Conservation of momentum of a rocket

In summary, the last stage of a rocket is made up of two parts, a rocket case with a mass of 330.00 kg and a payload capsule with a mass of 155.00 kg, clamped together and traveling at a speed of 8000 m/s. When the clamp is released, the two parts separate with a relative speed of 910 m/s due to a compressed spring. The speed of the smaller payload is 6284 m/s, while the speed of the larger rocket case is 8806 m/s.
  • #1
Felix83
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0
The last stage of a rocket is traveling at a speed of 8000 m/s. This last stage is made up of two parts that are clamped together, namely, a rocket case with a mass of 330.00 kg and a payload capsule with a mass of 155.00 kg. When the clamp is released, a compressed spring causes the two parts to separate with a relative speed of 910 m/s. What are the speeds of the two parts after they have separated? Assume that all velocities are along the same line. What is the speed of the payload? What is the velocity of the rocket case?

i got 8291m/s and 7381m/s but the computer says its wrong
:mad:
 
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  • #2
Yes, the smaller payload should have a larger change in velocity than the heavier rocket if momentum is to be conserved.

It would be nice if you had shown what you did to get your answers. From your numbers, it looks like you made a silly mistake at the end and swapped which objects you should have added/subtracted velocities to.
 
  • #3
when I solve the problem, I get an answer of the samller parts speed being 6284m/s and the bigger parts being 8806m/s.
This is my set up:

[tex] (m_1 + m_2)V_i = m_{1}(V_i - (910m/s - x)) + m_{2}(V_i + x) [/tex]

Regards,

Nenad
 
  • #4
ok the computer had your 8806m/s as the speed for the smaller one and the bigger one was 7906 (remember the difference in speed is 910).
 

Related to Conservation of momentum of a rocket

1. What is conservation of momentum and how does it apply to rockets?

Conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant over time. This means that the total momentum before an event is equal to the total momentum after the event. In the case of a rocket, this means that the momentum of the exhaust gases expelled from the rocket must be equal and opposite to the momentum of the rocket itself.

2. How does the mass and velocity of a rocket affect its momentum?

According to the formula for momentum (p = mv), the momentum of a rocket is directly proportional to its mass and velocity. This means that a rocket with a larger mass or higher velocity will have a greater momentum. In order to conserve momentum, the rocket must either increase its mass (by carrying more fuel) or increase its velocity (by expelling exhaust gases at a higher speed).

3. How does conservation of momentum affect the trajectory of a rocket?

Conservation of momentum plays a crucial role in determining the trajectory of a rocket. As the rocket expels exhaust gases with a certain momentum, the rocket itself experiences an equal and opposite force in the opposite direction. This force causes the rocket to accelerate and change direction, allowing it to move through the atmosphere and into space.

4. Can the conservation of momentum be violated in a rocket launch?

No, the conservation of momentum is a fundamental law of physics and cannot be violated. In order for a rocket to successfully launch, the momentum of the exhaust gases must always be equal and opposite to the momentum of the rocket itself. Any violation of this law would result in the rocket failing to reach its intended trajectory.

5. How does the design of a rocket impact its conservation of momentum?

The design of a rocket can greatly impact its conservation of momentum. For example, a rocket with a more streamlined shape will experience less air resistance and therefore can more efficiently convert the momentum of the exhaust gases into forward motion. Additionally, the placement and direction of the rocket's engines can also affect the direction and efficiency of the momentum transfer.

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