Efficiency Transitional Reasoning Practice

Questions

1. 1.

   To load cargo into a delivery truck with a bed 1.5 m above the ground, a logistics worker pushes a 120 kg crate up a 6.0 m inclined ramp at a constant speed. The worker exerts a continuous force of 400 N parallel to the ramp surface to overcome both gravity and friction. Taking the acceleration due to gravity as $10\text{ m/s}^2$, what is the efficiency of this inclined ramp system?

   • A) 75%
   • B) 60%
   • C) 33%
   • D) 25%
2. 2.

   An escalator in a transit station carries passengers between two levels separated by a vertical height of 6.0 m. During peak hours, the escalator transports an average of 40 passengers per minute, with a mean passenger mass of 70 kg. To maintain this continuous flow, the electric drive motor draws a steady electrical power of 4.0 kW. Taking the acceleration due to gravity as 10 m/s², what is the energy efficiency of the escalator system in lifting passengers?

   • A) 42%
   • B) 58%
   • C) 70%
   • D) 84%
3. 3.

   During a braking test on a test track, an electric commuter train with a total mass of 40,000 kg decelerates uniformly from 20 m/s to 10 m/s. Its regenerative braking system captures part of the train's mechanical energy and feeds 4.5 MJ of electrical energy back into the power grid. What is the energy efficiency of the regenerative braking system during this deceleration?

   • A) 75%
   • B) 56%
   • C) 44%
   • D) 25%
4. 4.

   An automated mechanical press uses an electric actuator to compress a heavy-duty spring in a clamping fixture. The spring has a spring constant of 8000 N/m and is compressed by a distance of 0.30 m from its uncompressed length. If the actuator operates with an overall energy efficiency of 60% during the compression process, how much electrical energy must be supplied to it?

   • A) 216 J
   • B) 360 J
   • C) 600 J
   • D) 1200 J
5. 5.

   An industrial energy storage unit uses an electric motor to drive a mechanical compressor that stores energy in a high-pressure air tank. The motor draws 8.0 kW of electrical power from the mains supply and operates with an efficiency of 75% to deliver mechanical power to the drive shaft. The compressor then converts the shaft power into useful stored pneumatic power with an efficiency of 60%, with all losses across both stages dissipated as heat. What are the overall efficiency of the two-stage system and the total rate at which energy is dissipated as heat?

   • A) Efficiency: 35%; Waste power: 5.2 kW
   • B) Efficiency: 40%; Waste power: 4.8 kW
   • C) Efficiency: 67.5%; Waste power: 2.6 kW
   • D) Efficiency: 45%; Waste power: 4.4 kW
6. 6.

   An engineering team evaluates the energy performance of a prototype electric delivery cart on a flat, horizontal surface. Starting from rest, the 600 kg cart accelerates to a cruising speed of 10 m/s, during which its battery pack supplies 40 kJ of electrical energy to the motor. If gaining kinetic energy is the only useful outcome of this process, what is the overall efficiency of the cart's drive system?

   • A) 75%
   • B) 60%
   • C) 30%
   • D) 25%
7. 7.

   A solar-powered irrigation system uses an electric pump to lift water from an underground well to an elevated storage tank. The pump raises water through a vertical height of 15 m at a steady rate of 720 liters per hour, while the solar array delivers a continuous electrical power of 50 W to the motor. Taking the density of water as 1.0 kg/L and the acceleration due to gravity as $10\text{ m/s}^2$, what is the energy efficiency of the pumping system?

   • A) 30%
   • B) 40%
   • C) 50%
   • D) 60%
8. 8.

   A flywheel energy storage unit absorbs 120 kJ of electrical energy while charging to its maximum operating speed. During a subsequent power outage, the unit discharges its stored energy to run an emergency medical device, delivering a constant electrical power of 150 W for 10 minutes. What is the overall energy efficiency of the flywheel system during this charge-discharge cycle?

   • A) 25%
   • B) 60%
   • C) 75%
   • D) 80%
9. 9.

   An electric motor is used to pull a loaded cart horizontally across a workshop floor at a constant speed of 2.5 m/s. A constant frictional force of 180 N opposes the motion of the cart, while electrical instruments show that the motor continuously draws 600 W of power from the mains supply. What is the overall efficiency of the motor system during this operation?

   • A) 25%
   • B) 30%
   • C) 45%
   • D) 75%
10. 10.

    An electric crane lifts a 150 kg beam vertically at a constant speed to a platform 2.0 m above the ground, drawing 4.0 kJ of electrical energy from its power supply. Taking the acceleration due to gravity as $10\text{ m/s}^2$, what percentage of the input energy is converted into useful work, and how much energy is dissipated as waste?

    • A) 25% efficiency, with 3.0 kJ dissipated
    • B) 33% efficiency, with 1.0 kJ dissipated
    • C) 60% efficiency, with 1.6 kJ dissipated
    • D) 75% efficiency, with 1.0 kJ dissipated

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