The pressure gauge shown in Figure 1 consists of a spring inside a vacuum chamber. The chamber is isolated from the environment by a piston, which is free to move up or down. Ambient pressure exerts a force on the piston, which compresses the spring. The piston has a diameter of 30 mm.At sea level, where ambient pressure is 1 atm, the spring is compressed by a distance \( x_0 = 14 \, \text{mm} \) relative to its relaxed length. Suppose the pressure gauge is lowered into water at a lake. At depth \( D \), the spring is compressed by distance \( x_1 = 34 \, \text{mm} \) relative to its relaxed length. Calculate \( D \). Show and explain your work.**Figure Description:**In Figure 1, there is a diagram of a pressure gauge consisting of a vertical setup with a piston and a spring inside a vacuum chamber. The spring is labeled with a constant \( k \), and a downward force \( \vec{F} \) is applied on the piston. The piston is free to move within the chamber, compressing the spring due to external pressure. The chamber is labeled "Vacuum," emphasizing that it is isolated from the external environment.

Let the original length of the of the spring be L Case: 1: At sea level , Pressure P=1 atm=1.015×105…

1. The pressure gauge shown in Figure 1 consists of a spring inside a vacuum chamber. The chamber is isolated from the environment by a piston, which is free to move up or down. Ambient pressure exerts a force on the piston, which compresses the spring. The piston has a diameter of 30 mm. At sea level, where ambient pressure is 1 atm, the spring is compressed by distance xo = 14 mm relative to its relaxed length. Suppose the pressure gauge is lowered into water at a lake. At depth D, the spring is compressed by distance x1 = 34 mm relative to its relaxed length. Calculate D. Show and explain your work. Vacuum Figure 1

1. The pressure gauge shown in Figure 1 consists of a spring inside a vacuum chamber. The chamber is isolated from the environment by a piston, which is free to move up or down. Ambient pressure exerts a force on the piston, which compresses the spring. The piston has a diameter of 30 mm. At sea level, where ambient pressure is 1 atm, the spring is compressed by distance xo = 14 mm relative to its relaxed length. Suppose the pressure gauge is lowered into water at a lake. At depth D, the spring is compressed by distance x1 = 34 mm relative to its relaxed length. Calculate D. Show and explain your work. Vacuum Figure 1