ISNS 3371 - Phenomena of Nature
Solar energy striking Earth’s surface per second = 2.5 x 1017 J.Energy released by burning 1 liter of oil = solar energy striking square 100 m on a side in 1 second
Energy Comparisons
ISNS 3371 - Phenomena of Nature
Four Types of Forces:
• Gravitational – holds the world together
• Electromagnetic – attraction/repulsion of charged matter
• Strong Nuclear – holds nucleus together
• Weak Nuclear – involved in reactions between subatomic particles
Fundamental Forces of Nature
ISNS 3371 - Phenomena of Nature
Energy
Three basic categories:
Kinetic energy = energy of motion
KE = 1/2mv2
Potential energy = stored energy
gravitational, chemical, elastic,electrostatic, etc…
Radiative - energy carried by light
{MechanicalEnergy
ISNS 3371 - Phenomena of Nature
Potential Energy
One form of potential energy is gravitational potential energy - the energy which an object stores due to its ability to fall
•It depends on:– the object’s mass (m)– the strength of gravity (g)– the distance which it falls (h)
PE = mgh
Before the sun was formed - matter contained in cloud diffuse gas cloud - most far from the center - large gravitational energy. As cloud contracted under its own gravity - gravitational energy converted to thermal energy until hot enough to ignite nuclear fusion
m
h
g
ISNS 3371 - Phenomena of Nature
Potential Energy
• energy is stored in matter itself• this mass-energy is what would be released if an amount of
mass, m, were converted into energy
E = mcE = mc22
[ c = 3 x 108 m/s is the speed of light; m is in kg, then E is in joules]
The mass energy in a 1-kg rock is equal to as much energy as 7.5 billion liters of oil = enough to run all the cars in the U.S. for a weekA 1-megaton hydrogen bomb converts only about 3 ounces of mass into energy.
ISNS 3371 - Phenomena of Nature
Conservation of Energy
• Energy can be neither created nor destroyed.
• It merely changes it form or is exchanged between objects.
• This principle (or law) is fundamental to science.
• The total energy content of the Universe was determined in the Big Bang and remains the same today.
ISNS 3371 - Phenomena of Nature
Types of Energy
Energy cannot be created or destroyed, only changed
– Mechanical –
• Potential - stored energy
• Kinetic- energy of motion KE=1/2mv2
– Electrical
– Chemical
– Elastic
– Gravitational
– Thermal
– Radiant
– Nuclear
ISNS 3371 - Phenomena of Nature
Conversion of Energy
Throwing a baseball
Nuclear energy (nuclear fusion on sun) - Radiative energy (sunlight) - Chemical energy (photosynthesis) - Chemical energy in pitcher’s body (from eating plants) - Mechanical kinetic energy (motion of arm) - Mechanical kinetic energy (movement of the baseball). Thus, ultimate source of KE in baseball is mass energy stored in hydrogen of Sun - created in Big Bang.
Hydroelectric dam
Gravitational - mechanical - electrical
Nuclear reactor
Nuclear - thermal - mechanical - electrical
CarChemical - thermal - mechanical
ISNS 3371 - Phenomena of Nature
Power:Rate of change of energy
Power = work done/time interval = E/t
(remember: means a change in a quantity)
Power:1 watt = 1J/sThus for every second a 100 W light bulb is on, the electric company charges for 100 J of energy.The average daily power requirement for a human is about the same as for a 100-W light bulb.
Power
ISNS 3371 - Phenomena of Nature
Machines
Machines can be used to multiply force:
(force X distance)input = (force X distance)output
Decrease the distance and the force will increase.
Work/Energy is not changed!
ISNS 3371 - Phenomena of Nature
Levers
Fulcrum is in the center:d1 = d2
so
F1 = F2
Fulcrum is closer to one end:
d1 > d2
So
F2 > F1
Give me a long enough lever and a place to put the fulcrum and I can move the world (Archimedes, 250 BC).
ISNS 3371 - Phenomena of Nature
€
Fnet = −mgsinθ
For small angles, sin =
€
Fnet = −mgθ = ma
€
−mgθ = mαl
vt, at
r
= vt/r is the angularvelocity
= at/r is the angular acceleration
so = r
This becomes the differential equation:
€
d2θ
dt 2+g
lθ = 0
Pendulum solution (you are not expected to know this)
With solution
€
=max cosg
lt
For a complete oscillation:
€
g
lP = 2π so
€
P = 2πl
g
ISNS 3371 - Phenomena of Nature
For a small pendulum clock, P = 1s
So
€
P = 2πl
g
€
l =P 2g
4π 2
€
l =g
4π 2=
9.8
4π 2= 24.8cm
If P = 2s, then l = 0.993 m
This is the length of the typical grandfather clock’s pendulum which advances each time the pendulum reaches its maximum displacement or twice every period.
