Worksheet: Work Done by a Constant Force

In this worksheet, we will practice calculating the work done by a constant force on a particle moving horizontally or vertically.

Q1:

Calculate the work done by a force of 5 N acting on a body that moved 10 m to the north if the force was acting 3 0 ∘ south of west. State your answer in joules.

  • A 25 joules
  • B 50 joules
  • C βˆ’ 5 0 joules
  • D βˆ’ 2 5 joules

Q2:

A body of mass 0.9 kg moved a distance of 25 cm while accelerating at 8 cm/s2. Find the work done π‘Š .

  • A π‘Š = 1 8 0 e r g s
  • B π‘Š = 2 . 2 1 Γ— 1 0  j o u l e s
  • C π‘Š = 1 . 8 Γ— 1 0  j o u l e s
  • D π‘Š = 2 . 2 1 Γ— 1 0  e r g s
  • E π‘Š = 1 . 8 Γ— 1 0  e r g s

Q3:

A car of mass 1.5 metric tons was driving up a slope inclined to the horizontal at an angle whose sine is 0.3. The magnitude of the resistance to the motion of the car was 7 kg-wt per metric ton. If the car started moving from rest and accelerated uniformly over 15 seconds until it reached a velocity of 50 km/h, find the work done by the driving force while the car was accelerating. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s  .

  • A 4 . 7 0 Γ— 1 0  joules
  • B 1 . 2 3 Γ— 1 0  joules
  • C 4 . 5 9 Γ— 1 0  joules
  • D 6 . 1 5 Γ— 1 0  joules
  • E 1 . 0 7 Γ— 1 0 οŠͺ joules

Q4:

A particle is moving in a straight line under the action of a force of 685 dynes acting in the direction of motion. Find the work π‘Š in ergs done by the force over a displacement of 390 cm. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s  .

  • A π‘Š = 6 9 . 9 0 e r g s
  • B π‘Š = 2 . 6 2 Γ— 1 0  e r g s
  • C π‘Š = 1 . 7 6 e r g s
  • D π‘Š = 2 . 6 7 Γ— 1 0  e r g s
  • E π‘Š = 6 . 7 1 Γ— 1 0  e r g s

Q5:

The figure shows a force 𝐹 of magnitude 2 N and the displacement 𝑠 = 1 6 m covered by a body acted on by the force. Find the work done by the force.

  • A 32 J
  • B 8 J
  • C βˆ’ 1 6 J
  • D βˆ’ 1 6 √ 3 J

Q6:

Calculate the work done by a force of 13 N acting on a body that moved 40 m to the north if the force was acting towards the south. State your answer in joules.

Q7:

A force acted on a body of mass 400 g which had been at rest causing it to accelerate at 36 cm/s2. If the work done by this force was 0.72 joules, find the distance the body moved.

Q8:

A car is moving on a straight road with a constant velocity of 12 km/h. Given that the force generated by the engine of the car is 36 kg-wt, find the work done by the resistance of the road in one minute.

Q9:

A horizontal force 𝐹 started acting on a body of mass 4.5 kg that was at rest on horizontal plane. Given that the body moved a distance of 216 cm in 2 seconds against a constant resistance equal to 2 5 of the body’s weight, determine the work done by the force 𝐹 . Give your answer to one decimal place. Take 𝑔 = 9 . 8 / m s  .

Q10:

A body of mass 5 kg is dragged across a horizontal plane by two horizontal strings which make an angle of 6 0 ∘ to each other. The tension in each string is 4 9 √ 3 2 N. Given that the body started moving from rest against a resistive force equal to its weight, determine the time for the resultant to do 396.9 joules of work. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s  .

  • A 1 8 7 s
  • B 1 8 √ 2 7 s
  • C 9 √ 2 7 s
  • D 3 6 7 s

Q11:

A body of mass 27 kg was placed at the top of a smooth inclined plane of height 4.5 m. It slid down the line of the greatest slope until it reached the bottom of the plane. Calculate the work done by the weight of this body, given that the acceleration due to gravity 𝑔 = 9 . 8 / m s  .

Q12:

A body of mass 5 √ 2 kg was placed on a plane inclined at an angle of 3 0 ∘ to the horizontal. A force of magnitude 2 5 √ 2 N acted on the body causing it move 4 m up the plane. The line of action of the force was inclined at an angle of 3 0 ∘ to the plane’s line of greatest slope and it lay in the same vertical plane containing this line. Determine the work done by the force π‘Š  over this displacement and the work done by gravity π‘Š  . Take 𝑔 = 9 . 8 / m s  .

  • A π‘Š = 5 0 √ 2  j o u l e s , π‘Š = βˆ’ 9 8 √ 2  j o u l e s
  • B π‘Š = 5 0 √ 6  j o u l e s , π‘Š = βˆ’ 9 8 √ 2  j o u l e s
  • C π‘Š = 5 0 √ 6  j o u l e s , π‘Š = βˆ’ 9 8 √ 6  j o u l e s
  • D π‘Š = βˆ’ 5 0 √ 6  j o u l e s , π‘Š = 9 8 √ 2  j o u l e s

Q13:

A body of mass 900 g was projected vertically upward at 6.4 m/s. Find the work done by the weight of the body during the first 5 seconds of the motion of the body. Take 𝑔 = 9 . 8 / m s  .

  • A 1,362.69 J
  • B 1,878.66 J
  • C 2,443.14 J
  • D 798.21 J

Q14:

A streetcar was pulled 15 m along its track, by a rope making an angle of 2 1 ∘ with the track. Given that the tension in the rope was 193 kg-wt, find the work done by the tension in joules. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s  .

