Power and Collisions

Name: Power and Collisions
Author: StemPy Lab

Two motors lift the same load to the same height, and one is faster. Two cars crash, and they stick together or bounce apart. In this course we measure how fast work is done with power, we study elastic and inelastic collisions in one and two dimensions, and we use the coefficient of restitution and the ballistic pendulum to find speeds that are hard to measure.

3 lessons, about 1 h 15 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Power
Power is the rate of doing work: $P = \dfrac{W}{t}$ , in watts ( $1\ \text{W} = 1\ \text{J/s}$ ). For a force on a moving body, $P = \vec{F} \cdot \vec{v}$ . Efficiency is useful power out over power in. The kilowatt-hour, $3.6 \times 10^{6}\ \text{J}$ , is a unit of energy. Air drag grows as $v^2$ , so the power to beat it grows as $v^3$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set
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Lesson 2about 25 min
Elastic and inelastic collisions in one dimension
In every collision with no outside force, momentum is conserved. In an elastic collision kinetic energy is conserved too; in an inelastic one some becomes heat and sound; in a perfectly inelastic one the bodies stick and the loss is greatest. For a head-on elastic collision with the target at rest, $v_1 = \dfrac{m_1 - m_2}{m_1 + m_2}u_1$ and $v_2 = \dfrac{2m_1}{m_1 + m_2}u_1$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 25 min
Coefficient of restitution and collisions in two dimensions
The coefficient of restitution $e = \dfrac{\text{speed of separation}}{\text{speed of approach}}$ measures how bouncy a collision is: $e = 1$ elastic, $e = 0$ sticking. A ball dropped on a floor rises to $e^2$ of its height each bounce. The ballistic pendulum uses momentum for the hit and energy for the swing. In two dimensions, momentum is kept separately along each axis; equal masses in an elastic glancing collision fly apart at right angles.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 note
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Power, Collisions and Restitution: Practice Paper

20 questions · 40 min

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Power and Collisions

Course outline (3 lessons)

Power

Elastic and inelastic collisions in one dimension

Coefficient of restitution and collisions in two dimensions

Test Your Learning

Your teacher

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