Question

A 20 m steel tape was standardised on flat ground, at a temperature of 20°C and under a pull of 15 kg. The tape was used in catenary at a temperature of 30°C and under a pull of P kg. The cross-sectional area of the tape is 0.02 cm2, and its total weight is 400 g. The Young's modulus and coefficient of linear expansion of steel are 2.1 * 106 kg/cm2 and 11 x 10 6 per respectively. Find the correct horizontal distance if P is equal to 10 kg.

Answer 1

To find the correct horizontal distance if the pull is equal to 10 kg, we need to calculate the stress in the tape and use it to find the change in length. The stress in the tape is calculated using the formula stress = force/area. The change in length is found using the formula change in length = original length * coefficient of linear expansion * change in temperature. Finally, the correct horizontal distance is calculated using the formula horizontal distance = square root of (stretch)^2 - (change in length)^2.

Step-by-step explanation:

To find the correct horizontal distance if P is equal to 10 kg, we need to calculate the stress in the tape and use it to find the change in length.

Next, we need to find the change in length. The formula for change in length is change in length = original length * coefficient of linear expansion * change in temperature. The original length is 20 m, the coefficient of linear expansion is given as 11 x 10^(-6) per °C, and the change in temperature is 30°C - 20°C = 10°C. Therefore, the change in length is 20 m * 11 x 10^(-6) per °C * 10°C = 0.0022 m.

Finally, we can calculate the correct horizontal distance. The horizontal distance is given by the formula horizontal distance = square root of (stretch)^2 - (change in length)^2. Plugging in the values, the horizontal distance is square root of (20)^2 - (0.0022)^2 = 20 m.