Worksheet: Work Done by a Variable Force

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

Q1:

The figure shows the magnitude of a force acting on a body as it moves a distance 𝑑 . Given that the force is measured in newtons, and the distance is measured in metres, determine, the work done in joules by the force to move the body from 𝑑 = 0 to 𝑑 = 7 m .

  • A 99 J
  • B 24.75 J
  • C 74.25 J
  • D 49.5 J

Q2:

A body moves along the π‘₯ -axis under the action of a force, 𝐹 . Given that 𝐹 = ( 8 𝑠 + 1 2 ) N , where 𝑠 m is the displacement from the origin, determine the work done on the body by 𝐹 when the body moves from 𝑠 = 7 m to 𝑠 = 8 m .

Q3:

From Newton’s universal gravitational law, we know that a body at a distance 𝑠 from the centre of the Earth is affected by a gravitational force such that 𝐹 = π‘˜ 𝑠  , where π‘˜ is a constant. Assuming the radius of the Earth is 6β€Žβ€‰β€Ž371 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 𝐹 , measured in newtons, acting on a body and the distance 𝑆 , in metres, travelled by that body. Determine the work done between 𝑆 = 0 m and 𝑆 = 1 0 m .

Q6:

A block moves in a straight line under the action of a force 𝐹 = ο€Ή 1 2 𝑠 + 6 𝑠 + 𝑐  2 N , where 𝑠 metres is the displacement of the body from its initial position. The work done by the force in moving the block from 𝑠 = 0 m to 𝑠 = 3 m is 34 J. Determine the work done by 𝐹 in moving the block from 𝑠 = 3 m to 𝑠 = 6 m .

Q7:

A variable force 𝐹 , measured in new tons, is acting on a body, where 𝐹 = 3 𝑠 βˆ’ 5 2 . Find the work done by this force in the interval from 𝑠 = 4 m to 𝑠 = 5 m .

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