Question

A small electrical motor produces 5 W of mechanical power. What is this power in \((a) \mathrm{N}, \mathrm{m},\) and \(\mathrm{s}\) units; and (b) \(\mathrm{kg}, \mathrm{m},\) and s units?

Short answer

Answer: The power produced by the small electrical motor is (a) 5 N.m/s in N, m, and s units; and (b) 5 kg.m^2/s^3 in kg, m, and s units.

Step-by-step solution

Write down the given information and formula for power

The small electrical motor produces 5 W (watts) of mechanical power. We know that power (P) is the work done (W) per unit time (t), and it can be expressed as: P = W/t

Convert power from watts to N.m.s units

To convert the power from watts to N.m.s units, we can use the following conversion factors: 1 W = 1 N.m/s So, 5 W of power can be written in N.m.s units as: 5 W = 5 N.m/s

Convert power from N.m.s units to kg.m.s units

In order to convert the power from N.m.s units to kg.m.s units, we will need to use the conversion factor for force (F): 1 N = 1 kg.m/s^2 The power in N.m.s units can be expressed as force times distance (d) per unit time, i.e., P = F.d/t. So, we can write the power in kg.m.s units as: P = (F.d/t) = (kg.m/s^2 . m/s) 5 N.m/s = 5 kg.m^2/s^3 Hence, the power produced by the small electrical motor is (a) 5 N.m/s in N, m, and s units; and (b) 5 kg.m^2/s^3 in kg, m, and s units.