Question

Define the term velocity ratio. State its unit.

Answer 1

Hint:In this question, we have to discuss the term velocity ratio. The velocity ratio is defined as the ratio of the velocity of effort to the velocity of load. As the ratio predicts, it is between two velocities. Hence, the velocity ratio quantity is dimensionless. It has no units.

Complete answer:
Standard definition of the term velocity ratio is: - The velocity ratio is defined as the ratio of a distance through which any part of the machine moves to that which driving part moves during the same time.

For a machine, velocity ratio is the ratio of the velocity of effort $\left( {{v_e}} \right)$ to velocity of load $\left( {{v_l}} \right)$. Mathematically, represented as velocity ratio = $\dfrac{{{v_e}}}{{{v_l}}}$
As the definition says, the ratio is between the velocities. Hence, the velocity ratio is dimensionless. So, the term velocity ratio has no unit i.e., is a constant quantity.Another definition for velocity vector is the ratio of the displacement of the effort $\left( {{d_e}} \right)$ to the displacement of the load $\left( {{d_l}} \right)$. Mathematically, represented as velocity ratio $ = \dfrac{{{d_e}}}{{{d_l}}}$

Note:When the velocity ratio is less than one, then we can say that the machine provides speed gain. Ideal machines have a velocity ratio lesser than one. Examples of such types are scissors with long blades. And when the velocity ratio is more than one, then the machine will provide force multiplication. Examples of such are wheelbarrows.