Lesson: Work and Integration

The figure shows the magnitude of a force acting on a body as it moves a distance . Given that the force is measured in newtons and the distance is measured in meters, determine the work done in joules by the force to move the body from to .

A body moves along the -axis under the action of a force, . Given that , where m is the displacement from the origin, determine the work done on the body by when the body moves from to .

From Newton’s universal gravitational law, we know that a body at a distance from the center of Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of Earth is 6,371 km, find the magnitude of the work required for a satellite of mass 793 kg to achieve vertical takeoff from the ground and reach orbit at an altitude of 831 km.