Concept of Velocity Ratio of Screw Jack
In this post, I will apply simple steps to help you understand how to calculate the velocity ratio of a screw jack. We use a screw jack to raise heavy objects like one side of a car to remove it is wheel.
The formula for the velocity ratio (V.R) of the screw jack = 2πL / p
when the frictional forces are negligible, then velocity ratio, V.R id equal to the mechanical advantage, M.A
Thus.
M.A = 2πL / p
where L is the radius of the arm of rotation of the handle
and the distance between two consecutive threads is pitch, p
Examples of How to Calculate the Velocity Ratio of a Screw Jack
Here are a few examples of how to calculate the velocity ratio of a screw jack
Example 1
A screw jack whose pitch is 4.4 mm is used to raise a body of mass 8000kg through a height of 20cm. The length of the jack is 70cm. If the efficiency of the jack is 80%, calculate the velocity ratio of the jack.
Solution
Data:
Pitch, p = 4.4mm = 0.0044m (by converting the millimeter to the meter)
Length, L = 70 cm = 0.7m (by converting the millimeter to the meter)
π = 22/7
and the formula for the velocity ratio of a screw jack is
V.R = 2πL / p
substituting our data into the above formula, we now have
V.R = 2πL / p = ( 2 x 22/7 x 0.7 ) / 0.0044 = ( 2 x 22 x 0.7 ) / 7 x 0.0044
We can now write the above expression as
V.R = 30.8/0.0308 = 1000
Example 2
A screw jack with a pitch of 0.5cm and the handle of the screw jack is 2cm long. Determine the velocity ratio of the screw jack. Considering the efficiency of the screw to be 35%.
Solution
Data:
pitch, p = 0.5cm
Length, L = 2cm
and the formula for velocity ratio of the screw jack is
Velocity Ratio = 2πL / p
Velocity Ratio = = 2π x 2 / 0.5 = 25
Example 3
The pitch of a screw jack is 0.5cm. The arm is 50cm long and it is a mechanical advantage is 250. Calculate it is velocity ratio.
Solution
Data:
Pitch, p = 0.5 cm
Length, L = 50 cm
we now apply the formula below
Velocity Ratio = = 2πL / p
Thus,
Velocity Ratio = = (2π x 50) / 0.5 = (2 x 22/7 x 50) / 0.5 = (2 x 22 x 50) / 7 x 0.5 = 2,200 / 3.5 = 628.57
Example 4
Calculate the velocity ratio of a screw jack of pitch 0.3cm if the length of the tommy bar is 21cm.
Solution
Data:
pitch, p = 0.3cm
length, L = 21cm
And the formula for the velocity ratio of a screw jack is 2πL / p
We substitute our data into the above formula
V.R = 2πL / p = (2 x π x 21) / 0.3 = (42 / 0.3) x π
Thus,
V.R = 140 x π = 140 x (22/7) = (140×22)/7 = 3,080/7 = 440
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You may also like to read:
How to Calculate Velocity Ratio of an Inclined Plane
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