Gravitation

Certain neutron stars (extremely dense stars) are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation?

Gravitation

A rocket is accelerated to speed v = 2 sq. root gRe near Earth's surface (where Earth's radius is Re), and it then coasts upward. a) Show that it will escape from Earth. b) Show that very far from Earth its speed will be v = sq. root 2gRe.

Calculating the linear speed of a satellite in a circular orbit and the period of revolution.

What linear speed must an Earth's satellite have to be in a circular orbit at an altitude of 160 km? What is the period of revolution?

Finding the total mechanical energy of an inelastic satellite collision.

Consider two satellites, A and B, both of mass m, moving in the same circular orbit of radius r around the Earth, of mass Me, but in opposite senses of rotation and therefore on a collision course. a) In terms of G, Me, m, and r, find the total mechanical energy Ea and Eb of the two satellites plus Earth's system before collision. b) If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass = 2m), find the total mechanical energy immediately after collision. c) Describe the subsequent motion of the wreckage.

Calculating the time it takes to heat a specified amount of water.

A 5000W heater is used to heat water. How long will it take to heat 20 kg of water from 20 degrees C to 100 degrees C assuming perfect efficiency?