Energy methods for particles: Power and efficiency

Vivek Yadav, PhD

MEC 262: Engineering Dynamics (4.1 to 4.4)

Power

Power is rate at which a force does work on a particle.

$$ P = \frac{dU}{dt} $$

As \( U = \int \vec{F} \circ d \vec{r} \),

$$ P = \frac{d(\int \vec{F} \circ d \vec{r})}{dt} = \vec{F} \circ \frac{d\vec{r}}{dt} = \vec{F} \circ \vec{v}$$

Unit of power is Watts.

$$ 1 W = 1 J/s = 1 N-m/s $$

US unit of power is hp,

$$ 1 hp = 550 ft-lb/s = 745.7 W $$

Efficiency

$$ Efficiency = \epsilon = \frac{Power ~output}{Power ~input} $$

Quiz

1. A person takes 16 s to lift a 200 lb crate to a height of 30 ft. Determine the average power supplied by the person.

2. A motor spends 100 W of power to pull a 4 Kg mass at a constant speed of 2 m/s. Compute the efficiency of the motor.