More Physics Questions

Question

Hi, I had some more physics questions:

1. A satellite of mass 200 kg completes a circular orbit of the Earth in 120 minutes. A 400 kg satellite is then put into orbit at the same height above the Earth. Which of the following represents the time, in minutes, for the 400 kg satellite to complete a circular orbit?

I know that the answer is still 120 minutes but WHY???

2. The amplitude of a body undergoing simple harmonic motion is doubled. Which of the following is doubled..?

The correct answer was maximum speed. why is this?

Answer 1

1. The force acting on the satellite depends on its mass, but the acceleration requires that you divide the force by the mass, which means that it is independent of the mass. Therefore, all velocities, displacements etc. are independent of the mass. That's why the time is the same regardless of whether it is the size of a bicycle or the size of a bus.

2. The energy of the body at any given point x is:

1/2 k x^2 + 1/2 k v^2, a constant. We assume that there is no damping that drains energy, of course.

This is the sum of the potential and kinetic energies. At the amplitude, only the first term survives, and x = A, the amplitude. At x = 0, the second term survives, and the value is the maximum velocity. Equate the two (since the energy is constant), and you see why the maximum velocity doubles.