Classical mechanicsLesson 1 of 1 in the course Work and Kinetic Energy

Work–Energy Theorem: Net Work, Motion, and Applications

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

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Summary

This lesson connects the work done by forces to changes in an object's motion. You will see how Newton's second law leads to the work-energy theorem and learn how the sign of net work reveals whether an object speeds up or slows down.

dWnet=F⃗net⋅dr⃗dW_{\text{net}} = \vec{F}_{\text{net}} \cdot d\vec{r}

dWnet=m dv⃗⋅v⃗dW_{\text{net}} = m\,d\vec{v}\cdot\vec{v}

Wnet,AB=12mvB2−12mvA2W_{\text{net},AB}=\frac{1}{2}m v_B^2-\frac{1}{2}m v_A^2

All flashcards

State the work-energy theorem.
The net work done on an object equals its change in kinetic energy: Wnet=Kf−Ki=ΔKW_{\text{net}}=K_f-K_i=\Delta K.
What is kinetic energy for a particle of mass mm and speed vv?
Kinetic energy is K=12mv2K=\frac{1}{2}mv^2.
How do you calculate infinitesimal work from a force and displacement?
Take their dot product: dW=F⃗⋅dr⃗dW=\vec{F}\cdot d\vec{r}. The dot product accounts for the direction of the force relative to the displacement.
What does positive net work mean?
The object's kinetic energy increases. Since its mass is unchanged, its speed at the end is greater than its speed at the start.
Does zero net work mean that no forces act?
No. Forces can act and do work that cancels in the total. Zero net work means only that the initial and final kinetic energies are equal.

Quiz questions

  1. A car starts from rest and moves without friction into a vertical loop of radius RR. What is the limiting starting height above the loop's bottom for maintaining contact at the top?Answer: 5R2\frac{5R}{2}
  2. At the top of a vertical loop, both the normal force and gravity point toward the center. Which radial force equation applies?Answer: N+mg=mv2RN+mg=m\frac{v^2}{R}
  3. On a frictionless curved track, with gravity as the only force doing work, what determines the change in kinetic energy between two points?Answer: The vertical height difference between the points.
  4. A moving object stops over distance Δs\Delta s under an average opposing force, with no other relevant work. What is the force's magnitude?Answer: KiΔs\frac{K_i}{\Delta s}
  5. An object slides down a frictionless incline at angle θ\theta, with distance Δs\Delta s measured down the slope. Which equation relates its initial and final speeds?Answer: vf2=vi2+2gΔssin⁡θv_f^2=v_i^2+2g\Delta s\sin\theta

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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