In this worksheet, we will practice calculating the work done by a variable force acting on a body over a displacement.

**Q2: **

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 .

**Q3: **

From Newtonβs universal gravitational law, we know that a body at a distance from the centre of the Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of the Earth is 6βββ371 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.

**Q4: **

A particle is moving in a straight line under the action of a force given by where the force is measured in newtons and the displacement is measured in metres. Calculate the work done by the force when the particle moves from to .

- A joules
- B joules
- C4 joules
- D joules

**Q5: **

The figure shows the relation between a force , measured in newtons, acting on a body and the distance , in metres, travelled by that body. Determine the work done between and .

**Q6: **

A block moves in a straight line under the action of a force , where metres is the displacement of the body from its initial position. The work done by the force in moving the block from to is 34 J. Determine the work done by in moving the block from to .

**Q7: **

A variable force , measured in new tons, is acting on a body, where . Find the work done by this force in the interval from to .