1. b. What is the coefficient of friction?
Do Now:
A 1200 kg car is traveling on a circular track going 5 m/s. If the track has a radius of 40 m, then what is the force of friction between the car and the road?
b. What is the coefficient of friction?

2. Aim: How much speed do we need to stay in a loop de loop?
HW:

3. Loop De Loop
What do we need to calculate the velocity needed to complete this loop de loop?
ac = V2/r
Radius- Approximately 6m
ac = 9.8 m/s2 at the top!
1 mile = 1609 meters
Draw a diagram

4. Loop de Loop Continued
How can we calculate the cars actual speed from the video? How does it compare?
V = d/t
Circumference = 2π x radius
t = Period (T): time for one complete revolution
We need to go a little faster to avoid slipping and have traction.

5. How can I calculate the force between myself and Earth?
Universal Law of Gravitation:
G = 6.67 x m3/kg. s2 : Universal gravitational constant
FG: Force between objects
r: distance between objects
Earth’s Mass & radius: 5.97 x 1024 kg & 6371 km
Use mass of a person… about 60 kg and you get a force of 600 N
Use a mass of 1 kg and see the Force is 9.8N!

6. Practice
An astronaut has a weight of 850N on Earth’s surface and is orbiting 2 Earth radii above Earth’s surface.
What distance should we use to calculate FG?
3 Earth radii (Always from center of large mass)
FG = 95 N
Notice this is 1/9 original weight!

7. Envelope Activity
Share the following questions with your group and answer them as a team.

8. Which graph represents the relationship between gravitational force vs
Which graph represents the relationship between gravitational force vs. distance from Earth? Explain. An object weighs 100N at a distance of 200 km above the center of a small planet. How much will the object weigh 400 km above the planet’s center?

9. Satellites What gets them up there and what keeps them up there???
HIGH SPEED! Circular orbits require the least speed. For Earth it’s only 27,000 km/hr!
Without speed it falls to Earth like a rock, but too much speed and it escapes Earth’s gravitational pull!

10. How does a satellites motion relate to both Centripetal Force and Gravitational Force?
FC = FG
How do we account for the satellites speed?
The satellite revolves around Earth with the same period that the Earth rotates on it’s axis!
V = 2πr/T
See ch.5 for notes on satellites
T = 1 day = 86,400 s
r is radius of orbit from Earth’s center to sat.
Solve for r!

11. White Board Activity
Determine the orbital speed of a 1,000kg satellite that is 4.2 x 107 meters from the center of the Earth. Remember FG = FC for satellites. Is the radius and distance different in this case?
m1 = 1000 kg m2 = 5.97 x 1024 kg r = 4.2 x 107 meters G = 6.67 x m3/kg. s2 FG = G(m1m2)/r2 FG = N = FC FC = mv2/r v = 3079 m/s

12. Summary Explain Newton’s Law of Universal Gravitation
How does a satellites motion relate to both Centripetal Force and Gravitational Force? Explain!
Why doesn’t the car fall at the top of it’s loop de loop?

13. Motorcycle Problem
A person is riding a motorcycle in a metal cage with a radius of 10 meters. Calculate the minimum velocity that the motorcycle needs at the top of the cage without falling.
A) Draw a free body diagram for him at the top of the cage.
B)What is centripetal force equivalent to in this case?