Worksheet: Potential Energy

In this worksheet, we will practice finding potential energy and the change in it and using it to solve different problems.

Q1:

A body of mass 4 kg had a gravitational potential energy of 2,136.4 joules relative to the ground. Determine its height. Consider the acceleration due to gravity to be 9.8 m/s2.

Q2:

A crane lifts a body of mass 132 kg to a height of 20 m. Find the increase in the body’s gravitational potential energy. Consider the acceleration due to gravity 𝑔=9.8/ms.

Q3:

A body of mass 543 g is at a height of 22 m above the surface of the ground. Determine its gravitational potential energy relative to the ground, rounding your answer to two decimal places. Take 𝑔=9.8/ms.

  • A 58,535.40 J
  • B58.54 J
  • C 117,070.80 J
  • D117.07 J

Q4:

A body of mass 7.5 kg is at a height of 14 cm above the ground. Determine the potential energy of the body relative to the ground, take 𝑔=9.8/ms.

  • A 1 . 0 2 9 × 1 0 ergs
  • B 1 . 0 2 9 × 1 0 ergs
  • C 1 . 0 2 9 × 1 0 ergs
  • D 1 . 0 2 9 × 1 0 ergs

Q5:

A man of mass 92 kg is going from the sixth floor to the tenth floor in a lift. Given that the height of each floor is 3.3 m, determine the gain in gravitational potential energy. Consider the acceleration due to gravity to be 9.8 m/s2.

Q6:

A helicopter of mass 2,630 kg descended vertically from a height of 250 m to a height of 150 m. Find its loss in gravitational potential energy. Consider the acceleration due to gravity to be 𝑔=9.8/ms and give your answer in Scientific Notation .

  • A 3 . 9 × 1 0 J
  • B 6 . 4 × 1 0 J
  • C 2 . 6 × 1 0 J
  • D 1 0 J

Q7:

A body of mass 7 kg moved 52 cm up the line of greatest slope of a smooth plane inclined at 60 to the horizontal. Find the increase in its gravitational potential energy. Take 𝑔=9.8/ms.

  • A30.89 joules
  • B 3,089.29 joules
  • C 3,567.2 joules
  • D35.67 joules

Q8:

A body of mass 8 kg moved 238 cm up the line of greatest slope of a smooth plane inclined at 30 to the horizontal. Calculate the increase in its gravitational potential energy. Take 𝑔=9.8/ms.

Q9:

A person of mass 105 kg was hiking up a hill which was inclined to the horizontal at an angle whose sine is 13. Given that he covered a distance of 87 m, find the change in his gravitational potential energy. Take 𝑔=9.8/ms.

Q10:

A ball of mass 317 g was projected vertically upward at 29 m/s from a point 𝐴. It passed through a point 𝐵 at 21 m/s, where 𝐵 is vertically above 𝐴. Neglecting air resistance, use the work–energy principle to find the increase in the ball’s gravitational potential energy as it moved from 𝐴 to 𝐵.

Q11:

A particle is moving from point (9,3) to point (7,9) under the action of the conservative force Fij=107 dynes. Determine the change in the particle’s potential energy, given that the displacement is in centimeters.

Q12:

A body is moving in a straight line from point 𝐴(6,0) to point 𝐵(5,4) under the action of the force Fij=(𝑚+2)N. Given that the change in the body’s potential energy is 2 joules and that the displacement is in meters, determine the value of the constant 𝑚.

  • A 1 0
  • B6
  • C 6
  • D1

Q13:

A body is moving under the action of a constant force Fij=(5+3)N, where i and j are two perpendicular unit vectors. At time 𝑡 seconds, where 𝑡0, the body’s position vector relative to a fixed point is given by rij=(𝑡+4)+(4𝑡+8)m. Determine the change in the body’s potential energy in the first 9 seconds.

Q14:

A body of mass 3 kg had a gravitational potential energy of 1,528.8 joules relative to the ground. Determine its height. Consider the acceleration due to gravity to be 9.8 m/s2.

Q15:

A crane lifts a body of mass 101 kg to a height of 6 m. Find the increase in the body’s gravitational potential energy. Consider the acceleration due to gravity 𝑔=9.8/ms.

Q16:

A particle is moving from point (8,1) to point (10,3) under the action of the conservative force Fij=63 dynes. Determine the change in the particle’s potential energy, given that the displacement is in centimeters.

Q17:

A body of mass 3 kg moved 120 cm up the line of greatest slope of a smooth plane inclined at 30 to the horizontal. Find the increase in its gravitational potential energy. Take 𝑔=9.8/ms.

  • A17.64 joules
  • B 1,764 joules
  • C 3,528 joules
  • D35.28 joules

Q18:

A body of mass 580 g is at a height of 10 m above the surface of the ground. Determine its gravitational potential energy relative to the ground, rounding your answer to two decimal places. Take 𝑔=9.8/ms.

  • A 28,420.00 J
  • B28.42 J
  • C 56,840.00 J
  • D56.84 J

Q19:

A helicopter of mass 2,550 kg descended vertically from a height of 190 m to a height of 130 m. Find its loss in gravitational potential energy. Consider the acceleration due to gravity to be 𝑔=9.8/ms and give your answer in Scientific Notation .

  • A 3 . 2 × 1 0 J
  • B 4 . 7 × 1 0 J
  • C 1 . 5 × 1 0 J
  • D 8 × 1 0 J

Q20:

A ball of mass 334 g was projected vertically upward at 22 m/s from a point 𝐴. It passed through a point 𝐵 at 18 m/s, where 𝐵 is vertically above 𝐴. Neglecting air resistance, use the work–energy principle to find the increase in the ball’s gravitational potential energy as it moved from 𝐴 to 𝐵.

Q21:

A body is moving in a straight line from point 𝐴(5,7) to point 𝐵(7,5) under the action of the force Fij=(𝑚+4)N. Given that the change in the body’s potential energy is 84 joules and that the displacement is in meters, determine the value of the constant 𝑚.

  • A 3
  • B6
  • C11
  • D 1 1

Q22:

A body of mass 7 kg fell vertically from point 𝐴 to the ground. Given that, when it reached the ground, its kinetic energy was 3,724 joules, find its gravitational potential energy relative to the ground when it was at point 𝐴. Consider the acceleration due to gravity to be 9.8 m/s2.

Q23:

A body of mass 55 g started sliding down a smooth inclined plane. Find the gravitational potential energy lost by the time the body’s speed reached 2 m/s.

  • A0.22 joules
  • B110 joules
  • C0.11 joules
  • D55 joules

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