What is the rocket's initial acceleration?

  • #1
JoeDGreat
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Homework Statement
A rocket is in outer space, far from any planet, when the rocket engine is turned on. In the first second of firing, the rocket ejects 1/120 of its mass with a relative speed of 2400m/s. What is the rocket's initial acceleration?
Relevant Equations
Vf-Vi = VeIn(Mi/Mf)
Help me solve... I'm getting errors here..
 
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  • #2
The rocket equation you have quoted is not very useful to find acceleration. For that you need to look at the fundamental conservation law that is behind the rocket equation, and specifically how the conserved quantities of the rocket and ejected propellant change the instant the rocket is turned on.
 
  • #3
JoeDGreat said:
Homework Statement: A rocket is in outer space, far from any planet, when the rocket engine is turned on. In the first second of firing, the rocket ejects 1/120 of its mass with a relative speed of 2400m/s. What is the rocket's initial acceleration?
Relevant Equations: Vf-Vi = VeIn(Mi/Mf)

Help me solve... I'm getting errors here..
Per forum rules, please post your attempt.
 
  • #4
a = -Ve/Me × dM/dt
dM/dt = Mi/120 ÷ 1sec = -Mi/120sec
a =-2400/Mi ( -Mi/120) = 20m/s²

PS: This is the textbook solving but, I don't know how dM= Mi/120
 
  • #5
JoeDGreat said:
a = -Ve/Me × dM/dt
dM/dt = Mi/120 ÷ 1sec = -Mi/120sec
a =-2400/Mi ( -Mi/120) = 20m/s²

PS: This is the textbook solving but, I don't know how dM= Mi/120
They are giving you the instantaneous rate of mass ejection at ##t=0##:

## \dot M(0) = -\frac{1}{120}M \frac{ \text{kg}}{ \text{s}} ##

Then apply "The Rocket Equation" at ##t = 0## (with no external forces).
 
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  • #6
JoeDGreat said:
In the first second of firing, the rocket ejects 1/120 of its mass with a relative speed of 2400m/s.
Is it this statement that is giving you interpretive issues? They should have just said something to the effect of " at the instant of firing", or we are just to assume the mass flow rate as constant over the first second for the sake of simplicity (i.e. being able to find a solution).
 
  • #7
A loss of 1/120th of total mass is sufficiently small that we don't need to worry about how it changes over the second, or, indeed, that it changes at all. Just use momentum conservation: m/120 * 2400m/s = m*v.
Then a=v/t.
 
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FAQ: What is the rocket's initial acceleration?

What is the rocket's initial acceleration?

The rocket's initial acceleration is the rate at which its velocity changes right after launch. It is typically calculated using Newton's Second Law, which states that acceleration is the net force acting on the rocket divided by its mass.

How do you calculate the initial acceleration of a rocket?

To calculate the initial acceleration of a rocket, you need to know the thrust produced by the rocket engines and the mass of the rocket. The formula is: Initial Acceleration = Thrust / Mass. You may also need to account for gravitational forces and air resistance.

What factors affect a rocket's initial acceleration?

Several factors affect a rocket's initial acceleration, including the thrust generated by its engines, the mass of the rocket, gravitational pull, and atmospheric drag. The efficiency of the propulsion system and the angle of launch can also play significant roles.

Why is initial acceleration important for a rocket launch?

Initial acceleration is crucial because it determines how quickly the rocket can overcome Earth's gravitational pull and atmospheric drag. Adequate initial acceleration ensures the rocket reaches the necessary velocity to achieve its intended trajectory and mission objectives.

Can a rocket have zero initial acceleration?

A rocket can have zero initial acceleration if the thrust produced by its engines is exactly balanced by the gravitational force acting on it. In such a case, the rocket would not lift off. To achieve lift-off, the thrust must exceed the gravitational force.

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