative.Lifting a box is positive work.Lowering the box is negative work.
Positive or Negative?Work done by gravity.
Fg = - Mg
y = - H
Work “done by force of gravity” is positive when an object is dropped.
Problem 7-77
W = 50J, given v, F, x.
What is theta?What is M?
1
1
(cos )
cos
cos
50.0 Jcos
(45.0 N)(1.50 m)
42.2
W F dW
FdW
Fd
2 2 2f i f
1 1( )
2 2W K m v v mv
2 2mfs
2 2(50.0 J)14.8 kg
2.60
Wm
v
Raindrops are falling on my head….
V1
F = - Mg
V2
y = -H
MgH
HMg
yFW
)()(
21
22 2
1
2
1MvMv
KW
)(2
1 21
22 vvMMgH
Special case: Object dropped from rest.
-Mg
Mass M dropped from height H. What is speed just before hitting the ground? (Neglect friction of air)
H
W=MgH
W=K=1/2 M v2
gHv 2
Thought provoking: The inclined plane.
Distance = hForce = mgW = mgh
Distance = L = h/sin Force = mg sin W = mgh
The work is the same in both cases. This is an example of conservation of energy, which we will see much more of in the future.
How about the speed?
H
If Block fell straight down through height H, its speed would be:
gHv 2
Use F=Ma to find speed down the ramp.
F=Mg sin
V=atL=1/2 a t2 so
aL
a
Lav
2
2
But a = g sinAnd L = H/sin
So…
gHv 2
Same magnitude of speed, but DIFFERENT DIRECTION!
When force is not constant.The area under a force-distance
curve is the work, W.
Distance
For
ce
The average force times the distance gives the work. This is the same as the area under the curve.
Back to our Spring Flings.
F = -K x
How much work is done to move the block?Be careful with the signs of the forces!The force to move the block must be equal and opposite to the force of the spring on the block.
F = K x
For
ce
Distance X
F=Kx
W = ½ F XW = ½ K X2
Work done to move a mass on a spring a distance “x”:
221 KxW
Conceptual Checkpoints
• What is work, in physics terms?
• What is kinetic energy?
• What is power?
Work is force in the direction of motion.
Kinetic energy is ½ Mv2
Power is Work (or Energy) per Unit time.
Work and the WeightlifterA weightlifter performs three steps. What is the work done for each of the steps? Assume the weight is 100 Kg, the height of the lift is 1 M, and the acceleration of gravity is 10 M/s^2.
Work done against gravity to lift an object a height H is W = MgH
W1: The weight is lifted up to the height of 1 M.W2: The weight is held at 1M for 5 seconds.W3: The weight is lowered down to the ground.
Cheryl Hawarth, USA gold medal.
Weightlifting Work.
1. 1000J, 5000J, 1000J2. 1000J, 0J, -1000J3. 1000J, 5000J, -1000J
W1: The weight is lifted up to the height of 1 M.W2: The weight is held at 1M for 5 seconds.W3: The weight is lowered down to the ground.
The work done W1, W2, W3 is:
The energy is kinetic, relatively speaking….
V = + 5 m/s
V = -5 m/s
Train moves to the right with speed V. A baseball is thrown to the left with the same speed.
What is the kinetic energy of the baseball? Its mass is 1 kg.
What is the kinetic energy?
1. 12.5 J2. 5 J3. Zero4. Either zero or 12.5J,
depends on your frame of reference.
V = + 5 m/s
V = -5 m/s
K = ½ M V2
M = 1 kg
The Power to overcome Friction.Work is Force times distance. Power is Work per unit time.
F
Frictional Force, Ff = N
Block moves with STEADY SPEED under influence of applied force that EXACTLY balances friction, so V is CONSTANT.
AN IMPORTANT SPECIAL CASE
Force of friction Under these conditions,
vFT
XF
T
WP
THIS IS A SPECIAL CASE IN WHICH AN APPLIED FORCE RESULTS IN CONSTANT SPEED.IT OCCURS BECAUSE THE NET FORCE IS ZERO (SUM OF ALL APPLIED FORCES).
How about this case?
Total work is just the sum of the work for each spring.
221
22
21
2
12
1
2
1
xKK
xKxKW
And this one?This is harder. The two springs DO NOT stretch the same distance (they have different K values).
2
2
1
1
222
111
21
k
F
k
Fx
xkF
xkF
xxx
But F1 = F2 (why?), so let it be called F.
21
11
kkFx
So, can create an effective spring constant, Keff, 1
21
21
1111
1
kkkk
keff
Then, we can apply the usual formula: 2
2
1xkW eff