the velocity ratio of an inclined plane whose angle is a I
a). VR=1/sinA
b). VR=1/tanA
c). VR=1/cosA
d). VR=1/cotA?
To determine the velocity ratio of an inclined plane with an angle of A, we need to understand the concept of velocity ratio in the context of simple machines.
The velocity ratio is defined as the ratio of the distance moved by the effort to the distance moved by the load. In the case of an inclined plane, the effort is the input force applied to move an object up or down the incline, and the load is the weight of the object being moved.
To find the velocity ratio for an inclined plane, we can consider the trigonometric relationships between the angle of the incline and the forces involved. The key force at play is the component of the weight of the object acting parallel to the incline, which is known as the effective weight (Weff).
Using trigonometry, we can determine that Weff = Weight of object * sin(A), where A is the angle of the incline. This is because the weight of the object can be broken down into two components: one perpendicular to the incline and one parallel to the incline. The component acting parallel to the incline is Weff.
Given that the effort force (Fe) is generally applied parallel to the incline, we can conclude that the velocity ratio (VR) is calculated as:
VR = Distance moved by effort (De)/Distance moved by load (Dl)
Now, let's evaluate the given options:
a). VR = 1/sin(A)
b). VR = 1/tan(A)
c). VR = 1/cos(A)
d). VR = 1/cot(A)
Based on the above explanation, the correct option is a). VR = 1/sin(A).
Therefore, the velocity ratio of an inclined plane with an angle A is VR = 1/sin(A).