I am using the derivative of momentum (dp/dt) with Newton’s 3rd Law with the gravitational force of Earth.
F - [Force of gravity on rocket] = dp/dt
F - (G * m_e * m_r / r2 ) = v * dm/dt + ma
F = Force created by fuel (at time t)
G = Gravitational Constant
m_e = Mass of Earth
m_r = Mass of...
Homework Statement
While solving equation of rocket motion with Newton's law in 1-d,I pondered to apply Lagrangian method on this. However, I didn't get correct result. Because I can eliminate last 2nd equation using last equation and get some other equation which is certainly not rockets...
Homework Statement
I want to try to derive the rocket equation and then add additional effects like gravity, air resistance, etc. Here's the equation that I found online:
Homework Equations
p (momentum) = mass * velocity
F (force) = Δp / Δt
The Attempt at a Solution
[/B]
pi = mv
Here...
Watching "Mars" on National Geographics I try to calculate what the cost would be to bring anything usefull back to Earth. More specifically I wonder what fuel-payload ratio a rocket could have when lifting off from Mars. I want to use Tsiolkovsky's rocket equation
Δv = ve ln(m0/mf)
or
Δv =...
So if you have a rocket lets say that discards all the structural and engine mass continuously at zero velocity that is relative to the rocket until only the payload is traveling at the final velocity - then what will the equation of motion will look like? we can neglect the drag and...
I stumbled upon a 3-year old article from Wired that poses this question on rockets:
Suppose I have two rockets with a mass M and fuel mass m. Rocket A shoots all the fuel at once (again, like a nuclear propulsion engine) with a fuel speed of u and rocket B shoots two blobs of fuel—first a shot...
Homework Statement
A rocket (initial mass ##m_o##, constant exhaust velocity ##v_{ex}## needs to use its engines to hover stationary, just above the ground.
a) If it can afford to burn no more than a mass ##\lambda m_o## of its fuel (##\lambda \lt##), for how long can it hover?
b) If ##v_{ex} =...
Homework Statement
A rocket has weight 10,000 kg and it needs to carry 5000 kg with acceleration 3.5 m/s². How much thrust force is necessary for the rocket to have a flight from earth to space?
Homework Equations
F=ma[/B]
The Attempt at a Solution
I try that, According to Newton's law, (...
The problem states:
Typical chemical fuels yield exhaust speeds of the order of 103 m/s. Let us imagine we had a fuel that gives v0 = 3 × 105 m/s. What initial mass of fuel would the rocket need in order to attain a final velocity of 0.1c for a final mass of 1 ton?
I derived the equation in the...
Based on my current understanding of the problem I do not see this following derivation as valid, although this is what was given in my course notes. Although this particular example is from an undergraduate physics course this is not a homework problem: I'm confused about the underlying...
Homework Statement
To solve this problem you will need to construct a differential equation. A picture of the situation will help. Ignore all gravitational forces. A Rocket ship of structural mass M and fuel mass m, begins at rest relative to a gas cloud. The ship burns fuel at the rate ω which...
I do not get why systems such as the rocket in space are defined as "variable mass" since the mass of the system is not varying.
The equation used for such systems $$\sum F^{(E)}=\frac{d\vec{P}}{dt} \tag{1}$$ (sum of external forces on the system equals the change in momentum) holds true only...
Homework Statement
A rocket with an initial mass of 60,000kg ignites its engines and burns fuel at a rate of 300 kg/s with an exhaust velocity of 2220 m/s. How long after the engines start does the rocket lift off the ground?
Homework Equations
From Newton's second law
F = Ma this equation can...
Homework Statement
A truck hauling a big tank of oil starts at position x=D (Chicago) and heads due west (–x direction) toward its destination at x = 0 (Des Moines). At Chicago, the total mass of the loaded truck is M and the mass of oil it is carrying is λM. (Thus M(1–λ) is the "tare" mass =...
Homework Statement
(a) Show ##a = \frac{a_0}{\gamma^3}##.
(b) Find proper acceleration of rocket
(c) Find speed as a function of time.
(d) Find acceleration of second rocket.
Homework Equations
The Attempt at a Solution
Part(a)
4-vector acceleration is given by ##\gamma^2 \left[...
Homework Statement
I am trying to derive the formula for time varying thrust given that I know the initial mass/volume of water in a water rocket. Knowns will include initial pressure, initial volume of water, and nozzle cross sectional area.
Homework Equations
Bernoullis equation: (p/ρg) +...
Hello all, I am currently trying to solve a differential equation numerically. The equation is as follows:
dv/dt = (u*q)/(m0-q*t) - g - (cd*ρ*A*0.5)*v2
If you haven't already guessed, it's the rocket equation with added gravity and drag. Now, I'm not even sure if that's what it's supposed to...