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Lesson Worksheet: Potential Energy Mathematics

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

Q1:

Fill in the blank: The potential energy of a particle of mass 𝑚 moving on the greatest slope line of a smooth inclined plane when it is at a height ℎ above the ground surface equals .

  • A𝑚𝑔ℎ
  • B14𝑚𝑔ℎ
  • C12𝑚𝑔ℎ
  • D−𝑚𝑔ℎ
  • E2𝑚𝑔ℎ

Q2:

True or False: The change in the potential energy of a particle when it moves from an initial position to a final position is equal the work done by the force during the motion.

  • AFalse
  • BTrue

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.

Q4:

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.

Q5:

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.

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.

  • A3.9×10 J
  • B6.4×10 J
  • C2.6×10 J
  • D10 J

Q7:

A body of mass 4 kg is moving down an inclined smooth plane with angle 30∘ under its own weight. If the body starts its motion from rest, what is the change in the potential energy of the body, in joules, 2 seconds after it starts moving? Let 𝑔=9.8/ms.

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 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.

Q10:

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 𝑡≥0, 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.

This lesson includes 34 additional questions and 198 additional question variations for subscribers.

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