1.

Scientists want to place a 3300 kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 2.3 times the radius of Mars above the surface of the planet. Here is some information that will help solve this problem:

m_mars = 6.4191 x 10²³ kg r_mars = 3.397 x 10⁶ m G = 6.67428 x 10^-11 N-m²/kg²

What is the force of attraction between Mars and the satellite?

__N

What speed should the satellite have to be in a perfectly circular orbit?

__ m/s

How much time does it take the satellite to complete one revolution?

__hrs

What should the radius of the orbit be (measured from the center of Mars), if we want the satellite to take 8 times longer to complete one full revolution of its orbit?

__m

2.

A single mass m₁= 3.8 kg hangs from a spring in a motionless elevator. The spring is extended x = 10 cm from its unstretched length.

What is the spring constant of the spring?

__ N/m

Now, three masses m₁= 3.8 kg, m₂= 11.4 kg and m₃= 7.6 kg hang from three identical springs in a motionless elevator. The springs all have the same spring constant that you just calculated above.

What is the force the top spring exerts on the top mass?

__ N

What is the distance the lower spring is stretched from its equilibrium length?

__ cm

Now the elevator is moving downward with a velocity of v = -3.7 m/s but accelerating upward with an acceleration of a = 4.7 m/s². (Note: an upward acceleration when the elevator is moving down means the elevator is slowing down.)

What is the force the bottom spring exerts on the bottom mass?

__N

What is the distance the upper spring is extended from its unstretched length?

__cm

What is the distance the MIDDLE spring is extended from its unstretched length?

__cm