Question

Difficulty: MediumWork, Energy, and Power

In mechanical systems, energy exists in various forms and transitions through work and power. Match each physical scenario on the left with its corresponding energy classification or power characteristic on the right.

  • A compressed coil spring inside an automotive shock absorberElastic potential energy stored through mechanical deformation
  • A transport aircraft cruising at a steady altitude and airspeedSimultaneous presence of gravitational potential energy and kinetic energy
  • Friction brake pads clamping a spinning wheel rotor to a stopDissipation of mechanical kinetic energy into thermal energy
  • An electric hoist doing 2,000 J2,000\text{ J} of lifting work every secondMechanical power delivery rated at 2 kilowatts2\text{ kilowatts} (2,000 W2,000\text{ W})

Answer

The compressed spring matches with elastic potential energy stored through mechanical deformation; the cruising aircraft matches with simultaneous gravitational potential and kinetic energy; the friction brake pads match with the dissipation of kinetic energy into thermal energy; and the electric hoist lifting rate matches with a mechanical power delivery of 2 kilowatts.
Each scenario correctly illustrates a fundamental principle of work, energy, and power: deformation stores elastic potential energy; elevated motion embodies simultaneous kinetic and gravitational potential energy; frictional braking converts kinetic energy to heat; and a work rate of 2,000 joules per second represents 2,000 watts (2 kW) of power.

Step-by-Step Solution

1
Analyze the energy state of the compressed spring.
Identified as elastic potential energy stored by mechanical strain.
Potential energy is stored energy resulting from position or configuration, such as a compressed or stretched spring.
2
Analyze the mechanical state of the cruising aircraft.
Contains both gravitational potential energy (mghmgh) and kinetic energy (12mv2\frac{1}{2}mv^2).
The aircraft is elevated above ground level and simultaneously moving at a high velocity.
3
Analyze the energy transformation occurring during vehicle braking.
Conversion of mechanical kinetic energy into thermal energy via friction.
Non-conservative frictional forces do negative work on the wheel, dissipating motion into heat.
4
Calculate the power output of the electric hoist performing 2,000 J2,000\text{ J} of work per second.
P=2000 J1 s=2000 W=2 kWP = \frac{2000\text{ J}}{1\text{ s}} = 2000\text{ W} = 2\text{ kW}.
Power is the time rate at which work is performed or energy is converted (1 W=1 J/s1\text{ W} = 1\text{ J/s}).

Key Concept

Classification of energy forms (kinetic, gravitational potential, elastic potential), energy dissipation via friction, and the calculation of power as the rate of doing work.
Estimated Time:1m 0s
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