Calculate Velocity Ratio of a Screw Jack
How can we calculate the velocity ratio of a screw jack?
A screw Jack whose pitch is 2mm is used to raise a bus of mass 900kg through height of 20cm. The length of the Tommy of the jack is 40cm. Calculate the velocity ratio of the machine.
Calculation and Explanation of Velocity Ratio
The velocity ratio of the screw jack in question can be calculated by dividing the circular distance travelled by the end of the Tommy (2.51m) by the linear distance the bus is raised (0.2m), which yields a VR of 12.57.
The velocity ratio (VR) of a machine is a measure of the machine's efficiency. In a perfectly efficient machine, the VR would exactly equal the mechanical advantage. But in the case of a screw jack, which is a type of simple machine, the VR is determined by the ratio of the circular distance traveled by the effort (input) to the linear distance traveled by the load (output).
In this specific question, the circular distance is the circumference of the circle described by the end of the Tommy, or lever, of the screw jack. We calculate it using the formula for circumference, 2πr, where r is the length of the Tommy, or 40cm. So, in metric units, the circular distance is 2π × 0.4 = 2.51m.
The linear distance is the height the bus is raised or 20cm. In metric units, that's 0.2m.
So the velocity ratio is the circular distance divided by the linear distance, or 2.51/0.2 = 12.57.