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

3.

In a classic carnival ride, patrons stand against the wall in a cylindrically shaped room. Once the room gets spinning fast enough, the floor drops from the bottom of the room! Friction between the walls of the room and the people on the ride make them the "stick" to the wall so they do not slide down. In one ride, the radius of the cylindrical room is R = 6.2 m and the room spins with a frequency of 23.4 revolutions per minute.

What is the speed of a person "stuck" to the wall?

__m/s

What is the normal force of the wall on a rider of m = 49 kg?

__N

What is the minimum coefficient of friction needed between the wall and the person?

If a new person with mass 98 kg rides the ride, what minimum coefficient of friction between the wall and the person would be needed?

Which of the following changes would decrease the coefficient of friction needed for this ride?increasing the rider's mass

increasing the radius of the ride

increasing the speed of the ride

increasing the acceleration due to gravity

To be safe, the engineers making the ride want to be sure the normal force does not exceed 2 times each persons weight - and therefore adjust the frequency of revolution accordingly. What is the minimum coefficient of friction now needed?