Rocket problem: Newton's 2nd Law

In summary, the problem explores a model of a rocket's acceleration with a constant rate of fuel burning. The velocity and mass of the rocket are not constant, and Newton's second law can be used to derive an equation for the mass at time t in terms of M1, M2, and b. This equation can then be substituted into the given equation to solve for b using separation of variables. The burnout velocity and height of the rocket at that time can also be determined.
  • #1
hana.e.kim
3
0

Homework Statement


In this problem we explore a slightly more realistic model of a rocket's acceleration still neglecting air resistance. Consider a rocket fired straight up from rest burning fuel at the constant rate of b kg/s. Let v=v(t) be the velocity of the rocket at time t and suppose that the velocity u of the exhaust gas is constant. Let m=m(t) be the mass of the rocket at time t, and note that m is not constant. From Newton's second law it can be shown that F=m(dv/dt) - uv where the force F= -mg and g is acceleration due to gravity, thus, m(dv/dt) - uv = -mg. Let M1 be the mass of the rocket without fuel and M2 be the initial mass of the fuel.

a. Find an equation for the mass m at time t in terms of M1, M2, and b.
b. Substitute this expression for m in equation one and solve the resulting equation for b. Use separation of variables.
c. Determine the velocity of the rocket at the time that the fuel is exhausted. This is called the burnout velocity.
d. Find the height of the rocket at the burnout time.


Homework Equations


See Newton's 2nd Law above.


The Attempt at a Solution


I honestly don't even know how to start this problem, so any help would be greatly appreciated. Thank you!
 
Physics news on Phys.org
  • #2
Hi hana! :smile:
hana.e.kim said:
… I honestly don't even know how to start this problem, so any help would be greatly appreciated. Thank you!

ok, start with a. …

what is the mass m at time t in terms of M1, M2, and b ?
 

Related to Rocket problem: Newton's 2nd Law

1. What is Newton's 2nd Law?

Newton's 2nd Law, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

2. How does Newton's 2nd Law apply to rockets?

In the context of rockets, Newton's 2nd Law explains how a rocket is able to accelerate and produce thrust by expelling exhaust gases in one direction, creating an equal and opposite force in the opposite direction.

3. What is the equation for Newton's 2nd Law?

The equation for Newton's 2nd Law is F = ma, where F represents the net force acting on an object, m represents the mass of the object, and a represents the acceleration of the object.

4. Can you provide an example of Newton's 2nd Law in action in a rocket?

An example of Newton's 2nd Law in action in a rocket is when the rocket's engines are fired, creating a force that propels the rocket forward. As the exhaust gases are expelled in one direction, the rocket experiences an equal and opposite force in the opposite direction, causing it to accelerate.

5. How does Newton's 2nd Law affect the design and operation of rockets?

Newton's 2nd Law is a fundamental principle in the design and operation of rockets. It is used to calculate the necessary force and thrust required to achieve a desired acceleration and trajectory. It also plays a role in determining the mass and size of the rocket components, as a heavier rocket will require more force to accelerate. Additionally, Newton's 2nd Law must be taken into consideration during the rocket's flight to ensure proper control and stability.

Similar threads

Rocket acceleration problem: confused about Newton's 2nd Law
    • Introductory Physics Homework Help
2
Replies
42
Views
3K
How do you solve the problem of a rocket with variable mass?
    • Calculus and Beyond Homework Help
Replies
4
Views
2K
I Meaning of the terms in the formula of the net external force
    • Mechanics
Replies
17
Views
992
Insights How to Apply Newton’s Second Law to Variable Mass Systems
    • Mechanics
Replies
0
Views
1K
How to calculate velocity of infinite-stage rocket?
    • Introductory Physics Homework Help
Replies
2
Views
276
Why is the thrust equation same under gravitational force?
    • Introductory Physics Homework Help
Replies
10
Views
724
B Which equation should be used to calculate impulse: I=F(t) or I=m1v1-m0v0?
    • Classical Physics
Replies
12
Views
887
Second order(?) ODE + Runge-Kutta method question
    • Calculus and Beyond Homework Help
Replies
5
Views
3K
Understanding calculation of 2nd order LTI DE response to step input
    • Calculus and Beyond Homework Help
Replies
8
Views
344
Exploring Electron Rockets for Interstellar Travel
    • Aerospace Engineering
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top