How is work defined for a force acting along a path?

As the line integral $W_{AB}=\int_A^B \vec{F}\cdot d\vec{r}$.

For a constant force, what does the work depend on?

The net displacement between the endpoints: $W=\vec{F}\cdot\vec{d}$.

When does a normal force do zero work on an object moving along a surface?

When the displacement is along the surface and therefore perpendicular to the normal force.

Why is gravity conservative near Earth's surface?

Its work over any closed path is zero because the net change in height is zero.

What is the work done by an ideal spring from $x_A$ to $x_B$?

$W_{spring}=-\frac{1}{2}k(x_B^2-x_A^2)$.

Classical mechanicsLesson 1 of 4 in the course Work and Kinetic Energy

Work by Constant, Variable, Gravitational, and Spring Forces

5 flashcards · 5 quiz questions · 5 match pairs · 4 fill-in sentences · English

Save course

Lesson progress

0 / 5

Your progress is kept in this browser only.Sign up to save it

Summary

In physics, work describes energy transferred to or from an object when a force acts while the object moves. This lesson introduces the work equation, explains how direction affects work, and identifies its units.

$dW = \vec{F} \cdot d\vec{r} = F\,dr\cos\theta$ .

Here, $F$ is the force magnitude, $dr$ is the displacement magnitude, and $\theta$ is the angle between them. The dot product selects the part of the force parallel to the displacement. Equivalently, it selects the part of the displacement parallel to the force.

All flashcards

How is work defined for a force acting along a path?: As the line integral $W_{AB}=\int_A^B \vec{F}\cdot d\vec{r}$ .
For a constant force, what does the work depend on?: The net displacement between the endpoints: $W=\vec{F}\cdot\vec{d}$ .
When does a normal force do zero work on an object moving along a surface?: When the displacement is along the surface and therefore perpendicular to the normal force.
Why is gravity conservative near Earth's surface?: Its work over any closed path is zero because the net change in height is zero.
What is the work done by an ideal spring from $x_A$ to $x_B$ ?: $W_{spring}=-\frac{1}{2}k(x_B^2-x_A^2)$ .

Quiz questions

A constant kinetic-friction force of 4 N opposes an object sliding 8 m along a surface. What work does friction do?Answer: $-32\text{ J}$ , based on the sliding distance.
Near Earth's surface, with the vertical axis positive upward, what work does gravity do when an object moves from height $y_A$ to $y_B$ ?Answer: $-mg(y_B-y_A)$
For an ideal spring with equilibrium at $x=0$ , which expression gives its force when displacement is $x$ ?Answer: $F_x=-kx$
Quasistatically stretching an ideal spring from equilibrium to distance $x$ requires work $W$ . How much work is required to stretch it to $2x$ ?Answer: $4W$
A force varies with position along a path. Which method gives the total work it does?Answer: Integrate the force's component along each infinitesimal displacement over the path.

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.

All Classical mechanics lessons

Classical mechanicsNewton’s Third Law, Motion, and System Boundaries5 flashcards · 5 quiz questions · 4 gamesPlay free →Classical mechanicsSimple Harmonic Motion: Spring Oscillators, Phase, and Equilibrium5 flashcards · 5 quiz questions · 4 gamesPlay free →Classical mechanicsAngular Kinematics and Acceleration in Circular Motion5 flashcards · 5 quiz questions · 4 gamesPlay free →Classical mechanicsGravitational Fields, Weight, Rotation, and Gravity Inside Spheres5 flashcards · 5 quiz questions · 4 gamesPlay free →Classical mechanicsFree-Body Diagrams: Components, Contact Forces, and Constraints5 flashcards · 5 quiz questions · 4 gamesPlay free →Classical mechanicsCommon Forces and Fictitious Forces in Newtonian Mechanics5 flashcards · 5 quiz questions · 4 gamesPlay free →

Summary

All flashcards

Quiz questions

More in Classical mechanics