Work and Kinetic Energy

Name: Work and Kinetic Energy
Author: StemPy Lab

You carry a heavy bag along a level road. Are you doing work? In physics, the answer may surprise you. In this course we define work with the scalar product of two vectors, we find that work changes the kinetic energy of a body, and we learn to find the work of a force that changes along the path, as the force of a spring does.

3 lessons, about 1 h 10 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
The scalar product and the work done by a constant force
Work is done when a force moves its point of action along the motion: $W = \vec{F} \cdot \vec{d} = Fd\cos\theta$ , in joules. The work is positive when the force helps the motion, zero when it is at right angles to it, and negative when it opposes it. The scalar product of two vectors is $AB\cos\theta$ , or $A_xB_x + A_yB_y + A_zB_z$ from their parts.
1 simulation2 practice questions1 Python program5 problems1 Python lab1 question set
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Lesson 2about 20 min
Kinetic energy and the work-energy theorem
A moving body has kinetic energy $K = \tfrac12 mv^2$ . The work-energy theorem says that the net work done on a body equals its change in kinetic energy: $W_{\text{net}} = K_{\text{f}} - K_{\text{i}}$ . Positive net work speeds a body up, negative work slows it down. Since $K \propto v^2$ , a car at twice the speed needs four times the braking distance.
1 simulation2 practice questions1 Python program4 problems
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Lesson 3about 25 min
Work done by a variable force
When a force changes along the path, its work is the area under the force-displacement graph, $W = \int F\,dx$ . For a spring, $F = kx$ gives a triangle, so the work to stretch it from $x_1$ to $x_2$ is $\tfrac12 k(x_2^2 - x_1^2)$ . The further out the stretch, the more each centimetre costs.
1 simulation2 practice questions1 Python program3 problems1 Python lab1 note
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Work and Kinetic Energy: Practice Paper

15 questions · 20 min

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Work and Kinetic Energy

Course outline (3 lessons)

The scalar product and the work done by a constant force

Kinetic energy and the work-energy theorem

Work done by a variable force

Test Your Learning

Your teacher

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