Power Knowledge-Based Practice

Questions

1. 1.

   A vehicle of mass $m$ accelerates along a straight, horizontal track under a constant mechanical power output $P$. Neglecting all resistive forces, what is the acceleration of the vehicle when its instantaneous speed is $v$?

   • A) $a = \frac{P v}{m}$
   • B) $a = \frac{P}{m v}$
   • C) $a = \frac{P}{m}$
   • D) $a = \frac{P}{m v^2}$
2. 2.

   A car of mass 1000 kg moves along a straight, horizontal road. When its speed is 24 m/s, the engine delivers 48 kW of mechanical power while the total resistive force opposing its motion is 500 N. What is the instantaneous acceleration of the car at this moment?

   • A) 0.5 m/s²
   • B) 1.2 m/s²
   • C) 2.0 m/s²
   • D) 1.5 m/s²
3. 3.

   A water pump lifts $120\text{ kg}$ of water per minute through a vertical height of $15\text{ m}$ and discharges it with a speed of $10\text{ m/s}$. Taking $g = 10\text{ m/s}^2$, what is the useful mechanical power output of the pump?

   • A) 100 W
   • B) 300 W
   • C) 500 W
   • D) 400 W
4. 4.

   An electric motor consumes 500 W of electrical power while performing 36 kJ of useful mechanical work in 2.0 minutes. What is the efficiency of the motor?

   • A) 40%
   • B) 60%
   • C) 72%
   • D) 83%
5. 5.

   An electric hoist operating with an efficiency of 75% consumes 4.0 kW of electrical power. What maximum mass can this hoist lift vertically at a constant speed of 2.0 m/s, assuming the acceleration due to gravity is 10 m/s²?

   • A) 200 kg
   • B) 300 kg
   • C) 50 kg
   • D) 150 kg
6. 6.

   A sled is pulled across a level surface by a constant force of 240 N directed at an angle of $60^\circ$ above the horizontal. If the sled travels a horizontal distance of 20 m in 8.0 s, what is the average power delivered by this force?

   • A) 150 W
   • B) 240 W
   • C) 600 W
   • D) 300 W
7. 7.

   A motor accelerates a 500 kg cart from rest to a speed of 10 m/s along a frictionless horizontal track in 5.0 s. What is the average power delivered to the cart during this acceleration?

   • A) 1.0 kW
   • B) 5.0 kW
   • C) 10 kW
   • D) 25 kW
8. 8.

   A car travels along a straight, horizontal road at a constant speed of 25 m/s against total resistive forces of 600 N. What is the mechanical power output developed by the car's engine to sustain this motion?

   • A) 24 W
   • B) 2.4 kW
   • C) 15 kW
   • D) 375 kW
9. 9.

   An electric winch lifts an 80 kg crate vertically through a height of 15 m at a constant speed in 12 s. Assuming $g = 10\text{ m/s}^2$, what is the average power delivered by the winch to the crate?

   • A) 800 W
   • B) 1000 W
   • C) 1200 W
   • D) 12,000 W

Answers and step-by-step solutions appear after you finish the test.