1. Lecture 19 Satellites

2. Quick Review Newton’s Law of gravity

3. Circular Orbits M is mass of parent and m the mass of the satellite. M>>m Kepler’s Law

4. Geostationary Satellite At the equator, how far above the earth’s surface should a satellite orbit so it stays overhead? R earth = 6.37 x 10 6 m G=6.67 x 10 11 Nm 2 /kg 2 M earth = 5.98 x 10 24 kg

5. A cyclist goes around a level, circular track at constant speed. Since the cyclist’s speed is constant, her acceleration is constant 1.True 2.False

6. QUIZ A motor cycle is in a loop-the-loop. At the top of the loop… A) Draw a free body diagram B) What is the minimum speed the motor cycle must have if the radius of the loop is 15. m?

7. Homework due Friday Problems: 6: 24, 25, 27, 29, 33, 44, 45, 51, 58, 59

8. Problem 6:27 What is the ratio between the sun’s gravitational force on you and the earth’s gravitational force on you? R earth = 6.37 x 10 6 m G=6.67 x 1011 Nm 2 /kg 2 M earth = 5.98 x 10 24 kg R earth-sun =1.5 x 10 11 m M sun = 1.99x10 30 kg

9. Problem 6:27 cont Take ratio

10. 6:33 The space shuttle is in an orbit 250 miles high. What are its orbital period (in minutes) and orbital speed? R earth = 6.37 x 10 6 m G=6.67 x 10 -11 Nm 2 /kg 2 M earth = 5.98 x 10 24 kg 1 mi = 1.609 km

11. 6:33 250 mi *1.609km/mi=326.5 km r= 6.37 x 10 6 m+3.265 x 10 5 m =6.70 x 10 6 T=5.46 x 10 3 s = 90.9 minutes

12. 6:44 A 5g coin is placed 15cm from the center of a turntable. µs = 0.80, µk = 0.50. As turntable starts from rest and speeds up to 60 rpm, does coin slide off?

13. So coin does not slip

14. T W=mg r=0.20m 1.0m θ 6:45 Conical Pendulum Find T, ω

15. 6:51 Ultracentrifuge R=0.10 m 70,000 rpm Δm= 10 mg = 0.000010 kg What is net force? r a

16. 6:58 Martian geostationary satellite What are its speed and altitude? dayMars:=24.8 hours

17. 6:59 g on Mars, Maximum walking speed?