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Lesson Worksheet: The Work–Energy Principle Mathematics

In this worksheet, we will practice using the work–energy principle to solve problems of motion of a particle.

Q1:

A particle of mass 150 g was projected at 13 m/s across a horizontal plane. It decelerated uniformly at 2 m/s2. Find the change in its kinetic energy in the first 4 seconds of motion.

Q2:

A body of mass 96 kg was moving in a straight line at 17 m/s. A force started acting on it in the opposite direction to its motion. As a result, over the next 96 m, its speed decreased to 11 m/s. Using the work-energy principle, determine the magnitude of the force.

Q3:

A body of mass 400 g was projected at 4 m/s vertically downward from a point 5 m above the ground. Use the work–energy principle to calculate the body’s kinetic energy when it was about to hit the ground. Take 𝑔=9.8/ms .

Q4:

A body of mass 5 kg fell vertically from a height of 15 m above the surface of the earth. Using the work-energy principle, find the kinetic energy of the body just before it hit the ground. Take 𝑔=9.8/ms.

Q5:

A tram of mass 2 metric tons was being towed by a rope inclined at an angle of 60 to the track against a resistance of 20 kg-wt. Given that the tension in the rope was 121 kg-wt, use the work–energy principle to find the kinetic energy of the tram 𝐸 and its speed 𝑣 after moving a distance of 16 m. Take the acceleration due to gravity to be 𝑔=9.8/ms.

  • A𝐸=2,256kg-wtm, 𝑣=4.7/ms
  • B𝐸=648kg-wtm, 𝑣=2.52/ms
  • C𝐸=1,616kg-wtm, 𝑣=3.98/ms
  • D𝐸=1,288kg-wtm, 𝑣=3.55/ms

Q6:

A body of mass 15 kg fell from a height of 15 m above the ground. Using the work–energy principle, find its kinetic energy just before it hit the ground. Consider the acceleration due to gravity to be 9.8 m/s2 .

Q7:

A ring of mass 1.5 kg was sliding down a vertical pole. Starting from rest, it accelerated over a distance of 3.3 m until its speed became 6.2 m/s. Using the work-energy principle, determine the work done by the resistance to the ring’s motion. Take 𝑔=9.8/ms.

Q8:

The coordinates of the points 𝐴 and 𝐵 are (8,8) and (9,3). A body of unit mass moved from 𝐴 to 𝐵 in the direction of 𝐴𝐵 under the action of the force F, where Fij=(6+7) force units. Given that the body started moving from rest, use the work-energy principle to find its kinetic energy at point 𝐵.

Q9:

A body of mass 125 kg fell vertically from a height of 112 cm onto a section of sand. It sank 5 cm into the sand before it came to rest. Using the work-energy principle, calculate the resistance of the sand to the body’s motion. Take 𝑔=9.8/ms.

Q10:

Two bullets of equal mass were fired toward a target at the same speed but in opposite directions. The target was formed of two different pieces of metal stuck together. The first was 9 cm thick, and the second was 12 cm thick. When the bullets hit the target, the first one passed through the first layer and embedded 4 cm into the second before it stopped, whereas the other bullet passed through the second layer and embedded 5 cm into the first layer before it stopped. Using the work–energy principle, calculate the ratio of the resistance of the first metallic layer to that of the second.

  • A75
  • B811
  • C21
  • D87

This lesson includes 66 additional questions and 468 additional question variations for subscribers.

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