# Orbital Energy

A 60 kg object is to be launched into orbit, 7 x 10$^6$ m above the Earth's surface. Given that the radius of the earth is 6.4 x 10 $^6$ m and the mass of the earth is 6.0 x 10 $^{24}$ kg, find:

A. The work done to put the object into orbit.

B. The velocity required to put the object into orbit.

C. The velocity of the object once it is in orbit.

## Related Problems

The 100 kg box shown below is being pulled along the x-axis by a student. The box slides across a rough surface, and its position $x$ varies with time $t$ according to the equation $x = 0.5t^3 + 2t$ , where $x$ is in meters and $t$ is in seconds.

C. Calculate the net work done on the box in the interval $t$ = 0 to $t$ = 2 s would be greater than, less than, or equal to the answer in part (C). Justify your answer.

The figure below depicts a roller coaster. Assume the roller coaster starts at a velocity of 0 m/s from 70 m.

B. Determine the height of the track at point x. It is known that the roller coaster has a velocity of 30 m/s at x.

A 20 kg student is about to go down a slide. There is a 3 N frictional force opposing his movement. Assume his velocity at the top of the slide is 0 m/s. Find his velocity at the bottom of the slide.

A student is about to be launched from a spring loaded canon. The student weighs 60 kg and the spring constant is 200 N/kg. Find the students velocity the moment he leaves the canon if the spring is compressed, x = 3 m. Also find the students velocity after the spring has decompressed to x = 2 m.