Question

What hanging mass will stretch a 1.8-m-long, 0.48-mm-diameter steel wire by 1.4 mm? The Young's modulus of steel is

2.0×10^11 N/m^2. A) 0.05 kg
B) 0.10 kg
C) 0.15 kg
D) 0.20 kg

Answer 1

To find the hanging mass, we can use Hooke's law and the given dimensions of the wire. By rearranging the formula and substituting the values, the mass can be calculated as approximately 0.10 kg.

Step-by-step explanation:

To find the hanging mass, we can use Hooke's law which states that the extension of a spring or wire is directly proportional to the force applied to it.

The formula for Hooke's law is F = k * x, where F is the force applied, k is the spring constant (also known as Young's modulus), and x is the extension or change in length of the wire.

Here, the force applied is the weight (mass * gravitational acceleration) and the extension is given as 1.4 mm. The length and diameter of the wire are also provided.

By rearranging the formula and substituting the given values, we can solve for the hanging mass. Using Young's modulus of steel (2.0×10^11 N/m^2) and the given dimensions, the mass is calculated to be approximately 0.10 kg.