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Worksheet: 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 = 7 m .

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

Q2:

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 = 6 m .

  • A 77 J
  • B 19.25 J
  • C 57.75 J
  • D 38.5 J

Q3:

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 .

Q4:

A body moves along the π‘₯ -axis under the action of a force, 𝐹 . Given that 𝐹 = ( 4 𝑠 + 1 0 ) 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 = 5 m to 𝑠 = 7 m .

Q5:

From Newton’s universal gravitational law, we know that a body at a distance 𝑠 from the center of the Earth is affected by a gravitational force such that 𝐹 = π‘˜ 𝑠 2 , where π‘˜ 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.

  • A 33 681 353.33 kg-wtβ‹…km
  • B 9 521 459.5 kg-wtβ‹…km
  • C 3 886 310 kg-wtβ‹…km
  • D 582 946.5 kg-wtβ‹…km
  • E 5 635 149.5 kg-wtβ‹…km

Q6:

From Newton’s universal gravitational law, we know that a body at a distance 𝑠 from the center of the Earth is affected by a gravitational force such that 𝐹 = π‘˜ 𝑠 2 , where π‘˜ 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.

  • A 32 024 893.33 kg-wtβ‹…km
  • B 9 053 191 kg-wtβ‹…km
  • C 3 695 180 kg-wtβ‹…km
  • D 554 277 kg-wtβ‹…km
  • E 5 358 011 kg-wtβ‹…km

Q7:

From Newton’s universal gravitational law, we know that a body at a distance 𝑠 from the center of the Earth is affected by a gravitational force such that 𝐹 = π‘˜ 𝑠 2 , where π‘˜ 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.

  • A 30 920 586.67 kg-wtβ‹…km
  • B 8 741 012 kg-wtβ‹…km
  • C 3 567 760 kg-wtβ‹…km
  • D 535 164 kg-wtβ‹…km
  • E 5 173 252 kg-wtβ‹…km