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Suppose a distant world with surface gravity of 5.92 m/s2 has an atmospheric pressure of 7.24 x 104 Pa at the surface. (a) What force is exerted by the atmosphere on a disk-shaped region 2.00 m in radius at the surface of a methane ocean? N (b) What is the weight of a 10.0-m deep cylindrical column of methane with radius 2.00 m? Note: The density of liquid methane is 415 kg/m3. (c) Calculate the pressure at a depth of 10.0 m in the methane ocean. Pa

Suppose a distant world with surface gravity of 5.92 m/s2 has an atmospheric pressure of 7.24 x 104 Pa at the surface. (a) What force is exerted by the atmosphere on a disk-shaped region 2.00 m in radius at the surface of a methane ocean? N (b) What is the weight of a 10.0-m deep cylindrical column of methane with radius 2.00 m? Note: The density of liquid methane is 415 kg/m3. (c) Calculate the pressure at a depth of 10.0 m in the methane ocean. Pa

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### Exploring Pressure, Force, and Gravity on a Distant World #### Background Information Consider a distant world that has a surface gravity of \(5.92 \, \text{m/s}^2\) and an atmospheric pressure of \(7.24 \times 10^4 \, \text{Pa}\) at its surface. ### Problem Set #### (a) Force Exerted by the Atmosphere **Question:** What force is exerted by the atmosphere on a disk-shaped region with a radius of \(2.00 \, \text{m}\) at the surface of a methane ocean? **Solution:** To find the force, we use the formula \( F = P \times A \), where \( F \) is the force, \( P \) is the pressure, and \( A \) is the area of the disk-shaped region. 1. Calculate the area \( A \) of the disk: \[ A = \pi r^2 = \pi (2.00 \, \text{m})^2 = 4\pi \, \text{m}^2 \] 2. Compute the force: \[ F = 7.24 \times 10^4 \, \text{Pa} \times 4\pi \, \text{m}^2 = 2.90 \times 10^5 \pi \, \text{N} \] **Answer:** The force exerted by the atmosphere is \( 9.12 \times 10^5 \, \text{N} \). #### (b) Weight of Liquid Methane Column **Question:** What is the weight of a \(10.0\)-meter deep cylindrical column of methane with a radius of \(2.00 \, \text{m}\)? Note: The density of liquid methane is \(415 \, \text{kg/m}^3\). **Solution:** To find the weight, we first determine the mass of the methane column and then calculate the weight using \( W = mg \) where \( W \) is the weight, \( m \) is the mass, and \( g \) is the gravitational acceleration. 1. Calculate the volume \( V \) of the cylinder: \[ V = \pi r^2 h = \pi (2.00 \, \text
Transcribed Image Text:### Exploring Pressure, Force, and Gravity on a Distant World #### Background Information Consider a distant world that has a surface gravity of \(5.92 \, \text{m/s}^2\) and an atmospheric pressure of \(7.24 \times 10^4 \, \text{Pa}\) at its surface. ### Problem Set #### (a) Force Exerted by the Atmosphere **Question:** What force is exerted by the atmosphere on a disk-shaped region with a radius of \(2.00 \, \text{m}\) at the surface of a methane ocean? **Solution:** To find the force, we use the formula \( F = P \times A \), where \( F \) is the force, \( P \) is the pressure, and \( A \) is the area of the disk-shaped region. 1. Calculate the area \( A \) of the disk: \[ A = \pi r^2 = \pi (2.00 \, \text{m})^2 = 4\pi \, \text{m}^2 \] 2. Compute the force: \[ F = 7.24 \times 10^4 \, \text{Pa} \times 4\pi \, \text{m}^2 = 2.90 \times 10^5 \pi \, \text{N} \] **Answer:** The force exerted by the atmosphere is \( 9.12 \times 10^5 \, \text{N} \). #### (b) Weight of Liquid Methane Column **Question:** What is the weight of a \(10.0\)-meter deep cylindrical column of methane with a radius of \(2.00 \, \text{m}\)? Note: The density of liquid methane is \(415 \, \text{kg/m}^3\). **Solution:** To find the weight, we first determine the mass of the methane column and then calculate the weight using \( W = mg \) where \( W \) is the weight, \( m \) is the mass, and \( g \) is the gravitational acceleration. 1. Calculate the volume \( V \) of the cylinder: \[ V = \pi r^2 h = \pi (2.00 \, \text
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