  • A 28,371 J
  • B 10,167 J
  • C 30,389 J
  • D 79,167 J
  • E 26,487 J

Q15:

A body of mass 111 g was resting on a horizontal plane. A horizontal force acted on the body causing it to accelerate at 14 cm/s2. If the resistance to the motion of the body was 5 g-wt, find the work done by the force over a displacement of 1 m. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s  .

Q16:

A car of mass 800 kg started moving in a straight line along a section of horizontal road. It accelerated uniformly at 40 cm/s2 under the action of a driving force 𝐹 . The work done by this force in the first 7 seconds was 966 kg-wtβ‹…m. Find the work done by the resistance to the car’s movement. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s  .

Q17:

A parent started pushing their child in a pushchair along a horizontal road by applying a force of 7 kg-wt to the handle of the pushchair. The force’s line of action was inclined downwards at an angle of 6 0 ∘ to the horizontal. Given that the joint mass of the pushchair and the baby was 22.5 kg, and that the resistance to the movement of the pushchair was 3.45 kg-wt, determine the work done by the resultant of the forces in the first minute. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s  .

Q18:

A man covered a horizontal distance of 8 m, pulling a box up an inclined plane using a rope.What is the work done by the rope if the tension in the rope is 90 N and the inclination angle of the inclined plane has tangent 5 1 2 ? Give your answer to two decimal places.

Q19:

A particle moved 100 cm up the line of greatest slope of a plane inclined at an angle of 1 5 ∘ to the horizontal. Given that the particle was moving under the action of a force of 20 N whose line of action is angled upwards at 4 0 ∘ to the horizontal, find the work done by this force.

Q20:

A body of mass 390 g is placed at the top of an inclined plane of height 20 cm and length 40 cm. Given that the resistance to the body’s motion is 161 g-wt, find the work done on the body untill it reaches the bottom of the inclined plane. Take 𝑔 = 9 . 8 / m s  .

Q21:

A car of 2.5 metric tons is moving up a plane inclined to the horizontal at an angle whose sine equals 0.3. The resistance to its motion is 7 kg-wt per tonne of its mass. Given that the car started moving from rest and accelerated uniformly for 15 seconds until it reached a velocity of 50 km/h, determine the work done by the car’s weight while the car was accelerating. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s  .

  • A βˆ’ 7 . 8 3 Γ— 1 0  joules
  • B βˆ’ 7 . 6 6 Γ— 1 0  joules
  • C βˆ’ 1 . 0 2 Γ— 1 0  joules
  • D βˆ’ 2 . 0 5 Γ— 1 0  joules
  • E βˆ’ 1 . 7 9 Γ— 1 0 οŠͺ joules

Q22:

A man was walking along a road inclined at an angle of 2 7 ∘ to the horizontal. He moved 188 meters in one direction and then came back to where he had started. Given that the resistance to his motion was a constant 3 kg-wt, and that the acceleration due to gravity 𝑔 = 9 . 8 / m s  , determine the work done by the resistive force π‘Š during the whole walk.

Q23:

A train of mass 40 metric tons ascended a section of track inclined to the horizontal at an angle whose sine is 0.2 at a constant velocity. The work done by the force of the engine to reach the top of the incline was 1 . 4 Γ— 1 0  kg-wtβ‹…m, whereas, over the same distance, the work done by the resistance was 1 . 2 Γ— 1 0  kg-wtβ‹…m. Find the length of the track 𝑙 and the magnitude of the resistance 𝑅 per tonne of the train’s mass. Take the 𝑔 = 9 . 8 / m s  .

  • A 𝑙 = 3 2 m , 𝑅 = 9 3 . 7 5 k g - w t
  • B 𝑙 = 1 6 . 3 3 m , 𝑅 = 1 8 3 . 7 5 k g - w t
  • C 𝑙 = 1 9 0 m , 𝑅 = 1 5 . 7 9 k g - w t
  • D 𝑙 = 1 6 0 m , 𝑅 = 1 8 . 7 5 k g - w t

Q24:

A car of mass 2.5 metric tons is moving on a straight horizontal road. The resistance to its motion is 7 kg-wt per tonne of its mass. Given that the car started moving from rest and accelerated uniformly for 15 seconds until it reached a velocity of 50 km/h, determine the work done by the resistance force while the car was accelerating. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s  .

  • A βˆ’ 5 . 1 8 Γ— 1 0  joules
  • B βˆ’ 2 . 4 1 Γ— 1 0  joules
  • C βˆ’ 2 . 5 9 Γ— 1 0  joules
  • D βˆ’ 1 . 8 2 Γ— 1 0  joules
  • E βˆ’ 1 . 7 9 Γ— 1 0 οŠͺ joules

Q25:

A parent started pushing their child in a stroller along a horizontal road by applying a force of 2.6 kg-wt to the handle of the stroller. The force’s line of action was inclined downward at an angle of 6 0 ∘ to the horizontal. Given that the joint mass of the stroller and the baby was 24 kg, and that the resistance to the movement of the stroller was 0.7 kg-wt, find the work done π‘Š  by the pushing force and the work done π‘Š  by the resistance of the road during the first 20 seconds. Take 𝑔 = 9 . 8 / m s  .

  • A π‘Š = 1 2 7  joules, π‘Š = βˆ’ 6 1 7  joules
  • B π‘Š = 6 2 4 . 2 6  joules, π‘Š = βˆ’ 3 3 6 . 1 4  joules
  • C π‘Š = 1 , 2 4 9  joules, π‘Š = βˆ’ 6 7 2  joules
  • D π‘Š = 6 4  joules, π‘Š = βˆ’ 3 4  joules

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