Worksheet: Work Done by a Variable Force

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 .

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 the Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of the Earth is 6371 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.

From Newton’s universal gravitational law, we know that a body at a distance from the center of the Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of the Earth is 6371 km, find the magnitude of the work required for a satellite of mass 754 kg to achieve vertical takeoff from the ground and reach orbit at an altitude of 831 km.

From Newton’s universal gravitational law, we know that a body at a distance from the center of the Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of the Earth is 6371 km, find the magnitude of the work required for a satellite of mass 728 kg to achieve vertical takeoff from the ground and reach orbit at an altitude of 831 km.