Download day 1 lesson plan - University of Chicago

Friday, November 18th, 2011: Gravity, chapter 9, day 1
Opener (5 min): Name all of the planets in our solar system. We know that on the
moon we would have a different weight than we do here on earth. Would you have
different weights on the other planets? If so, on which planet do you think you weigh
the least? the most?
Go over opener (5min)
Introduce todayʼs topics:
Universal Gravitation
(10 mins) Universal Gravitation:
Law of universal gravitation: Fgravity 
m1m2
where d is the distance between the centers
d2
of mass of two objects.
Now, what does it mean for two things to be proportional? It means that there is some
mm
constant, G, such that Fgravity = G 1 2 2
d
As it turns out G is the universal gravitational constant, not to be confused with the
9.8m / s 2 , since that one only works for earth. This gravitational constant is universal,
meaning that it can be used anywhere in the universe.
Now letʼs think of things here on earth. Earth has mass 5.9742 × 10 24 kg , I have mass
61kg. F=mg, with g-9.8, we get that my weight is 598N.
Now letʼs use that calculation to determine big G. We also need to know that the radius
of the earth is 6378.1km which is 6.3781 E6 m
5.9742 × 10 24 i61kg 2
598N = G
we get G = 6.675 × 10 −11 Nm 2 kg −2 .
6
2
(6.3781 × 10 m)
Now G was accurately measured by physicist Henry Cavendish in 1798 to be
6.674 × 10 −11 Nm 2 kg −2 . We were pretty close!
(10 min) Practice Problem 1: Using the table, pick a planet and figure out how much
you weigh (in N) on that planet. Here are the masses are radii of all of the planets in
our solar system:
(1kg = 2.20462262185 lbs, or equivalently 1lb = 0.45359237 kg)
Planet
Mercury
Venus
Earth
Moon
Mass (kg)
3.30 x 10ˆ23
4.87 x 10ˆ24
5.97 x 10ˆ24
7.35 x 10ˆ22
Radius (m)
2,440,000
6,051,000
6,378,000
1,738,000
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
6.42 x 10ˆ23
1.90 x 10ˆ27
5.69 x 10ˆ26
8.66 x 10ˆ25
1.03 x 10ˆ26
1.31 x 10ˆ22
3,397,000
71,492,000
60,268,000
25,559,000
24,764,000
1,160,000
(10 min) Practice Problem 2:
So letʼs find out what the gravitational force is between the earth and the moon. Here is
what you will need to know:
Mass of Earth: 5.9742 × 10 24 kg
Mass of Moon: 7.36 × 10 22 kg
Distance between Earth and Moon: ~384,402km
24
22
−11 5.9742 × 10 i7.36 × 10
From here we get that F = 6.674 × 10
(3.84402 × 10 8 )2
Which is 1.986 × 10 20 N
wow! That is HUGE.
(5 min) What can you now tell me about the law of universal gravitation?
End of Class!