Classical mechanicsLesson 4 of 4 in the course Work and Kinetic Energy

Mechanical Power: Work Rates, Force–Velocity Relation, and Applications

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

Work and the work-energy theorem describe how forces transfer energy, but they do not by themselves tell us how quickly that transfer happens. Power adds the time dimension: it measures how rapidly work is done or energy is transferred.

Two people can do the same amount of work but take different amounts of time. For example, sprinters may reach the same speed and undergo the same change in kinetic energy, but the runner who does the work in less time has greater power.

All flashcards

What is power?
Power is the rate at which work is done or energy is transferred.
How is average power calculated?
Divide work done over an interval by its duration: Pavg=ΔW/ΔtP_{\mathrm{avg}} = \Delta W/\Delta t.
How is instantaneous power defined?
It is the time derivative of work: P=dW/dtP = dW/dt.
How is power related to force and velocity?
Power delivered by a force is its dot product with velocity: P=F⃗⋅v⃗P = \vec{F}\cdot\vec{v}.
What determines whether a force does positive or negative power?
The force's direction relative to velocity: along it gives positive power; opposite it gives negative power.

Quiz questions

  1. A force of magnitude FF acts on an object moving at speed vv, with angle ϕ\phi between force and velocity. What is the power delivered by the force?Answer: P=Fvcos⁡ϕP = Fv\cos\phi
  2. An object moves at an instant in a direction perpendicular to an applied force. What instantaneous power does that force deliver?Answer: Zero power
  3. A force acts opposite an object's velocity. What is the sign of the power delivered by that force?Answer: Negative
  4. A road has a 15% grade. Which relation defines this percentage grade in terms of the slope angle θ\theta?Answer: tan⁡θ=0.15\tan\theta = 0.15
  5. A car climbs a hill at constant velocity. What happens to its kinetic energy during the climb?Answer: It remains constant.

Based on University Physics Volume 1 by William Moebs, Samuel J. Ling, Jeff Sanny (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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