Work, Energy and Power: Mechanism

≈ 30 min

Mechanism

Follow the mechanism step by step and distinguish what causes the change from what is merely observed.

This extension applies that lens specifically to Work, Energy and Power.

Work done by a constant force $\vec{F}$ through a displacement $\vec{d}$ is

W = Fd\cos\theta

where $\theta$ is the angle between force and displacement. Work is a scalar, measured in joules, and it is zero whenever the force is perpendicular to the motion.

Kinetic energy is $K = \tfrac{1}{2}mv^2$ , and the work–energy theorem states

W_{\text{net}} = \Delta K = \tfrac{1}{2}mv_f^2 - \tfrac{1}{2}mv_i^2

For a conservative force such as gravity we may define a potential energy, $U = mgh$ near the Earth's surface, and then mechanical energy $E = K + U$ is conserved when no non-conservative force (friction, air drag) does work.

Power is the rate of energy transfer:

P = \frac{W}{\Delta t} = Fv \quad (\text{for } \vec F \parallel \vec v)

Worked example. A $50\ \text{kg}$ student runs up a $4.0\ \text{m}$ staircase in $8.0\ \text{s}$ .

Work done against gravity:

W = mgh = (50)(9.8)(4.0) = 1960\ \text{J}

Average useful power:

P = \frac{W}{\Delta t} = \frac{1960}{8.0} = 245\ \text{W}

That is roughly the output of a small ceiling fan — a useful reminder of how modest sustained human power really is.

Physics — Year 1 — Mechanism: A shopper carries a $10\ \text{kg}$ box horizontally at constant speed for $20\ \text{m}$ . How much work does her upward carrying force do on the box?

$0\ \text{J}$

$200\ \text{J}$

$1960\ \text{J}$

$98\ \text{J}$

Physics — Year 1 — Mechanism: How much work is done in lifting a $20\ \text{kg}$ bag of maize meal a vertical height of $1.5\ \text{m}$ at constant speed? Take $g = 9.8\ \text{m/s}^2$ and give the answer in joules.

Physics — Year 1 — Mechanism: A $1000\ \text{kg}$ car speeds up from $10\ \text{m/s}$ to $20\ \text{m/s}$ on a level road. What is the net work done on the car, in joules?

Name the original topic being extended by this mechanism lesson.

Which statement is the best evidence-led starting point for Work, Energy and Power: Mechanism?

Work done by a constant force $\vec{F}$ through a displacement $\vec{d}$ is

W = Fd\cos\theta

where $\theta$ is the angle between force and displacement. Work is a scalar, measured in joules, and it is zero whenever the force is perpendicular to the motion. Kinetic energy is $K = \tfrac{1}{2}mv^2$ , and the work–energy theorem states $$W_{\

Kinematics in One Dimension

Newton's Laws and Free-Body Diagrams

A conclusion needs no observations, calculations or stated assumptions.