ISNS 3371 - Phenomena of Nature
Objects Moving Down an Inclined Plane
Compare the speed of an object rolling down an inclined plane without slipping and one sliding without friction. Which gets to the bottom first?
We simulate this with two cylinders of the same mass - one is a solid cylinder, and one has wheels on the sides which turn while the cylinder itself doesn’t.
The sliding object will always reach the bottom first because all the initial potential energy is converted into translational energy with none wasted in rotation.
ISNS 3371 - Phenomena of Nature
Which will roll down the inclined plane faster - a solid cylinder or a hollow cylinder (of the same mass and outer radius)?
As the object rolls down the plane, its initial potential energy is converted into both translational energy of the center-of-mass and also into rotational energy.
- ratio of rotational to translational energy is I / mr2 where I is the moment of inertia, m is the mass and r is the radius of the object. - moment of inertia is mr2/2 for the solid cylinder and m(r1
2 + r22)/2 for
the hollow cylinder. - Since r2 of the hollow cylinder is equal to r of the hollow cylinder, and the mass is the same, the moment of inertia of the hollow cylinder is mr1
2/2 + mr2/2 or larger than the moment of inertia of the solid cylinder by mr1
2/2.
Thus ratio of the rotational to the translational energy for the hollow cylinder is greater than for the hollow cylinder. The hollow cylinder therefore acquires the most rotational energy and the least translational energy (and velocity) and thus takes the longest to get down the plane.
ISNS 3371 - Phenomena of Nature
€
m1v1 + m2v2 = m1V1 + m2V2
1
2m1v1
2 +1
2m2v2
2 =1
2m1V1
2 +1
2m2V2
2
m1v1 −m1V1 = m2v2 −m2V2
m1(v12 −V1
2) = m2(v22 −V2
2)m1(v1 −V1)(v1 +V1) = m2(v2 −V2)(v2 +V2)
v1 +V1 = v2 +V2
V1 =V2 + v2 − v1
Using Conservation of Energy and Momentum to Calculate the Velocity of Two Bodies After a Collision
Conservation of momentum says
Conservation of energy says
(1)
(2)
(1) Can be written
(1a)
(2a)
(2) Can be written
From (1a) we see that m1(v1 - V1) cancels out m2(V2 - v2) so that
Which can be rewritten as
ISNS 3371 - Phenomena of Nature
€
m1v1 + m2v2 = m1(V2 + v2 − v1) + m2V2
m1v1 + m2v2 = m1v2 + m1V2 −m1v1 + m2V2
2m1v1 + m2v2 −m1v2 = m1V2 + m2V2
2m1v1 + (m2 −m1)v2 = (m1 + m2)V2
V2 =2m1v1
m1 + m2
+m2 −m1
m1 + m2
v2
V1 =m1 −m2
m1 + m2
v1 +2m2v2
m1 + m2
Substitute V1 = V2 + v2 - v1 into (1)
This leaves us with one equation with one unknown, V2
Similarly
ISNS 3371 - Phenomena of NatureThe Ballistic Pendulum
The ballistic pendulum is used to determine the speed of a projectile. Invented in the 18th century by Benjamin Robins to determine the speed of a bullet.
A bullet of mass m is fired at a block of wood (mass M) hanging from a string. The bullet embeds itself in the block, and causes the combined block plus bullet system to swing up a height h. Conservation of momentum and conservation of energy are used to determine the bullet’s speed.
ISNS 3371 - Phenomena of NatureConservation of momentum
(1)
b = before collision- mb and vb are for the ball/bulleta = after collision- ma and va are for the ball/bullet and pendulum
Conservation of energy
Kinetic Energy of ball and pendulum just after collision = Potential Energy of ball and pendulum at end of swing:
h = height of pendulum at end of swing
Substitute into (1):
€
mbvb = mava
vb =mavamb
€
1
2mava
2 = magh
€
va2 = 2gh
€
va = 2ghmamb
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