# Mechanical power, definition, equation, examples, and more.

In physics, power is a concept, where the rate of doing work in unit time is called power. Further, it may be said that the amount of energy converted or transferred per unit of time is called power. Then what is mechanical power? It is the power of the machine and the movement of the different components such as the drivetrain of a vehicle.

## Mechanical power definition;

In physics, power is a concept, where the rate of doing work in unit time is called power. Further, it may be said the amount of energy converted or transferred per unit of time is called power. Then what is mechanical power? It is the power of the machine and the movement of the different components such as the drivetrain of a vehicle. Mechanical power is associated with the moving components of a machine or a mechanical system.

The machine may be driven by electricity, steam, gas, or any combustion of fuel, etc. It is power output means how fast the engine can start working, after receiving the power from fuel. However, the power input is different, where how fast the energy of the fuel is converted to power to use for the vehicle.

SI unit of power is applied to any power including mechanical power. Thus,

• In the SI system, a unit of power is the watt(w), which is Joules per second (J/S).
• SI base units-kg.m2.s-3
• Dimensional formula-M1L2T-3

Physically the mechanical power of a moving object is defined by the amount of energy or work W is converted or transferred within a specific time. Hence

• Power is expressed as=P= w/t, where P is power, w is work, and time is t.
• or the amount of change in energy divided by the change in time, P= ΔE/ Δt

Sometimes the power of motor vehicles and machines is expressed in the term horsepower (hp). One horsepower is approximately 745.7 watts.

### Power in linear motion:

When any force is applied to an object in linear motion, the object moves either forward or backward along a straight line. In such a situation power can be expressed by a simple formula taking force, distance, and velocity into account. Now work W can be defined as force F multiplied by distance d.

#### Equation of power;

Now equation of power can be;

P=Fd/t

In linear motion, velocity (v )is calculated by dividing distance by time. Now power can be expressed as;

P=Fd/t=Fv

### Power in Rotational motion;

Power in rotational motion is as important as power in linear motion. Here power is delivered to a system, that is rotating a fixed axis. In such cases, power is the product of a force on an object and the product of torque on a shaft, and the angular velocity of the shaft.

In variable force over a three-dimensional curve C, then the work is expressed in terms of the line integral,

W=ʃc F.dr=ʃΔt F.dr/dt dt=ʃΔt F

From the fundamental theorem of calculus (integration), It is clear that

P=dw/dt=d/dt(F.S)=F.ds/dt=F.v.

P=Fv

Hence the above formula is valid for any situation.

It is further to note that higher force F can only be achieved with a correspondingly lower speed V.

F=P/V

Further more work done within a specific period means more power is consumed. However, if mechanical power is from a heat engine like a power plant, it is limited by the second law of thermodynamics.

## Examples of mechanical power.

Some examples are;

• The engine of a motor car.
• The engine of a train.
• The engine of an aircraft.
• Pulleys inside an antique clock.

## Conclusion;

Mechanical power is referred to as time derivatives of work and is associated with machines and the movement of their different components. Normally it is a combination of force and movement. More power consumed means more work is done.

## 1 Comment

• […] Mechanical power is a type of power defined as the rate at which work is done or energy is transferred by a machine or a mechanical system. It is usually measured in watts (W) or horsepower (hp) and is calculated by multiplying the force applied by a machine with the distance over which the force is applied per unit time. In other words, mechanical power is the amount of work done per unit time. It is a key concept in the field of engineering and is used to quantify the performance of various mechanical systems such as engines, motors, and turbines. […]