A rocket engine uses fuel and oxidizer in a reaction that produces gas particles having a velocity of 1380 ms-1. The desired thrust is to be 195000 N.
1-What must be the fuel/oxidizer consumption rate (in kg s-1)?
2-f the initial weight of the rocket is 125000 N, what is its initial acceleration?
3-What are the weight and acceleration of the rocket at t = 15.0 s after ignition?
4-What are the weight and acceleration of the rocket at t = 20.0 s after ignition?
Please help all my classmates doesn't know how to solve this and its due tomorrow *face crying*
1- To find the fuel/oxidizer consumption rate (in kg s-1), we need to use the principle of conservation of momentum. The momentum change per unit time (thrust) is equal to the mass flow rate (fuel/oxidizer consumption rate) times the change in velocity.
Thrust = mass flow rate * change in velocity
Rearranging the equation, we get:
mass flow rate = Thrust / change in velocity
Given that the desired thrust is 195000 N and the gas particles have a velocity of 1380 m/s, the fuel/oxidizer consumption rate can be calculated as follows:
fuel/oxidizer consumption rate = 195000 N / 1380 m/s = 141.30 kg/s
Therefore, the fuel/oxidizer consumption rate is 141.30 kg/s.
2- To find the initial acceleration of the rocket, we 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.
Force = mass * acceleration
Given that the initial weight of the rocket is 125000 N, we can convert it to mass using the acceleration due to gravity (9.8 m/s^2) as follows:
mass = weight / acceleration due to gravity
mass = 125000 N / 9.8 m/s^2 ≈ 12755.10 kg
Using the equation force = mass * acceleration, we can rearrange it to solve for acceleration:
acceleration = force / mass
acceleration = 125000 N / 12755.10 kg ≈ 9.80 m/s^2
Therefore, the initial acceleration of the rocket is approximately 9.80 m/s^2.
3- To find the weight and acceleration of the rocket at t = 15.0 s after ignition, we need to consider the change in mass due to the fuel/oxidizer consumption.
The weight of the rocket at any time can be calculated using the equation:
Weight = mass * acceleration due to gravity
Given that the initial weight of the rocket is 125000 N, and assuming a constant fuel/oxidizer consumption rate of 141.30 kg/s, we can calculate the weight at t = 15.0 s as follows:
Weight at t = 15.0 s = (initial weight - fuel/oxidizer consumption rate * time) * acceleration due to gravity
Weight at t = 15.0 s = (125000 N - 141.30 kg/s * 15.0 s) * 9.8 m/s^2 ≈ 123522.30 N
To find the acceleration at t = 15.0 s, we can use the equation:
acceleration = Thrust / (initial weight - fuel/oxidizer consumption rate * time)
acceleration = 195000 N / (125000 N - 141.30 kg/s * 15.0 s) ≈ 11.49 m/s^2
Therefore, at t = 15.0 s after ignition, the weight of the rocket is approximately 123522.30 N and the acceleration is approximately 11.49 m/s^2.
4- To find the weight and acceleration of the rocket at t = 20.0 s after ignition, we can follow the same procedure as in step 3.
Based on the given information and assuming a constant fuel/oxidizer consumption rate, we can calculate:
Weight at t = 20.0 s = (initial weight - fuel/oxidizer consumption rate * time) * acceleration due to gravity
Weight at t = 20.0 s = (125000 N - 141.30 kg/s * 20.0 s) * 9.8 m/s^2 ≈ 122044.00 N
acceleration at t = 20.0 s = Thrust / (initial weight - fuel/oxidizer consumption rate * time)
acceleration at t = 20.0 s = 195000 N / (125000 N - 141.30 kg/s * 20.0 s) ≈ 11.68 m/s^2
Therefore, at t = 20.0 s after ignition, the weight of the rocket is approximately 122044.00 N and the acceleration is approximately 11.68 m/s^2.
I can help you break down and solve these problems step by step! Let's start by discussing some concepts related to rocket engines and Newton's laws of motion.
1. To determine the fuel/oxidizer consumption rate (in kg s^-1), we need to use the concept of impulse. The impulse experienced by the rocket is equal to the change in momentum. In this case, the impulse is equal to the thrust multiplied by the time for which the thrust is applied. Mathematically, impulse (I) is given by the equation:
I = mΔv
where m is the mass flow rate (the fuel/oxidizer consumption rate) and Δv is the change in velocity.
Since the desired thrust is given as 195,000 N and the velocity change is 1380 m/s, we have:
195,000 N * Δt = m * 1380 m/s
Solving for m (mass flow rate), we get:
m = (195,000 N * Δt) / 1380 m/s
where Δt is the time in seconds.
2. To find the initial acceleration, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. Mathematically, it is represented as:
F = m * a
Given that the initial weight of the rocket is 125,000 N, which is equal to its initial force (F), and using the formula above, we have:
125,000 N = m * a
Since mass (m) is related to weight (W) through the equation m = W / g, where g is the acceleration due to gravity (usually taken as 9.8 m/s^2), we can substitute it into the formula above:
125,000 N = (W / g) * a
Simplifying:
125,000 N = (125,000 N / 9.8 m/s^2) * a
Solving for a, we get:
a = (125,000 N * 9.8 m/s^2) / 125,000 N
3. At t = 15.0 s after ignition, we can find the weight and acceleration of the rocket by using the same principles as before. The weight of the rocket remains the same, which is 125,000 N. However, the acceleration will change as thrust is applied. To find the new acceleration, we need to calculate the change in momentum using the impulse equation from the first question:
I = m * Δv
Given that we know the time (Δt) is 15.0 s and the velocity change (Δv) is 1380 m/s, we can rearrange the equation to solve for m:
m = I / Δv
Substituting the impulse and velocity change values:
m = (195,000 N * 15.0 s) / 1380 m/s
Now, we can calculate the new acceleration using the formula:
a = (m * g) / (m + mass of the rocket)
Here, the mass of the rocket is the total mass (fuel + oxidizer).
4. At t = 20.0 s after ignition, we follow the same procedure as in question 3. We use the same concepts and equations, but with the time value of 20.0 s.
Now you have an overview of how to approach each question. Apply the explained steps and equations to get the numerical answers for each question. If you need further clarification or assistance with any step, feel free to ask!
force=massfuelrate*velocity
massfuelrate= forcedesired/velocty
Initial,it has to operate against gravity.
Thrust=mg+ma=m(9.8+a)
solve for a. mass=initialweight/9.8
3. figure the mass lost in 15 sec(massrate*time)
then do 2 over with the new weight
3.same thing again.