https://www.tcd.ie/Physics/local/undergraduate/JF/foundation/
Energy and Power
Foundation Physics
Lecture 2.2
19 Jan ´10
Energy
• Energy is defined as the ability to do work.
Work done by a system takes energy out
of it, and conversely work done on a
system puts energy into it.
ƒ ΔE=W
W: work done on a body. The additional energy
enables the body to do work.
‘Energy is stored work’
Kinetic and potential energy
are the two main forms of energy.
Kinetic energy
Energy of motion
• Translational motion:
Ekin = ½ m.v2
• Rotational motion:
Ekin = ½ J.ω2
Potential Energy
Energy of the ‘position’
Potential energy (in the gravitational field of the earth)
Epot = m.g.h
Potential energy (of a spring under tension)
Epot = ½ D.x2
Potential Energy
What kind of energy is ΔE of frictional work?
The work done for the transport of a body
with friction:
W=μg.m.g.s
W is transformed into thermal or internal
energy.
ΔEthermal = W
Work done by the heart
The hearth provides work of ca. 1.3J per contraction (systole). With a
hearth frequency of 70 pulses/min this results in ~130kJ/day. In 70
years this equals to a work of 3.3x109J.
The heart keeps the blood in motion. It is an acceleration work and work
against friction. Finally the energy due to friction is converted into heat.
During the expansion phase the elastic walls of the aorta expand. The
work is being stored in form of potential energy (deformation work).
Epot=D/2.Δs2 with D: spring constant of the aorta. Δs: expansion of the
vascular wall. Experimentally Epot ~ 50% of the systolic work. This
energy is provided ~0.22sec after the expansion back to the
bloodstream and helps to a temporal smoothing of the pulse.
Aorta stores potential energy
Expansion phase (systole)
Potential energy is released
(diastole)
Problems
• Compare the kinetic energy of a 50-kg
athlete running a speed of 3.0 m/sec with
that of a 25-kg cheetah running at 30
m/sec.
Problems
• How much thermal energy is generated by
the breaks of a 1.0x1014-kg train in causing
the train to slow from a speed of 30 m/sec
to a speed of 10 m/sec (Neglect any other forces that
might also slow the train).
Problems
• Severe stresses can be produced in the joints by jogging
on hard surfaces or with insufficiently padded shoes. If
the downward velocity of the leg is 7 m/sec when the
jogger’s foot hits the ground, and if the leg stops in a
distance of 2.0 cm, calculate the force in the ankle joint.
The mass of the jogger’s leg is 12 kg. (You may neglect
the weight of the rest of the jogger’s body.) Compare this
force with the weight of a 75-kg jogger.
Other forms of energy
• Stored energies:
Chemical energy
electromagnetic energy of the position of atoms and molecules (combustion, galvanic
elements (battery), food)
Nuclear energy
energy of the position within the fields of the elements of the nucleus (nucleons). Nuclear
fusion (sun), nuclear fission in nuclear power plants.
Electrical energy
Electromagnetic energy of the position of charges and magnetic dipoles, energy in
electromagnetic fields (electrically charged capacitor, energy of electromagnetic waves
• Energy in transit
light (if light is captured or stopped it is converted into other forms of energy, even tough
light is a moving it has no mass so -> ½ mv2 = 0)
• Thermal energy
Vibration energy of atoms, friction induced
• Mass
can be converted into energy and vice versa
Caloric content (kcal/g)
COMMON FOODS
Average carbohydrate
Average protein
Average fat
4.1
4.1
9.3
Common Foods
Apples
Avocado
Baby formula
Beans, kidney
Beer
Big Mac
Butter
Carrots
Celery
Cheese, cheddar
Cheese, cottage
Chicken, roasted
Chocolate
Coffee, black
Cola, carbonated
0.58
1.67
0.67
1.18
0.42
2.89
7.20
0.42
0.15
4.00
1.06
1.60
5.28
0.008
0.36
Corn flakes
Eggs
Grapes
Ham, cooked
Hamburger, lean
Ice cream, chocolate
Lard (fat)
Lobster, raw
Milk, whole
Milk, low-fat
Oranges
Peanuts, roasted
Peas
Potato, baked
Raisins
Rice, white, cooked
Shrimp, snails, raw
Sirioin, lean
Sugar
Tomato
T\rna, in oil
Wine
1000 cal = 4186 J
3.93
1.63
0.69
2.23
1.63
2.22
9.30
0.91
0.64
0.42
0.49
5.73
0.71
0.93
2.90
1.09
0.91
1.66
4.00
0.22
1.97
0.85
Caloric content (kcal/g)
Common Fuels
•
•
•
•
•
•
Coal
Gasoline
Furnace oil
Methanol
Natural gas
Wood (average)
8.0
11.4
10.5
5.2
13.0
4.0
Energy Consumption Rate for various activities
Activity
Sleeping
Sitting at rest
Standing relaxed
Sitting in class
Walking slowly (4.8 km/hr)
Cycling (13-18 km/hr)
Playing tennis
Swimming breaststroke
Iee skating (14.5 km./lrr)
Climbing stairs (116/min)
Cycling (2lkmlhr)
Playing basketball
Cycling, professional racer
Energy Consumption Rate (kcal/min)
1.2
1.7
1.8
3.0
3.8
5.7
6.3
aNormal 76-kg male.
6.8
Adapted from J. Cameron
7.8
and J. Skofronick, Medical
Physics (Wiley Interscience,
9.8
New York, 1988)
10.0
11.4
26.5
How many calories per day?
1.87 m
2413
Calories/day
2614
Calories/day
2815
Calories/day
3016
Calories/day
Problems
• How many minutes of lecture can you sit
through on the energy supplied by a 32g of
peanuts (the average amount in a vending
machine pack)?
Conversion of mass to energy
• Following the relativity theory of Einstein
the quantitative mass-energy relationship
is given in his famous equation
E = m.c2
C=2.997924.108 m/s speed of light in vacuum
By combusting 2 Mol H2 (4g) and 1 Mol O2 (32g) an energy
of 4.85.105J is released. The mass-energy relationship
predicts a mass release Δm
E 4.85 ⋅105 Js 2
−12
Δm = 2 =
=
5
.
4
⋅
10
kg
8 2
2
c
(3 ⋅10 ) m
5.4 ⋅10 kg
−12
9.1⋅10
−31
kg
= 5.9 ⋅1018 Electrons
Example: Conservation of Energy
Conservation of total energy
Energy is transferred from system A to
system B when the box is lifted. Neither
system is closed.
A larger single system containing both
the person and the box is closed.
Energy is transferred between
components inside the system, none
enters or leaves the system.
Conservation of total energy
•Energy can not be generated
nor can it be destroyed.
•Energy only can be converted
from one form into an other
Next Lecture
• To Be Covered:
ƒ Power
ƒ Energy consumption efficiency
• Reading: Chapter 4
ƒ Section 4.4 till the end