Work, Power and Energy flashcards

$W=Fd\cos \theta$: force (N) times displacement (m) times cosine of the angle between them, in joules. 40 N at 60° over 5 m does 100 J. A force opposing motion does negative work.

When nothing moves (holding a barbell still) or the force is perpendicular to the motion (carrying a tray level, cos 90° = 0). Effort alone is not work.

$KE=\frac{1}{2}m{v}^2$: mass in kg, speed in m/s, giving joules. Speed is squared, so doubling speed gives four times the energy; tripling gives nine times.

Gravity: $PE=mgh$ (weight times height). Spring: $P{E}_s=\frac{1}{2}k{x}^2$, with spring constant k in N/m and stretch x in m. Doubling the stretch quadruples stored energy.

Net work on an object equals its change in kinetic energy: $W_{net}=K{E}_f-K{E}_i$. Positive net work speeds it up, negative slows it, zero leaves speed unchanged.

$v=\sqrt{2gh}$, from $mgh=\frac{1}{2}m{v}^2$; mass cancels. A wrench dropped 3.2 m with g = 10 lands at 8 m/s.

$P=\frac{W}{t}=Fv$: work (J) over time (s), or force (N) times speed (m/s), in watts (1 W = 1 J/s). Same work in half the time means twice the power.

1 hp is about 746 W. 1 kWh = 3,600,000 J and is an energy unit, not power. A 500 W freezer running 6 hours uses 3 kWh.