Worksheet: Work and Integration

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In this worksheet, we will practice using 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 𝑑. 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 𝑑=0 to 𝑑=7m.

  • A24.75 J
  • B99 J
  • C74.25 J
  • D49.5 J

Q2:

A body moves along the π‘₯-axis under the action of a force, 𝐹. Given that 𝐹=(8𝑠+12)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=7m to 𝑠=8m.

Q3:

From Newton’s universal gravitational law, we know that a body at a distance 𝑠 from the center of Earth is affected by a gravitational force such that 𝐹=π‘˜π‘ οŠ¨, 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.

Q4:

A particle is moving in a straight line under the action of a force 𝐹 given by 𝐹=2ο€»πœ‹π‘ 2cos where the force 𝐹 is measured in newtons and the displacement 𝑠 is measured in meters. Calculate the work done by the force 𝐹 when the particle moves from 𝑠=1m to 𝑠=2m.

  • A-2 joules
  • B4 joules
  • C-6 joules
  • D βˆ’ 4 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=0m and 𝑆=10m.

Q6:

A block moves in a straight line under the action of a force 𝐹=ο€Ή12𝑠+6𝑠+π‘ο…οŠ¨N, where 𝑠 meters is the displacement of the body from its initial position. The work done by the force in moving the block from 𝑠=0m to 𝑠=3m is 34 J. Determine the work done by 𝐹 in moving the block from 𝑠=3m to 𝑠=6m.

Q7:

A variable force 𝐹, measured in newtons, is acting on a body, where 𝐹=3π‘ βˆ’5. Find the work done by this force in the interval from 𝑠=4m to 𝑠=5m.

Q8:

A particle is moving in a straight line under the action of a constant force of magnitude 47 N acting in the direction of motion. The displacement of the particle is given by the relation sc(𝑑)=ο€Ό103𝑑+5π‘‘οˆοŠ©, where c is a unit vector parallel to the direction of motion. Given that the displacement is measured in metres, find the work done, in joules, by this force in the first 9 seconds of motion.

Q9:

A particle moves in a straight line under the action of the force 𝐹, where 𝐹=0.5𝑆 and 𝑆 is measured in meters. Calculate the work done by the force 𝐹 when the particle moves from 𝑆=0 to 𝑆=10.

  • A50
  • B100
  • C 2 5 2
  • D25

Q10:

A particle moves in a straight line under the action of the force 𝐹, where 𝐹=πœ‹π‘†sin and 𝑆 is measured in meters. Calculate the work done by the force 𝐹 when the particle moves from 𝑆=0 to 𝑆=12.

  • A2 J
  • B 1 2 J
  • C 2 πœ‹ J
  • D 3 2 J
  • E 1 πœ‹ J

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