Question

The velocity ratio of a plane inclined at angle to the horizontal can be expressed as?

Answer 1

The velocity ratio of a plane inclined at an angle to the horizontal can be expressed as
`\( (1)/(\sin \theta) \).`

Step-by-step explanation:

The velocity ratio for an inclined plane is a crucial concept in physics, particularly in understanding how inclined planes affect the motion of objects.

The velocity ratio is defined as the ratio of the velocity of the effort (the force applied) to the velocity of the load (the resistance being moved) on the inclined plane. For an inclined plane making an angle theta with the horizontal, the velocity ratio can be expressed mathematically as:

`\[ VR = \frac{\text{Velocity of Effort}}{\text{Velocity of Load}} \]`

In the case of an inclined plane, the velocity of the effort and the velocity of the load can be related to the angle of inclination theta by the trigonometric function sine
`(\( \sin \))`. The expression for the velocity ratio
`(\( VR \))` becomes:

`\[ VR = (1)/(\sin \theta) \]`

This mathematical representation signifies that the velocity ratio is inversely proportional to the sine of the angle of inclination. As the angle increases, the sine of the angle decreases, leading to a higher velocity ratio. Understanding this relationship is essential for analyzing the mechanical advantage or disadvantage gained by using an inclined plane in various applications.