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Difficulty: Very hardWork, Energy, and Power

Arrange the following mechanical systems in order of their average power output, from lowest power to highest power. Assume ideal conditions and use g=10 m/s2g = 10\text{ m/s}^2.

  1. 1A linear accelerator increases the speed of a 100 kg100\text{ kg} test sled from 2 m/s2\text{ m/s} to 6 m/s6\text{ m/s} over a period of 4 seconds4\text{ seconds}.
  2. 2A hydraulic press performs 18,000 J18,000\text{ J} of mechanical work to steadily compress a heavy-duty steel spring over a duration of 30 seconds30\text{ seconds}.
  3. 3A forklift pushes a heavy pallet horizontally at a constant speed of 4 m/s4\text{ m/s} against a constant kinetic friction force of 200 N200\text{ N}.
  4. 4A motorized winch lifts a 60 kg60\text{ kg} payload vertically by 10 meters10\text{ meters} at a constant velocity in 5 seconds5\text{ seconds}.

Answer

The correct order from lowest to highest power is: the linear accelerator sled (400 W400\text{ W}), the hydraulic press (600 W600\text{ W}), the forklift (800 W800\text{ W}), and the motorized winch (1,200 W1,200\text{ W}).
The linear sled produces 400 W400\text{ W} (from a 1,600 J1,600\text{ J} change in kinetic energy over 4 s4\text{ s}). The hydraulic press produces 600 W600\text{ W} (18,000 J/30 s18,000\text{ J} / 30\text{ s}). The forklift produces 800 W800\text{ W} (200 N×4 m/s200\text{ N} \times 4\text{ m/s}). The motorized winch produces 1,200 W1,200\text{ W} (from a 6,000 J6,000\text{ J} change in potential energy over 5 s5\text{ s}). This results in the correct ascending sequence.

Step-by-Step Solution

1
Calculate the average power of the linear accelerator sled.
Power = 400 W400\text{ W}
Calculate the change in kinetic energy ΔKE=12m(vf2−vi2)\Delta KE = \frac{1}{2}m(v_f^2 - v_i^2) and divide by time. ΔKE=0.5×100×(36−4)=1600 J\Delta KE = 0.5 \times 100 \times (36 - 4) = 1600\text{ J}. 1600 J/4 s=400 W1600\text{ J} / 4\text{ s} = 400\text{ W}.
2
Calculate the average power of the hydraulic press.
Power = 600 W600\text{ W}
Use the direct power formula P=W/tP = W / t. 18,000 J/30 s=600 W18,000\text{ J} / 30\text{ s} = 600\text{ W}.
3
Calculate the average power of the forklift.
Power = 800 W800\text{ W}
Since the speed is constant, the applied force equals the kinetic friction force. Use P=F×vP = F \times v. 200 N×4 m/s=800 W200\text{ N} \times 4\text{ m/s} = 800\text{ W}.
4
Calculate the average power of the motorized winch.
Power = 1,200 W1,200\text{ W}
Calculate the change in gravitational potential energy ΔPE=mgh\Delta PE = mgh and divide by time. 60×10×10=6000 J60 \times 10 \times 10 = 6000\text{ J}. 6000 J/5 s=1200 W6000\text{ J} / 5\text{ s} = 1200\text{ W}.
5
Arrange the resulting power values in ascending order.
Sled (400 W400\text{ W}), Press (600 W600\text{ W}), Forklift (800 W800\text{ W}), Winch (1,200 W1,200\text{ W}).
The prompt requires ordering from lowest to highest average power output.

Key Concept

Calculating average power output by integrating different energy formulas (kinetic energy, potential energy, direct work, and force-velocity).
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Topics

Work, Energy, and Power

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