Lesson Worksheet: Power Mathematics

In this worksheet, we will practice finding the power of a constant force using the relation 𝑃 = 𝐹 × 𝑣.

Q1:

Given that a carโ€™s maximum speed is 270 km/h and its engine generates a force of 96 kg-wt, determine the power of its engine.

Q2:

A car with an engine of 164 hp is moving at its maximum speed of 216 km/h. Calculate the magnitude of the force generated by its engine.

Q3:

A tractor has an engine of 187 hp and it is pulling against a force of 374 kg-wt. Find its maximum speed.

Q4:

A car of mass 5 metric tons is moving along a straight horizontal road. The resistance to its motion is directly proportional to its speed. When the car is traveling at 78 km/h, the resistance is equal to 40 kg-wt per metric ton of the carโ€™s mass. Given that the maximum force of the engine is 300 kg-wt, determine the carโ€™s maximum speed ๐‘ฃ and the power ๐‘ƒ at which its engine operates at this speed.

  • A๐‘ฃ=117/kmh, ๐‘ƒ=130hp
  • B๐‘ฃ=585/kmh, ๐‘ƒ=2,340hp
  • C๐‘ฃ=32.5/kmh, ๐‘ƒ=130hp
  • D๐‘ฃ=117/kmh, ๐‘ƒ=468hp

Q5:

A small aeroplane is flying horizontally. The air resistance is proportional to the square of its speed and was 520 kg-wt when it was moving at 205 km/h. Given that the maximum speed of the aeroplane is 300 km/h, determine the power of its engine, stating your answer to the nearest horsepower if required. Take ๐‘”=9.8/ms๏Šจ.

Q6:

Some workers are loading boxes in the back of a truck. Each box has a mass of 75 kg and the height of the truck is 1 m. Given that the average total power that the group can work at is 0.5 hp, calculate the number of boxes they can load into the truck in a minute. Take ๐‘”=9.8/ms๏Šจ.

Q7:

At a particular instance, a train of mass 147 metric tons was accelerating along a horizontal section of track at 68 cm/s2 against a resistive force of 50 kg-wt for each tonne of its mass. Given that the maximum speed of the train along this section of track was 72 km/h, find the power of its engine.

Q8:

A person of mass 66 kg walked up an inclined plane to a height of 450 meters in 5 minutes. Determine their average power throughout the walk.

Q9:

A train of mass 170 metric tons is moving along a horizontal section of track at a constant speed of 60 km/h. Given that the engineโ€™s power output is 410 hp, find the magnitude of the resistance, ๐‘…, to the trainโ€™s motion per metric ton of the trainโ€™s mass.

  • A๐‘…=29.54newtonspermetricton
  • B๐‘…=8.21newtonspermetricton
  • C๐‘…=10.85newtonspermetricton
  • D๐‘…=106.36newtonspermetricton

Q10:

A vehicle of mass 3 metric tons was moving at 51 km/h along a horizontal section of road. When it reached the bottom of a hill inclined to the horizontal at an angle whose sine is 0.5, it continued moving at the same speed up the road. Given that the resistance of the two sections of road is constant, determine the increase in the vehicleโ€™s power to the nearest horsepower. Take the acceleration due to gravity ๐‘”=9.8/ms๏Šจ.

This lesson includes 47 additional questions and 459 additional question variations for subscribers.

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