To find the thickness of the plate using the screw gauge, we need to break down the information provided and apply the appropriate calculations step by step. Let's analyze the data given and derive the thickness systematically.
Understanding the Screw Gauge Measurements
A screw gauge, also known as a micrometer screw gauge, is a precision instrument used to measure small dimensions. It consists of a main scale and a circular scale. The main scale gives a direct reading, while the circular scale provides a finer measurement based on its divisions.
Given Data
- Distance moved by the screw in 4 rotations: 2 mm
- Number of divisions on the circular scale: 50
- Position of the circular scale when nothing is placed: 30th division coincides with the reference line, with zero above it.
- Main scale reading with the plate: 2 divisions
- Circular scale reading with the plate: 20 divisions
Calculating the Pitch of the Screw
The pitch of the screw is the distance moved by the screw for one complete rotation. Since the screw moves 2 mm in 4 rotations, we can calculate the pitch as follows:
Pitch = Total distance moved / Number of rotations
Pitch = 2 mm / 4 = 0.5 mm
Determining the Value of One Division on the Circular Scale
Next, we need to find out how much each division on the circular scale represents. Since there are 50 divisions on the circular scale, we can calculate the value of one division:
Value of one division on the circular scale = Pitch / Number of divisions
Value of one division = 0.5 mm / 50 = 0.01 mm
Calculating the Total Reading with the Plate
Now, we can determine the total reading when the plate is placed between the jaws. The total reading is the sum of the main scale reading and the circular scale reading:
Total Reading = Main Scale Reading + (Circular Scale Reading × Value of One Division)
Main Scale Reading = 2 divisions = 2 mm (since each division on the main scale is typically 1 mm)
Circular Scale Reading = 20 divisions = 20 × 0.01 mm = 0.2 mm
Now, adding these values together:
Total Reading = 2 mm + 0.2 mm = 2.2 mm
Adjusting for the Initial Zero Error
Before we conclude, we must consider the initial zero error. When nothing is placed between the jaws, the 30th division of the circular scale coincides with the reference line, indicating a zero error. Since the zero of the circular scale is above the reference line, this is a positive zero error of:
Zero Error = (30 divisions) × (Value of one division)
Zero Error = 30 × 0.01 mm = 0.3 mm
Final Thickness Calculation
To find the actual thickness of the plate, we need to subtract the zero error from the total reading:
Thickness of the Plate = Total Reading - Zero Error
Thickness = 2.2 mm - 0.3 mm = 1.9 mm
Thus, the thickness of the plate is 1.9 mm.
