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Question

Difficulty: HardWork, Energy, and Power

Match each physical scenario on the left with its correct energy transformation or work-power principle on the right.

  • An electric crane lifting a 500 kg500\text{ kg} beam vertically at a constant speed of 2 m/s2\text{ m/s} (g=9.8 m/s2g = 9.8\text{ m/s}^2)Delivers a steady mechanical power output of 9800 W9{}800\text{ W} while translational kinetic energy remains constant
  • A descending elevator cabin being lowered at a constant speed by an overhead tension cableTension performs negative work on the system, removing gravitational potential energy without changing kinetic energy
  • A compressed pneumatic piston expanding rapidly to propel a projectile horizontally along a frictionless trackStored potential energy performs net positive work, converting directly into translational kinetic energy
  • A motor vehicle skidding to a complete halt on a level asphalt road with locked brakesA non-conservative friction force performs negative work, converting all kinetic energy into thermal energy

Answer

The electric crane matches delivering 9,800 W steady power with constant kinetic energy; the descending elevator matches tension doing negative work to remove potential energy; the pneumatic piston matches stored potential energy doing positive work to become kinetic energy; and the skidding vehicle matches friction doing negative work to convert kinetic energy into thermal energy.
Each match correctly links mechanical principles: the crane requires steady power calculated via P=Fv=(mg)v=9800 WP = Fv = (mg)v = 9{}800\text{ W}; lowering a load under tension performs negative work because force opposes displacement; expanding gas does positive work converting potential energy to kinetic energy; and sliding friction performs negative work converting kinetic energy into thermal energy.

Step-by-Step Solution

1
Analyze the electric crane lifting at constant speed to determine force and power.
Force F=mg=500 kg×9.8 m/s2=4900 NF = mg = 500\text{ kg} \times 9.8\text{ m/s}^2 = 4{}900\text{ N}, Power P=Fv=4900 N×2 m/s=9800 WP = Fv = 4{}900\text{ N} \times 2\text{ m/s} = 9{}800\text{ W}. Because velocity is constant, ΔKE=0\Delta KE = 0.
When velocity is constant, acceleration is zero, so applied upward force equals gravitational force, and instantaneous power equals force multiplied by velocity.
2
Evaluate the work done by tension on the descending elevator.
Upward cable tension is opposite to downward displacement (180∘180^\circ), so work is negative (W<0W < 0). Potential energy decreases while kinetic energy is unchanged.
Forces directed opposite to displacement extract mechanical energy by doing negative work.
3
Analyze the expanding pneumatic piston accelerating the projectile.
Internal potential energy exerts a force along the direction of motion, doing net positive work (W>0W > 0) that becomes kinetic energy.
According to the work-energy theorem, positive net work performed on a mass increases its kinetic energy.
4
Determine the energy transition for the braking vehicle.
Friction acts opposite to displacement, doing negative work to dissipate initial kinetic energy into heat.
Non-conservative frictional forces convert macroscopic kinetic energy into microscopic thermal energy.

Key Concept

Work-energy theorem, rate of energy transfer (power as P = Fv), sign conventions of mechanical work, and conservative versus dissipative energy transformations.
Estimated Time:1m 30s
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Topics

Work, Energy, and Power

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