1. Physics 1501: Lecture 15 Today’s Agenda
Midterm graded by next Monday (maybe …)
Homework #6: Due Friday Oct. 14 @ 11:00 AM
Topics
Gravity (Chap.8)
Review of Midterm I

2. Generalized Work Energy Theorem:
Suppose FNET = FC + FNC (sum of conservative and non-conservative forces).
The total work done is: WTOT = WC + WNC
The Work Kinetic-Energy theorem says that: WTOT = K.
WTOT = WC + WNC = K
WNC = K - WC
But WC = -U
So WNC = K + U = E

3. Conservative Forces and Potential Energy
We have defined potential energy for conservative forces
DU = -W
But we also now that
W = FxDx
Combining these two,
DU = - FxDx
Letting small quantities go to infinitessimals,
dU = - Fxdx
Or,
Fx = -dU/dx

4. New Topic - Gravity
Sir Isaac developed his laws of motion largely to explain observations that had already been made of planetary motion.
Earth
Sun
Moon
Note : Not to scale

5. Gravitation (Courtesy of Newton)
Things Newton Knew,
1. The moon rotated about the earth with a period of ~28 days.
2. Uniform circular motion says, a = w2R
4. Acceleration due to gravity at the surface of the earth is
g ~ 10 m/s2
5. RE = 6.37 x 106 m
6. REM = 3.8 x 108 m

6. Gravitation (Courtesy of Newton)
Things Newton Figured out,
1. The same thing that causes an apple to fall from a tree to the ground is what causes the moon to circle around the earth rather than fly off into space. (i.e. the force accelerating the apple provides centripetal force for the moon)
2. Second Law, F = ma
So, acceleration of the apple (g) should have some relation to the centripetal acceleration of the moon (v2/REM).

7. Moon rotating about the Earth :
Calculate angular velocity :
 = v / REM = 2 p REM / T REM = 2 p / T
 =
So  = 2.66 x 10-6 s-1.
Now calculate the acceleration.
a = 2R = m/s2 = g

8. Gravitation (Courtesy of Newton)
Newton found that amoon / g =
and noticed that RE2 / R2 =
This inspired him to propose the Universal Law of Gravitation:
|FMm |= GMm / R2
amoon g R RE
G = 6.67 x m3 kg-1 s-2

9. Gravity...
The magnitude of the gravitational force F12 exerted on an object having mass m1 by another object having mass m2 a distance R12 away is:
The direction of F12 is attractive, and lies along the line connecting the centers of the masses. m1 m2
F12
F21
R12

10. Gravity... Compact objects: R12 measures distance between objects
Extended objects:
R12 measures distance between centers
R12
R12

11. Gravity... Near the earth’s surface: R12 = RE
Won’t change much if we stay near the earth's surface.
i.e. since RE >> h, RE + h ~ RE. m Fg h M RE

12. Gravity... Near the earth’s surface...  =g So |Fg| = mg = ma a = g
All objects accelerate with acceleration g, regardless of their mass!
Where:

13. Example gravity problem:
What is the force of gravity exerted by the earth on a typical physics student?
Typical student mass m = 55kg
g = 9.8 m/s2.
Fg = mg = (55 kg)x(9.8 m/s2 )
Fg = 539 N Fg
The force that gravity exerts on any object is
called its Weight
W = 539 N