Exploring Our Universe:
From the Classroom to Outer Space
II. The FUSE Satellite
Activity #1 Solutions

1. When the cork is moving in a circle, the string is taut.

2. Tension will increase if the cork moves faster or moves at the same speed with a smaller radius.

3. If the string suddenly breaks:

a) There is no tension.
b) The cork flies off  tangent to the circle.
4. Student answers will vary. Sample values:
cork mass
radius of orbit
time for ten orbits
period = 
time for ten orbits/10
 13 g = 0.013 kg
 0.50 m
 4.0 s
 0.40 s

5. The arrow should point to the center of the circle.

6. Again, the arrow should point to the center of the circle.

7.

a) Yes. It requires greater tension to increase speed.
b) No. It should require greater tension to swing the cork with a smaller radius if the speed is kept the same. Students may confuse speed and period. Note that to keep the speed the same, if you use half  the radius you must use half  the period.
8. Student answers will vary. Using values from the table above:
 
v = 2p R / period =   7.9  m/s

Fc =     1.6   N

9. A common error is not converting to SI units. The force required has order of magnitude 1 N, the weight of an apple.

10.

M is the mass of  Earth = 6.0 x 10 24 kg
m is the mass of FUSE = 1.4 x 103 kg
R is the distance between the center of mass of FUSE and  the center of mass of  the Earth =  7.1 x 106 m

Fg =  1.1 x 104 N


11. The arrow representing force should point to the center of Earth. The arrow representing velocity should be perpendicular to the arrow representing force.

12.

a)    Fg =  F c = m v2
                          R
Plug in the values given in the solution to 10. above and solve for v.  v =  7.5 x 103 m/s.

b)  period = 100 minutes x 60 s/minute = 6000s

v = 2p R / period = 7.4 x 103 m/s.
 

13. The sketch should show the path curving down to the surface of Earth.

14. The paper model is difficult to fly because there is a good deal of air resistance.