To calculate the amount of hydrogen gas required to lift a 65 kg object vertically via combustion, we need to consider the force exerted by the gas and the gravitational force acting on the object.
Force from hydrogen gas: The force exerted by the hydrogen gas can be determined using Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In this case, the force exerted by the hydrogen gas is equal to the weight of the object it needs to lift. The weight (W) can be calculated using the formula: W = m * g where: W = weight (force) m = mass of the object g = acceleration due to gravity (approximately 9.8 m/s² on Earth)
Amount of hydrogen gas: Hydrogen gas (H2) has a molecular weight of approximately 2 g/mol. To determine the amount of hydrogen gas required, we need to convert the weight of the object into moles of hydrogen gas. The number of moles (n) can be calculated using the formula: n = m / M where: n = number of moles m = mass of the object M = molar mass of hydrogen gas (2 g/mol)
Combustion of hydrogen gas: When hydrogen gas undergoes combustion (burning), it reacts with oxygen (usually from the air) to produce water vapor. The reaction is typically represented as follows: 2H2 + O2 → 2H2O
Now, let's calculate the amount of hydrogen gas required and the velocity the object would move when lifted by combustion.
Assuming we want the object to move with a constant velocity, which means the force exerted by the hydrogen gas is equal to the weight of the object (W), we can calculate the required amount of hydrogen gas using the following steps:
Step 1: Calculate the weight of the object: W = m * g W = 65 kg * 9.8 m/s² W = 637 N
Step 2: Calculate the number of moles of hydrogen gas: n = m / M n = 65 kg / 2 g/mol n = 32500 mol
Step 3: Determine the number of moles of hydrogen gas required for combustion: The balanced chemical equation for the combustion of hydrogen gas shows that 2 moles of hydrogen gas are required to produce 2 moles of water vapor. Therefore, the number of moles of hydrogen gas required for combustion is also 32500 mol.
Step 4: Convert moles of hydrogen gas to mass: Mass = n * M Mass = 32500 mol * 2 g/mol Mass = 65000 g Mass = 65 kg
So, approximately 65 kg of hydrogen gas would be required to lift the 65 kg object vertically via combustion.
As for the speed at which the object would move, it depends on various factors, such as the design of the combustion system and the efficiency of the propulsion mechanism. Without specific details about the system, it is challenging to provide an accurate estimation of the velocity.