Worksheet: Power

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

Q1:

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 𝑔 = 9 . 8 / m s  .

Q2:

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

Q3:

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.

Q4:

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

Q5:

A train of mass π‘š tonnes was moving on a horizontal section of track at its maximum speed of 108 km/h. While the train was moving, the last carriage of mass 6 metric tons disconnected. The train continued moving and its maximum speed became 114 km/h. Given that the resistance to the train’s motion was 16 kg-wt per tonne of the train’s mass, determine the mass π‘š and the power of the train’s engine 𝑃 .

  • A π‘š = 1 1 4 m e t r i c t o n s , 𝑃 = 3 8 . 4 h p
  • B π‘š = 1 1 4 m e t r i c t o n s , 𝑃 = 7 2 9 . 6 h p
  • C π‘š = 1 0 8 m e t r i c t o n s , 𝑃 = 7 2 9 . 6 h p
  • D π‘š = 1 0 8 m e t r i c t o n s , 𝑃 = 6 9 1 . 2 h p

Q6:

A car of mass 5 tonnes 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, it is equal to 40 kg-wt per tonne of the car’s mass. Given that the maximum force of the engine is 300 kg-wt, determine the car’s maximum speed 𝑣 and the power 𝑃 its engine operates at this speed.

  • A 𝑣 = 3 2 . 5 / k m h , 𝑃 = 1 3 0 h p
  • B 𝑣 = 1 1 7 / k m h , 𝑃 = 4 6 8 h p
  • C 𝑣 = 5 8 5 / k m h , 𝑃 = 2 , 3 4 0 h p
  • D 𝑣 = 1 1 7 / k m h , 𝑃 = 1 3 0 h p

Q7:

A car of mass 3 metric tons with an engine of 79 hp is moving along a straight horizontal road at its maximum speed of 90 km/h. Given that the resistance to the car’s motion is proportional to its speed, find the resistance per tonne of the car’s mass when its momentum was 15,000 Nβ‹…s.

Q8:

A small airplane 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 airplane is 300 km/h, determine the power of its engine, stating your answer to the nearest horsepower if required. Take 𝑔 = 9 . 8 / m s  .

  • A 16,036 hp
  • B 184 hp
  • C 270 hp
  • D 1,237 hp

Q9:

A plane’s engine works at a rate of 259 kW when it is moving at 72 km/h. Given that the air resistance is proportional to the square of its speed, find the power the engine works at when the plane moves at 97 km/h. Round your answer to the nearest hundredth.

Q10:

A train of mass 290 metric tons is moving along a horizontal section of track. Its engine is running at a constant power of 4,640 hp. Given that the resistance to its motion is 50 kg-wt for each tonne of its mass, find its acceleration when its speed is 72 km/h. Take 𝑔 = 9 . 8 / m s  .

Q11:

An engine of mass 80 metric tons, initially at rest on a horizontal track, starts to move with constant acceleration. When its velocity is 84 km/h, its engine’s power is 2,520 kW. Given that the total resistance to the engine’s motion is 1 1 4 0 of its weight, determine the magnitude of its acceleration. Take 𝑔 = 9 . 8 / m s  .

Q12:

A lorry of mass 20 metric tons started moving along a horizontal section of road. The driving force generated by its engine is 1,000 kg-wt, and the resistance to its motion is 40 kg-wt per tonne of its mass. Determine its speed 𝑣 and its power 𝑃 1 2 0 seconds after it started moving. Consider the acceleration due to gravity to be 9.8 m/s2.

  • A 𝑣 = 1 1 . 7 6 / m s , 𝑃 = 1 6 h p
  • B 𝑣 = 5 . 8 8 / m s , 𝑃 = 7 8 . 4 h p
  • C 𝑣 = 1 0 5 . 8 4 / m s , 𝑃 = 1 , 4 1 1 . 2 h p
  • D 𝑣 = 1 1 . 7 6 / m s , 𝑃 = 1 5 6 . 8 h p

Q13:

When a car of mass 680 kg was moving along a straight horizontal road at its top speed, its engine was generating a driving force of 1,360 kg-wt. The driver then put the car in neutral and started coasting. Given that it covered a distance of 31.25 m before it came to rest, find the power of its engine. Take 𝑔 = 9 . 8 / m s  .

  • A 1 , 9 0 4 3 hp
  • B 9 5 2 3 hp
  • C 1 , 6 3 2 7 hp
  • D 1 , 3 6 0 2 1 hp

Q14:

A 210-horsepower pickup truck of mass 3.75 metric tons is ascending a section of a road inclined to the horizontal at an angle whose sine is 0.3. Given that the magnitude of the resistance to the truck’s motion is 50 kg-wt for each tonne of the truck’s mass, determine the truck’s maximum speed. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s  .

Q15:

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 vehicle’s power to the nearest horsepower. Take the acceleration due to gravity 𝑔 = 9 . 8 / m s  .

Q16:

A train of mass 160 metric tons was moving along a horizontal section of track at its maximum possible speed of 100 km/h. The resistance to its motion was 15 kg-wt for each tonne of its mass. The train started ascending a section of track which was inclined to the horizontal at an angle whose sine is 0.01. Given that the resistance was the same, determine the maximum speed 𝑣 of the train on the inclined track. Take 𝑔 = 9 . 8 / m s  .

Q17:

A car of mass 1,430 kg with an engine of 132 hp is ascending a section of road inclined to the horizontal at an angle whose sine is 1 1 3 . Its maximum speed on ascent is 36 km/h. Find the maximum speed that the car can move with on a horizontal section of road of the same resistance.

