Power Transitional Reasoning Download PDF

Questions

1. 1.

   An electric vehicle with a mass of 1200 kg accelerates along a straight, horizontal test track while its motor delivers a constant mechanical power of 60 kW to the drive wheels. At the instant the vehicle reaches a speed of 20 m/s, it experiences a combined resistive force of 600 N due to air resistance and mechanical drag. What is the instantaneous forward acceleration of the vehicle at this speed?

   • A) 1.0 m/s²
   • B) 2.5 m/s²
   • C) 3.0 m/s²
   • D) 2.0 m/s²
2. 2.

   An electric freight hoist is rated at a maximum electrical power input of 6.0 kW and operates with an overall efficiency of 75%. The hoist lifts a batch of identical 25 kg construction blocks placed on a 100 kg lifting platform through a vertical height of 12 m at a constant speed in a time interval of 20 s. Taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the maximum number of blocks that the hoist can raise in a single trip?

   • A) 22
   • B) 26
   • C) 30
   • D) 36
3. 3.

   An engineering team testing an aerodynamic vehicle on a straight, horizontal track determines that the opposing air resistance is directly proportional to the square of the vehicle's speed ($F_{\text{drag}} = k v^2$). To maintain a steady cruising speed of 20 m/s, the vehicle's engine must deliver a mechanical power output of 25 kW. Assuming all other resistive forces are negligible, what power must the engine deliver to cruise steadily at 40 m/s under the same conditions?

   • A) 50 kW
   • B) 100 kW
   • C) 150 kW
   • D) 200 kW
4. 4.

   A motorized winch pulls a 150 kg crate horizontally along a warehouse floor against a constant friction force of 180 N. Starting at an initial speed of 2.0 m/s, the winch accelerates the crate uniformly along a straight line to a final speed of 8.0 m/s over a time interval of 10 s. What average mechanical power does the winch deliver to the crate during this 10 s interval?

   • A) 900 W
   • B) 1350 W
   • C) 2160 W
   • D) 450 W
5. 5.

   An elevator system consists of an 800 kg cab connected by a cable over a motorized pulley to a 600 kg counterweight. When fully loaded, the cab carries passengers with a total mass of 400 kg and ascends vertically at a constant speed of 2.5 m/s. Assuming friction is negligible and taking the acceleration due to gravity as 10 m/s², what mechanical power must the motor deliver to maintain this upward motion?

   • A) 10 kW
   • B) 15 kW
   • C) 30 kW
   • D) 45 kW
6. 6.

   An agricultural irrigation pump draws water from an underground well at a depth of 20 m and discharges it at surface level through a nozzle at a speed of 10 m/s. The pump maintains a steady mass flow rate of 2.0 kg/s. Taking the acceleration due to gravity as $g = 10\text{ m/s}^2$, what is the useful mechanical power delivered to the water by the pump?

   • A) 100 W
   • B) 400 W
   • C) 500 W
   • D) 600 W
7. 7.

   A cyclist and bicycle have a combined mass of 80 kg and travel at a steady speed of 6.0 m/s up a straight road that rises 1.0 m vertically for every 20 m traveled along the slope. A total opposing force of 25 N from air drag and rolling resistance acts on the cyclist. Taking the gravitational acceleration as $g = 10\text{ m/s}^2$, what minimum mechanical power must the cyclist deliver to maintain this speed?

   • A) 150 W
   • B) 240 W
   • C) 390 W
   • D) 650 W
8. 8.

   An electric test vehicle of mass 250 kg accelerates uniformly from rest along a straight, horizontal track, reaching a velocity of 20 m/s in a time interval of 5.0 s. Assuming all resistive forces such as friction and air drag are negligible, the vehicle's motor delivers a constant forward thrust during this period. What are the average power delivered by the motor over the 5.0 s interval and the instantaneous power delivered at the end of the 5.0 s interval?

   • A) Average power is 10 kW; instantaneous power is 10 kW.
   • B) Average power is 20 kW; instantaneous power is 20 kW.
   • C) Average power is 20 kW; instantaneous power is 10 kW.
   • D) Average power is 10 kW; instantaneous power is 20 kW.
9. 9.

   A prototype electric transport pod travels along a straight, horizontal test track at a constant speed of 25 m/s against a total resistive force of 600 N. During this motion, the pod's electric drive system consumes electrical input power at a constant rate of 20 kW. Which statement correctly identifies the mechanical power delivered by the motor to sustain this motion and the operating efficiency of the drive system?

   • A) The motor delivers 15 kW of mechanical power, corresponding to an efficiency of 75%.
   • B) The motor delivers 15 kW of mechanical power, corresponding to an efficiency of 133%.
   • C) The motor delivers 24 kW of mechanical power, corresponding to an efficiency of 83%.
   • D) The motor delivers 12 kW of mechanical power, corresponding to an efficiency of 60%.
10. 10.

    In an automated distribution center, Crane X lifts a 300 kg crate vertically by 8.0 m in 12 s at a constant speed, while Crane Y lifts a 500 kg crate vertically by 6.0 m in 20 s at a constant speed. Assuming the gravitational field strength is $g = 10\text{ m/s}^2$, which statement correctly evaluates the total useful work performed and the average useful power output of the two cranes?

    • A) Crane Y delivers a greater power output because it performs more total work than Crane X.
    • B) Crane X performs more total work, and therefore it develops a greater power output than Crane Y.
    • C) Crane Y performs more total work, but Crane X delivers a greater useful power output.
    • D) Both cranes develop the same useful power output because their work-to-height ratios are equal.