Question

A sphere of copper has a radius of 9.00 cm and is compressed uniformly by a force of 9.00×10⁸

N. The bulk modulus for copper is 140×10⁹ N/m²
Calculate the sphere's change in volume after compression. ΔV= ________ m³
Calculate the sphere's final radius R. R= __________ m

Answer 1

To calculate the sphere's change in volume and final radius after compression, we use the formula for change in volume due to bulk stress and then apply the formula for the volume of a sphere to solve for the new radius.

Step-by-step explanation:

The question asks to calculate the change in volume and final radius of a copper sphere after compression using the bulk modulus of copper.

To find the change in volume (ΔV), we use the formula ΔV = -ΔP × V_0 / B, where ΔP is the change in pressure, V_0 is the initial volume, and B is the bulk modulus. The pressure change ΔP can be calculated as the force applied divided by the area over which it's applied, which for a sphere is 4πr^2.

Once the change in volume is calculated, we can find the new volume V = V_0 + ΔV. The volume of a sphere is V = ⅔πr^3; by solving this for the new radius R after compression, we can determine the sphere's new radius.