Mrs. Goe's Physics Class
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Contents |
Universal Gravitation
Units
F, Force - (Newtons or N)
G, Gravitation constant - 6.67 x 10^-11 (N m^2/kg^2)
m1, Mass of planet or mass 1 - (kilograms or kg)
m2, mass of object on planet or mass 2 - (kilograms or kg)
r, radius of planet or distance between mass 1 and mass 2 - (meters or m)
Questions to Think about:
1. How is the Earth able to pull on us?
2. Do we in turn pull on the Earth?
3. If everyone on Earth stood on one continent would we change the direction or magnitude of the Earth's orbit?
4. What is the strength of gravity between two objects - like the Moon and the Earth?
5. If we were able to chip off 25% of the Moon's mass would it be too light to resist movement towards the Earth?
Planet Stats
Mercury has a mass of 3.30 x 10ˆ23 kg, radius of 2,440,000 m and distance from the sun of 57.9 x 10ˆ6 km.
Venus has a mass of 4.87 x 10ˆ24 kg, radius of 6,051,000 m and distance from the sun of 108.2 x 10ˆ6 km.
Earth has a mass of 5.97 x 10ˆ24 kg, radius of 6,378,000 m and distance from the sun of 149.6 x 10ˆ6 km.
Mars has a mass of 6.42 x 10ˆ23 kg, radius of 3,397,000 m and distance from the sun of 227.9 x 10ˆ6 km.
Jupiter has a mass of 1.90 x 10ˆ27 kg, radius of 71,492,000 m and distance from the sun of 778.3 x 10ˆ6 km.
Saturn has a mass of 5.69 x 10ˆ26 kg, radius of 60,268,000 m and distance from the sun of 1,427 x 10ˆ6 km.
Uranus has a mass of 8.66 x 10ˆ25 kg, radius of 25,559,000 m and distance from the sun of 2,871 x 10ˆ6 km.
Neptune has a mass of 1.03 x 10ˆ26 kg, radius of 24,764,000 m and distance from the sun of 4,497 x 10ˆ6 km.
Sample Problem
Sample Problem : Earth a. What is the acceleration of gravity on Earth?
g = ( 6.67 x 10^-11 N m^2/kg^2 )( 5.97 x 10ˆ24 kg ) / ( 6,378,000 m ) ^2 = 9.788 m/s^2
b. What is the weight of a 50 kg mass on the Earth?
F = ( 6.67 x 10^-11 N m^2/kg^2 )( 5.97 x 10ˆ24 kg )(50kg) / ( 6,378,000 m ) ^2 = 9.788 m/s^2 x 50 kg = 489.44 N
c. What is the force that the sun pulls the earth?
F = ( 6.67 x 10^-11 N m^2/kg^2 )( 5.97 x 10ˆ24 kg )( 1.9891 ×10^30 kg) / ( 149.6 x 10ˆ6 km x 1000 m/km ) ^2 = 3.539 x 10^34 N
d. Why does the sun not appear to move although the Earth pulls it?
The sun pulls on the Earth with equal force that the Earth pulls on the sun. The greater mass of the sun means that the acceleration is very small (using 2nd law : a = F/m ). The sun is also being pulled on by other planets and every celestial body in space which makes it appear to be stationary relative to Earth.
Practice Problems
Problem #1 Mars
a.What is the acceleration of gravity on Mars?
b.What is the weight of a 50 kg mass on the Mars?
c.What is the force that the sun pulls Mars?
d.Draw a FBD of forces between Mars and Sun. Why does the sun not appear to move although Mars pulls it?
Problem #2 Venus
a.What is the acceleration of gravity on Venus?
b.What is the weight of a 50 kg mass on the Venus?
c.What is the force that the sun pulls Venus?
d.Draw a FBD of forces between Venus and Sun. Why does the sun not appear to move although Venus pulls it?
Problem #3 Jupiter
a.What is the acceleration of gravity on Jupiter?
b.What is the weight of a 50 kg mass on the Jupiter?
c.What is the force that the sun pulls Jupiter?
d.Draw a FBD of forces between Jupiter and Sun. Why does the sun not appear to move although Jupiter pulls it?
Links to Gravity Learning Interactives
Gravity Force Lab http://phet.colorado.edu/simulations/sims.php?sim=Gravity_Force_Lab
