A 7710-kg rocket is set for vertical firing from the earth's surface. If the exhaust speed is 1350 m/s, how much gas must be ejected each second in order for the thrust to be equal to the weight of the rocket?
How much gas must be ejected each second to give the rocket an initial upward acceleration of 17 m/s2?
mass/second*exaust speed=thrust force.
To find out how much gas must be ejected each second in order for the thrust to be equal to the weight of the rocket, you can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. In this case, the force acting on the rocket is the thrust, which must be equal to the weight (mass multiplied by acceleration due to gravity) for vertical firing.
Let's break down the steps to find the answer to the first question:
Step 1: Calculate the weight of the rocket
The weight of the rocket can be calculated using the formula:
weight = mass * acceleration due to gravity
In this case, the mass of the rocket is given as 7710 kg, and the acceleration due to gravity on the Earth is approximately 9.8 m/s^2. Therefore, the weight of the rocket is:
weight = 7710 kg * 9.8 m/s^2
Step 2: Calculate the thrust
Since the thrust should be equal to the weight of the rocket, the thrust can be calculated as:
thrust = weight = 7710 kg * 9.8 m/s^2
Step 3: Calculate the mass of gas ejected per second
To find the mass of gas ejected per second, we need to use the concept of conservation of momentum. According to this principle, the change in momentum of the rocket must be equal and opposite to the momentum of the expelled gas. The momentum of the expelled gas can be calculated using the formula:
momentum = mass of gas ejected per second * exhaust speed
Since the thrust must be equal to the weight of the rocket, the thrust can be equated to the momentum of the expelled gas:
thrust = momentum = mass of gas ejected per second * exhaust speed
Rearranging the equation, we can solve for the mass of gas ejected per second:
mass of gas ejected per second = thrust / exhaust speed
mass of gas ejected per second = (7710 kg * 9.8 m/s^2) / 1350 m/s
Now, to answer the first question, you can calculate the mass of gas ejected per second using the given values.
To answer the second question, you need to find the mass of gas that must be ejected per second to give the rocket an initial upward acceleration of 17 m/s^2. The approach would be similar to the first question, but this time you would use the given acceleration value in the calculation.
I hope this explanation helps you understand how to find the answers to the questions.