Q18:

A car of mass 7.26 metric tons was ascending a section of road inclined to the horizontal at an angle whose sine is 0.01 at its maximum speed of 39 km/h. The resistance to the car’s motion was 20 kg-wt for each ton of the car’s mass. Determine the power of the engine 𝑃 assuming it is constant, and find the maximum speed 𝑣 the car can descend the same road. Consider the acceleration due to gravity to be 9.8 m/s2.

  • A 𝑃 = 1 0 . 4 9 h p , 𝑣 = 1 3 / k m h
  • B 𝑃 = 3 1 . 4 6 h p , 𝑣 = 4 0 . 5 9 / k m h
  • C 𝑃 = 3 1 . 4 6 h p , 𝑣 = 1 1 7 / k m h
  • D 𝑃 = 1 2 . 6 3 h p , 𝑣 = 5 9 / k m h

Q19:

The combined mass of a cyclist and their bike is 64 kg. The greatest power the cyclist can produce is 4 3 metric horsepower. Given that the maximum speed of the cyclist on a horizontal section of road is 18 km/h, calculate the resistance 𝑅 to their motion in kilogram-weight. If the cyclist started ascending a hill inclined to the horizontal at an angle whose sine is 1 4 , what would their maximum speed 𝑣 m a x be in kilometres per hour given that the resistance of the road remains the same?

  • A 𝑅 = 6 . 2 5 k g - w t , 𝑣 = 1 0 / m a x k m h
  • B 𝑅 = 3 k g - w t , 𝑣 = 1 0 / m a x k m h
  • C 𝑅 = 2 2 . 5 k g - w t , 𝑣 = 2 0 / m a x k m h
  • D 𝑅 = 2 0 k g - w t , 𝑣 = 1 0 / m a x k m h

Q20:

A car of mass 2.1 metric tons was moving along a horizontal section of road at its maximum speed of 60 km/h. When the car reached the top of a section of road that was inclined to the horizontal at an angle whose sine is 0.5, the driver put the car in neutral and coasted down the hill. Given that the car kept moving at the same speed and that the resistance of the two roads was the same, determine the power of the car’s engine, rounding your answer to the nearest horsepower. Consider the acceleration due to gravity to be 9.8 m/s2.

Q21:

A locomotive of mass 30 metric tons is pulling a train of mass 105 metric tons along a straight horizontal track at its maximum speed of 24 m/s. When the same locomotive pulls a train of mass 60 metric tons up a section of track inclined to the horizontal at an angle whose sine is 1 5 0 , it maximum speed is the same. Given that the resistance per tonne of the train’s mass it constant on both sections of track, determine the resistance 𝑅 in kg-wt per tonne of the train’s mass, and find the power of the locomotive 𝑃 .

  • A 𝑅 = 6 0 k g - w t per tonne, 𝑃 = 2 , 5 9 2 h p
  • B 𝑅 = 4 0 k g - w t per tonne, 𝑃 = 1 , 7 2 8 h p
  • C 𝑅 = 4 0 k g - w t per tonne, 𝑃 = 1 , 1 5 2 h p
  • D 𝑅 = 5 , 4 0 0 k g - w t per tonne, 𝑃 = 1 , 7 2 8 h p
  • E 𝑅 = 5 , 4 0 0 k g - w t per tonne, 𝑃 = 1 , 1 5 2 h p

Q22:

A car of mass 3 metric tons was ascending a road inclined to the horizontal at an angle whose sine is 1 4 0 at its maximum speed of 54 km/h. Later on, the same car ascended another road which was inclined to the horizontal at an angle whose sine is 1 1 2 0 . On this hill its maximum speed was 72 km/h. Given that the resistance to the cars motion was the same on both roads, determine the horsepower of the car’s engine 𝑃 and the resistance of the roads 𝑅 .

  • A 𝑃 = 4 0 h p , 𝑅 = 1 2 5 k g - w t
  • B 𝑃 = 4 0 h p , 𝑅 = 5 0 k g - w t
  • C 𝑃 = 2 5 h p , 𝑅 = 1 2 5 k g - w t
  • D 𝑃 = 6 0 h p , 𝑅 = 2 2 5 k g - w t

Q23:

A lorry of mass 4 tonnes was carrying a load of 3 tonnes of stone. It started descending a hill inclined to the horizontal at an angle whose sine is 1 5 0 at its maximum speed of 78 km/h. When the lorry reached the bottom, it unloaded the stone and went back up the hill. Find its the maximum speed of ascent assuming the resistance of the road is constant and equal to 84 kg-wt per tonne of the lorry’s mass.

Q24:

When a truck of mass 6 metric tons was moving up a hill that was inclined to the horizontal at an angle whose sine is 1 2 0 , its maximum speed was 72 km/h. When it reached the top, a load of 2 metric tons was added to the truck, and it descended the hill. Its maximum speed on descent was 108 km/h. Determine the magnitude of the resistance 𝑅 to the truck’s motion assuming that it was constant, and find the maximum power 𝑃 of the truck’s engine in horsepower.

  • A 𝑅 = 1 , 8 0 0 k g - w t , 𝑃 = 8 4 0 h p
  • B 𝑅 = 1 , 8 0 0 k g - w t , 𝑃 = 5 6 0 h p
  • C 𝑅 = 6 0 0 k g - w t , 𝑃 = 2 4 0 h p
  • D 𝑅 = 2 , 1 0 0 k g - w t , 𝑃 = 5 6 0 h p

Q25:

A car of mass 5.4 metric tons was moving along a horizontal road at 126 km/h. When the driver reached the top of a descent inclined to the horizontal at an angle whose sine is 1 2 4 , she put the car in neutral and started to freewheel down the slope. The car kept moving at the same speed. Given that the resistance of the inclined road was 3 4 that of the horizontal road, determine the horsepower the engine had been outputting on the horizontal section of the road.

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