Download Ch 7: Energy

Ch 7 Notes ~ Energy: 7.1 – 7.3
Interpret Ft = mv
7.1 Work
There are 2 things that will impart a change in momentum:
1.
2.
How large the FORCE with which you push is just as important as how long
(TIME) you exert the force.
2 Ways to change “how long force is applied”
1.
2.
Fd = E, and E  Work, so, exerting an impulse causes work to be done.
Q: What would be the units for work?
A: N∙m = Joules, or J
Types of Energy:
1.
2.
3.
4.
5.
6.
7.
8.
Everything has E, as given by Einstein’s celebrated equation E = mc2
Einstein said E and mass are really two sides of the same coin. You know what
your mass is?
The more mass you have, the more Energy you have. Einstein’s equation
relates E of the massive kind to Energy of the radiant kind, like what happens
in the sun = FUSION.
Ex:
To lift a block requires work; the higher you lift, the more work you
do, therefore, the more E it has. That E is PE, the E of position.
Ex:
2 slingshots pulled all the way back. Even if the forces are
equivalent, the slingshot pulled back the farthest will be able to do more work
because the mass will travel through a longer d. If the larger slingshot is also
more forceful, then momentum will be increased even more.
Ex:
2 cannons; same-same 
7.2 Power
Q: What do we mean when we talk about the power something has?
A: Power means how long it takes you to do the work. P = _work done__
Time interval
So, something is considered powerful if it can do a lot of work in a little time
Q: What would be the units of power?
A: J/s = 1 Watt = 1 W or just W
7.3 Mechanical Energy
Let’s talk about Emechanical = simplest kind; related to work.
W = E
Potential Energy
An object has stored energy due to its position. This stored energy is called
potential energy, since it has the potential to do work if you let the object move
back to its normal resting spot.
EX’s:
What about within the bonds between two or morr
?
What about the comparative PE’s of the following objects that are at the same
height?
If you were to place a ball at the top of either the post, the ramp, or the stairs,
you would need to do work (F∙d) to push it there. The work required would
have to be done against the gravitational pull of the earth.
Q: What force are we talking about?
A: gravity, or g
So, to calculate how much potential energy something has due to its height, use
PE = m g h, because you have to push its weight (mg) up to a certain height. In
other words, it has the potential to do work due to its position.
Kinetic Energy
Lots of KE comes from lots of PE, and vice-versa.
If we do work on an object, we can set it in motion because we change
the velocity, thus the energy, of the object.
Q: Is it true that anything in motion is capable of doing work?
A: Yep!
DEF: Kinetic Energy:
 the energy of motion.
 KE = ½ mv2
 KE is dependent on the frame of reference
If you triple the velocity of a car, how much more distance do you
need to stop?
A: Nine times morr; that is why they (schmoes on a mountain) say
“Don’t follow too closely!!”
7.3 A Teensey Bit Morr on KE and Stopping a Speeding Car
The work done to stop a speeding car is the work done to stop its motion, thus,
its KE
Q: Specifically, what does the work?
A: The brakes
Q: What does work mean? What does work cause?
A: Work = Fd, which causes a change in energy, or KE.
Think about it: If you truly do exert force on an object in a direction, you will
change the speed of the object (or accelerate it), thus, change its KE.
Q: For a speeding car, what is the evidence of the work done to stop a speeding
car?
A: The skid marks left on the road
So, to recap, work causes ∆ KE. Since KE = ½ mv2, and the “ ½ m" part stays
the same no matter what the speed*, that “ ½ m" part is irrelevant. Thus, the
only factor contributing to the variance in KE, exhibited by the length of the
skid mark, is v2.
Force (from brakes) x distance (shown by the skid mark) α v2
Consider any car traveling at a given beginning speed, and slam on the brakes
to leave a skid mark. If you then double the speed, the skid mark left by
slamming on the brakes will be 4 times longer than it was originally.
IF you triple the speed, it will increase nine-fold.
IF you quadruple the speed, it will increase sixteen-fold, and so on.
*As long as you’re not traveling at the speed of light squared
Work-Energy Theorem
Let’s review for a bit.
Q: What is Newton’s Second Law of Motion?
A: F = ma
If you multiply both sides of the equation by d, you get Fd = mad. For objects
in free-fall, d = ½ a t2. Substitute this into the equation, and you get
Fd = ma( ½ a t2) = ½ maat2 = ½ m (at)2
Q: What does at equal?
A: velocity, specifically, Δv
So, Fd = ½ m (Δv)2
Q: What does Fd equal? What does ½ m Δv2 equal?
A: Work and KE, respectively
Thus, W = ΔKE This is the work-energy theorem.
:
Ft is called____________________and causes_____________________
Fd is called____________________and causes_____________________
Work is always conserved. Can you rewrite this in terms of “big F
little d,” and so on?
200 J
200 J
200 J
Using the above drawings, let’s say it takes 200 J of work to lift a
boulder to the top of a grassy knoll. Since work is conserved, what do
the modifications do to the amount of force you need to do to lift that
boulder along the indicated path?
W = Fd
W = Fd
W = Fd
200 J = F(2m)
200 J = F(4m)
200J = F(2m)