# Mechanical operation and power

Mechanical work

The mechanical work W (scalar value) is found by the formula:

W = $\overrightarrow{F}$·$\overrightarrow{r}$·cosΘ

$\overrightarrow{F}$ — force, N;
$\overrightarrow{r}$ — movement, m.
when Θ=900, W=0.
Mechanical work is measured in Joules (J).

The concept of mechanical work is closely related to the scalar product of two vectors.

Mechanical power

The mechanical power P (scalar physical quantity) is found by the formula:

$P=\frac{W}{t}$

t-time, s.
Mechanical power is measured in Watts (W).

Example

A person pulls the sled by applying a force $\overrightarrow{F}$=1000 N at an angle α=30° to the horizon. Under this force, the sled moves horizontally at a speed of $\overrightarrow{v}$=5 m/s. Find the power P of the force $\overrightarrow{F}$.

Solution

$P=\frac{\overrightarrow{F}\overrightarrow{r}cosα}{t}=FVcosα$

$P=1000N\cdot5m/s\cdot\cos30\approx4330,127$

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