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In this lesson, we will learn how to use integration to find the work done by a variable force.
Q1:
The figure shows the magnitude of a force acting on a body as it moves a distance π. 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 π=0 to π=7m.
Q2:
A body moves along the π₯-axis under the action of a force, πΉ. Given that πΉ=(8π +12)N, where π m is the displacement from the origin, determine the work done on the body by πΉ when the body moves from π =7m to π =8m.
Q3:
From Newtonβs universal gravitational law, we know that a body at a distance π from the center of Earth is affected by a gravitational force such that πΉ=ππ ο¨, where π 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.
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