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 bodyโ€™s gravitational potential energy. Consider the acceleration due to gravity ๐‘” = 9 . 8 / m s ๏Šจ .

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 ๐‘” = 9 . 8 / m s ๏Šจ .

  • A 58.54 J
  • B 117,070.80 J
  • C 58,535.40 J
  • D 117.07 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 ๐‘” = 9 . 8 / m s ๏Šจ .

  • A 1 . 0 2 9 ร— 1 0 ๏Šฌ ergs
  • B 1 . 0 2 9 ร— 1 0 ๏Šซ ergs
  • C 1 . 0 2 9 ร— 1 0 ๏Šฉ ergs
  • D 1 . 0 2 9 ร— 1 0 ๏Šฎ 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 ๐‘” = 9 . 8 / m s ๏Šจ and give your answer in Scientific Notation .

  • A 3 . 9 ร— 1 0 ๏Šฌ J
  • B 6 . 4 ร— 1 0 ๏Šฌ J
  • C 1 0 ๏Šญ J
  • D 2 . 6 ร— 1 0 ๏Šฌ J

Q7:

A body of mass 7 kg moved 52 cm up the line of greatest slope of a smooth plane inclined at 6 0 โˆ˜ to the horizontal. Find the increase in its gravitational potential energy. Take ๐‘” = 9 . 8 / m s ๏Šจ .

  • A 3,089.29 joules
  • B 35.67 joules
  • C 3,567.2 joules
  • D 30.89 joules

Q8:

A body of mass 8 kg moved 238 cm up the line of greatest slope of a smooth plane inclined at 3 0 โˆ˜ to the horizontal. Calculate the increase in its gravitational potential energy. Take ๐‘” = 9 . 8 / m s ๏Šจ .

Q9:

A person of mass 105 kg was hiking up a hill which was inclined to the horizontal at an angle whose sine is 1 3 . Given that he covered a distance of 87 m, find the change in his gravitational potential energy. Take ๐‘” = 9 . 8 / m s ๏Šจ .

Q10:

A ball of mass 317 g was projected vertically upwards at 29 m/s from a point ๐ด . It passed through a point ๐ต , at 21 m/s, where ๐ต is vertically above ๐ด . Neglecting air resistance, use the work-energy principle to find the increase in the ballโ€™s gravitational potential energy as it moved from ๐ด to ๐ต .

Q11:

A particle is moving from point ( 9 , 3 ) to point ( โˆ’ 7 , 9 ) under the action of the conservative force โƒ‘ ๐น = โˆ’ 1 0 โƒ‘ ๐‘– โˆ’ 7 โƒ‘ ๐‘— dynes. Determine the change in the particleโ€™s potential energy, given that the displacement is in centimetres.

Q12:

A body is moving in a straight line from point ๐ด ( โˆ’ 6 , 0 ) to point ๐ต ( โˆ’ 5 , 4 ) under the action of the force โƒ‘ ๐น = ๏€บ ๐‘š โƒ‘ ๐‘– + 2 โƒ‘ ๐‘— ๏† N . Given that the change in the bodyโ€™s potential energy is 2 joules and that the displacement is in metres, determine the value of the constant ๐‘š .

  • A โˆ’ 6
  • B6
  • C1
  • D โˆ’ 1 0

Q13:

A body is moving under the action of a constant force โƒ‘ ๐น = ๏€บ 5 โƒ‘ ๐‘– + 3 โƒ‘ ๐‘— ๏† N , where โƒ‘ ๐‘– and โƒ‘ ๐‘— are two perpendicular unit vectors. At time ๐‘ก seconds, where ๐‘ก โ‰ฅ 0 , the bodyโ€™s position vector relative to a fixed point is given by โƒ‘ ๐‘Ÿ = ๏’ ( ๐‘ก + 4 ) โƒ‘ ๐‘– + ( 4 ๐‘ก + 8 ) โƒ‘ ๐‘— ๏ž ๏Šจ ๏Šจ m . Determine the change in the bodyโ€™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 bodyโ€™s gravitational potential energy. Consider the acceleration due to gravity ๐‘” = 9 . 8 / m s ๏Šจ .

Q16:

A particle is moving from point ( 8 , โˆ’ 1 ) to point ( โˆ’ 1 0 , โˆ’ 3 ) under the action of the conservative force โƒ‘ ๐น = 6 โƒ‘ ๐‘– โˆ’ 3 โƒ‘ ๐‘— dynes. Determine the change in the particleโ€™s potential energy, given that the displacement is in centimetres.

Q17:

A body of mass 3 kg moved 120 cm up the line of greatest slope of a smooth plane inclined at 3 0 โˆ˜ to the horizontal. Find the increase in its gravitational potential energy. Take ๐‘” = 9 . 8 / m s ๏Šจ .

  • A 1,764 joules
  • B 35.28 joules
  • C 3,528 joules
  • D 17.64 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 ๐‘” = 9 . 8 / m s ๏Šจ .

  • A 28.42 J
  • B 56,840.00 J
  • C 28,420.00 J
  • D 56.84 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 ๐‘” = 9 . 8 / m s ๏Šจ and give your answer in Scientific Notation .

  • A 3 . 2 ร— 1 0 ๏Šฌ J
  • B 4 . 7 ร— 1 0 ๏Šฌ J
  • C 8 ร— 1 0 ๏Šฌ J
  • D 1 . 5 ร— 1 0 ๏Šฌ J

Q20:

A ball of mass 334 g was projected vertically upwards at 22 m/s from a point ๐ด . It passed through a point ๐ต , at 18 m/s, where ๐ต is vertically above ๐ด . Neglecting air resistance, use the work-energy principle to find the increase in the ballโ€™s gravitational potential energy as it moved from ๐ด to ๐ต .

Q21:

A body is moving in a straight line from point ๐ด ( 5 , โˆ’ 7 ) to point ๐ต ( โˆ’ 7 , 5 ) under the action of the force โƒ‘ ๐น = ๏€บ ๐‘š โƒ‘ ๐‘– + 4 โƒ‘ ๐‘— ๏† N . Given that the change in the bodyโ€™s potential energy is โˆ’ 8 4 joules and that the displacement is in metres, determine the value of the constant ๐‘š .

  • A11
  • B6
  • C โˆ’ 1 1
  • D โˆ’ 3

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