Screw Jack

$\text{M.A} = \dfrac{\text{Load}}{\text{Effort}}$

$\text{V.R} = \dfrac{\text{Circumference of handle circle}}{\text{Pitch of screw}} = \dfrac{2\pi R}{p}$

A screw jack with a pitch of 0.2 cm and a handle of length 50 cm is used to lift a car of weight $1.2 \times 10^4 \, \text{N}$. If the efficiency of the screw is 30%, find:

(i) The velocity ratio and mechanical advantage of the machine

(ii) The effort required to raise the car

Solution:

Data Given:

Pitch, $p = 0.2 \, \text{cm}$

Radius, $R = 50 \, \text{cm}$

Load, $L = 1.2 \times 10^4 \, \text{N}$

Efficiency, $\eta = 30\%$

Step 1: Calculate Velocity Ratio (V.R)

$\text{V.R} = \dfrac{2\pi R}{p} = \dfrac{2 \times 3.14 \times 50}{0.2}$

$\text{V.R} = \dfrac{314}{0.2} = 1570$

Step 2: Use Efficiency Formula to find M.A

$\eta = \dfrac{\text{M.A}}{\text{V.R}} \times 100\%$

$\dfrac{30}{100} = \dfrac{\text{M.A}}{1570}$

$\text{M.A} = 0.3 \times 1570 = 471$

Step 3: Use M.A to find Effort

$\text{M.A} = \dfrac{\text{Load}}{\text{Effort}}$

$471 = \dfrac{1.2 \times 10^4}{\text{Effort}}$

$\text{Effort} = \dfrac{1.2 \times 10^4}{471}$

$\text{Effort} \approx 25.48 \, \text{N}$

Final Answer:

Velocity Ratio = 1570

Mechanical Advantage = 471

Effort ≈ 25.48 N

1. Lifting Vehicles; Screw jacks are commonly used in car repair to lift vehicles for tasks like changing tires or inspecting the underside of the car.
2. Adjustable Furniture; They are found in adjustable chairs, tables, and hospital beds to raise or lower height easily and safely.
3. Industrial Machinery Positioning; Screw jacks are used to lift, push, pull or position heavy machinery during installation or maintenance.
4. Stage and Platform Elevation; In theaters and stages, screw jacks help to adjust the height of platforms or props smoothly and precisely.
5. Construction Equipment; Used in scaffolding or lifting structural components into place, especially where stability and locking are essential.
6. Tightening and Pressing Mechanisms; Screw jacks are used in mechanical presses or vises to apply force when clamping or assembling parts.