Work/energy/kinematics rocket ship problem

In summary: To find the required thrust, you need to convert the mass of the rocket into Newtons by multiplying it by the acceleration. In summary, the required thrust for the rocket is 2.79x10^7 N. The fuel is being burned at a rate of 14,500 kg/s and to find the speed at which it is ejected from the rocket, we can use the equation for force as equal and opposite to the rate of change of momentum of the ejected rocket gases. Since we are given all variables except for vgas, we can solve for it using the equation dp_gas/dt =
  • #1
1barcafan
6
0

Homework Statement


A rocket of initial mass of 2.85x10^6 kg is on the surface of the earth. if the initial acceleration is .20g, what is the required thrust? if the fuel is burned at a rate of 14,500 kg/s, with what speed is it ejected from the rocket?


Homework Equations





The Attempt at a Solution



The only thing i thought to do was convert the mass and acceleration of the rocket into Newtons. I also tried making the mass of the rocket into the rate of the fuel burning and tried to find how many seconds it would take to finish burning, but that was just a desperate attempt.
 
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  • #2
1barcafan said:

Homework Statement


A rocket of initial mass of 2.85x10^6 kg is on the surface of the earth. if the initial acceleration is .20g, what is the required thrust? if the fuel is burned at a rate of 14,500 kg/s, with what speed is it ejected from the rocket?

Homework Equations

The force accelerating the rocket (the rate of change of momentum of the rocket + gravity) is equal and opposite to the rate of change of of momentum of the ejected rocket gases.

[tex]\vec{F} = m_{rkt}a_{rkt} + m_{rkt}g = dp_{gas}/dt = v_{gas}dm_{gas}/dt[/tex]

You are given all but vgas.

AM
 

1. How does a rocket ship use work and energy to move through space?

A rocket ship uses a combination of work and energy to move through space. The work is done by the rocket engine, which exerts a force on the rocket and causes it to accelerate. This work is converted into kinetic energy, which is the energy of motion. As the rocket moves through space, it continually expends fuel to maintain its speed and overcome the resistance of air and gravity.

2. What is the role of kinematics in understanding rocket ship movement?

Kinematics is the study of the motion of objects without considering the forces that cause the motion. In the case of a rocket ship, kinematics helps us understand the position, velocity, and acceleration of the ship as it moves through space. This information is crucial in predicting the trajectory and behavior of the rocket.

3. How is the energy of a rocket ship calculated?

The energy of a rocket ship is calculated by taking into account its mass, velocity, and height above a reference point. The kinetic energy of the rocket is equal to half of its mass multiplied by the square of its velocity. The potential energy of the rocket is equal to its mass multiplied by the acceleration due to gravity and its height above the reference point. The total energy of the rocket is the sum of its kinetic and potential energy.

4. What factors affect the work and energy of a rocket ship?

The work and energy of a rocket ship are affected by several factors, including the mass of the rocket, the force of the rocket engine, and the resistance of air and gravity. The mass and force determine the acceleration of the rocket, while air resistance and gravity act as opposing forces that must be overcome by the rocket engine. The efficiency of the engine also plays a role in the work and energy of the rocket.

5. How can we use equations of motion to solve rocket ship problems?

The equations of motion, such as Newton's second law and the equations for displacement, velocity, and acceleration, can be used to solve rocket ship problems. By plugging in the known values and using algebraic manipulation, we can find the unknown variables, such as the velocity or position of the rocket at a given time. These equations allow us to make predictions and analyze the motion of the rocket in a mathematical and scientific way.

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