A ball of aluminum is at a depth of 100.0 m under water whose density is 1,000 kg/m³. Atmospheric pressure is 101.3 kPa. What is the volume stress on the ball? Use g = 9.80 m/s². A) 9.80 × 10⁵ Pa. B) 1.08 × 10⁶ Pa. C) 1.28 × 10⁵ Pa. D) 2.13 × 10⁶ Pa. E) 2.33 × 10⁶ Pa.

Question

Quizplus · Accepted Answer

The volume stress is the sum of the atmospheric pressure and the pressure due to the water. The pressure due to the water is given by:$$P = ho g h$$where:* $ ho$ is the density of the water (1,000 kg/m³)* g is the acceleration due to gravity (9.80 m/s²)* h is the depth of the ball (100.0 m)So, the pressure due to the water is:$$P = (1,000 ext{ kg/m}^3)(9.80 ext{ m/s}^2)(100.0 ext{ m}) = 9.80 imes 10^5 ext{ Pa}$$The volume stress is then:$$P = P_ ext{atm} + P_ ext{water} = 101.3 ext{ kPa} + 9.80 imes 10^5 ext{ Pa} = 1.08 imes 10^6 ext{ Pa}$$

A Ball of Aluminum Is at a Depth of 100