Question

A 76.2 mm gauge block is used under one end of a 254 mm sine bar with roll diameter of 25.4 mm. The height of gauge blocks required at the other end of the sine bar to measure an angle of 30° is \(\underline{\hspace{2cm}}\) mm (round off to two decimal places).
 

Hint:

To calculate the required gauge block height in a sine bar, use the trigonometric relation between the angle, the length of the sine bar, and the required height.

Answer 1

Correct Answer: 200 - 206

Step 1: Understand the Sine Bar Setup

In a sine bar setup, the sine of the angle is given by:

$$\sin \theta = \frac{H}{L}$$

where:

• $H$ = height difference between the two ends
• $L$ = center-to-center distance between the rollers

Step 2: Calculate the Center-to-Center Distance

The sine bar length of 254 mm is the center-to-center distance between the two rolls.

$$L = 254 \text{ mm}$$

Step 3: Calculate the Height Difference Required

For an angle of $30°$:

$$H = L \times \sin \theta$$

$$H = 254 \times \sin(30°)$$

$$H = 254 \times 0.5 = 127 \text{ mm}$$

Step 4: Calculate the Gauge Block Height at the Other End

The height difference $H$ is the difference between the gauge block heights at both ends:

$$H = h_2 - h_1$$

$$h_2 = H + h_1$$

$$h_2 = 127 + 76.2 = 203.2 \text{ mm}$$

Answer: The height of gauge blocks required at the other end is 203.20 mm.