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# An electric motor creates a tension of 4500N in a hoisting cable and reels it in at the rate of $2m{s^{ - 1}}$. What is the power of the electric motor?A) $15kW$B) $9kW$C) $225kW$D) $9000HP$

Last updated date: 14th Jul 2024
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Hint: An electric motor is a rotating device that converts electrical energy into mechanical energy. The power of the electric motor is the force that it applies on the cable or the tension it generates times the velocity or rate at which it pulls it in. It can be calculated using a simple formula. Make sure to convert everything in S.I. units.

Formulae used:
$P = F \times v$
Where $P$ is the power of the electric motor, $F$ is the force or tension in cable and $v$ is the velocity of rate at which the cable is reeled in.

Complete step by step solution:
An electric motor is based on the principle that a current carrying coil placed in a magnetic field experiences some form of a torque. This constant generation of torque gives rise to mechanical energy in the motor that can be used to, in cases like this, hoist a cable and reel it in to reduce the strain on an individual.

The power required in such cases is calculated by the formula;
$P = F \times v$
Where $P$ is the power of the electric motor, $F$ is the force or tension in cable and $v$ is the velocity of rate at which the cable is reeled in.
Here $F = 4500N$ and $v = 2m{s^{ - 1}}$
Therefore,
$P = F \times v$
$\Rightarrow P = 4500 \times 2$
$\Rightarrow P = 9000Nm{s^{ - 1}}$
$\Rightarrow P = 9000W$
$\Rightarrow P = 9kW$

Therefore the power of the electric motor is $9kW$ which is option (B).

Note: In an electric motor, both emf and current are generated. This is largely responsible for the power of the motor and the power can also be calculated with respect to the current and resistance, had the following been provided in the question. Since only force and velocity were mentioned in the question, we have to use this formula.