Lesson Worksheet: Conservation of Energy Mathematics

In this worksheet, we will practice applying the conversion of energy principle to solve problems on moving bodies.


True or False: The change in kinetic energy + the change in potential energy = the work done.

  • ATrue
  • BFalse


A body of mass 20 kg fell from a height of 42.3 m above the surface of the ground. Find the sum of its kinetic energy and its potential energy relative to the ground 2 seconds after it started falling. Take 𝑔=9.8/ms.


A body of mass 9 kg fell vertically from a point 3.4 m above the ground. At a certain moment, the speed of the body was 3.9 m/s. Determine the change in the body’s gravitational potential energy from this point until it reached a point 68 cm above the ground. Take 𝑔=9.8/ms.


A body of mass 4 kg fell vertically from a height of 28 m above the surface of the ground. Find its gravitational potential energy 𝑃 relative to the ground and its kinetic energy 𝑇 when it was 7 m above the ground. Consider the acceleration due to gravity to be 9.8 m/s2.

  • A𝑃=823.2joules, 𝑇=274.4joules
  • B𝑃=274.4joules, 𝑇=84joules
  • C𝑃=1,097.6joules, 𝑇=823.2joules
  • D𝑃=823.2joules, 𝑇=84joules
  • E𝑃=274.4joules,𝑇=823.2joules


A body of a mass of 20 kg was projected vertically upward from the ground with a velocity of 30 m/s. It passed by a point A when its velocity was 10 m/s.

Calculate the potential energy of the body at point A. Neglect the air resistance and consider the acceleration due to gravity to be 9.8 m/s2.

Find the distance between point A and the ground surface, in meters, Give your answer to one decimal place.


A body started to slide down a smooth inclined plane of height 504 cm from its top. Find its speed when it reached the bottom. Take 𝑔=9.8/ms.

  • A21√3525 m/s
  • B21√7025 m/s
  • C42√3525 m/s
  • D84√355 m/s


A car descended 195 m on a slope from rest, which is equivalent to a vertical distance of 14 m. Given that 27 of the potential energy was lost due to resistance and that the resistance remained constant during the car’s motion, determine the car’s velocity after it had traveled the mentioned distance of 195 m. Take 𝑔=9.8/ms.


A particle of mass 281 g was projected at 37 cm/s up the line of greatest slope of a smooth plane inclined to the horizontal at an angle whose sine is 1011. Determine the change in the particle’s gravitational potential energy from the moment it was projected until its speed became 29 cm/s.


A body started sliding down the line of greatest slope of a smooth inclined plane. When it was at the top of the plane, its gravitational potential energy relative to the bottom of the plane was 1,830.51 joules. When it reached the bottom of the plane, its speed was 8.6 m/s. Find the mass of the body.


A body was projected up a rough inclined plane from its bottom. Its initial kinetic energy was 242 joules. The body continued moving until it reached its maximum height and then slid back down to the bottom. When it reached the bottom, its kinetic energy was 186 joules. Find the work done against friction π‘Š during the ascent and the gain in gravitational potential energy 𝑃 when the body was at its maximum height.

  • Aπ‘Š=28joules, 𝑃=214joules
  • Bπ‘Š=56joules, 𝑃=186joules
  • Cπ‘Š=14joules, 𝑃=228joules
  • Dπ‘Š=56joules, 𝑃=158joules

This lesson includes 21 additional questions and 213 additional question variations for subscribers.

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