1. Welcome back to semester 2!!!!
Energy (continued)
Welcome back to semester 2!!!!

2. What we have seen so far….
We have studied the pendulum system
We have observed that the gravitational potential energy (mgh) is converted to kinetic energy (1/2 mv2) with some energy loss from the system as thermal energy = Ffr ΔX
We have represented the transformation of the energy from one form to the other using a visual known as an energy profile. Diagram on board
Period of pendulum depends mainly on the length of the pendulum

3. Energy Units KE, gPE, TE, EPE … Units: Newton meter
= kg (m/s2) (m) = kg m2/s2 =
Joule
Watch your units – mass in kg, distance in m !

4. Notice that: The Newton is a unit of Force
The meter is a unit of displacement

5. Work parallel
Work = Force applied parallel to the displacement of an object = F x d.
If I carry books across the floor, I apply a force up (against the F of gravity) and I move horizontally across the floor.
Therefore, I do no work on the books
Because my force is not parallel to the displacement!

6. Work Example:
If I push a cart with a force of 10 N across the floor for 10 meters
What would a force –vs- displacement graph of this situation look like?

7. Like this 10 F (N) displacement (m) 10
displacement (m)
What does the area under the curve represent?

8. If you said: The work done – then you are one smart cookie!!!!
Notice area = height x length =
N x m = Nm = Joules!

9. But wait just one minute mister!
I thought you said that the units of energy were the Joules
That is correct I did!
Look at these next example please

10. Potential E and work equivalence
If you are on top of a diving board diagram
gPE = mg h
W = F d
F = mg and h = d therefore:
W = mg h

11. How sick is that????
Way sick!!!!

12. This work/energy equivalence and energy transformations
Allows us to do some cool calculations!
Like this…

13. E pbm. #1
If you are on a roller coaster that is 40 m high, what is your velocity at the bottom of the ride (ignore E loss to TE) Etop = Ebottom
gPE = KE
mgh = ½ mv2 therefore:
V = mgh/ 1/2 m = 2gh =
28 m/s

14. E pbm #2 What would your velocity be 20 from the top?
gPE40m = gPE20m + KE
mg(40) = mg(20) + 1/2mv2
m(9.8)(40) = m(9.8)(20) + ½ mv2
= ½ v2
(392 – 196)(2) = v2
V = 19.8 m/s

15. Pbm. #3
A 200g baseball is hit straight up with an initial velocity of 20 m/s. How high will it go?
KE = gPE
½ mv2 = mgh
h = ½ v2 / g (* just like earlier in the year)
h = 20.4 m high

16. Pbm #4
If the ball only goes 19.5 m high (instead of the calculated 20.4 m) then what is the force of friction acting on the ball?
KE (when hit) = gPE (at max height) + TE (lost to universe)
Rearrange: TE = KE - gPE
Substitute in: TE = Ffr ΔX
Ffr ΔX = KE - gPE
Solve for friction: Ffr = KE - gPE / ΔX
Ffr = ~ .09N