How Do You Calculate a Rocket's Initial Upward Acceleration?

In summary, the problem asks to compute the initial upward acceleration of a rocket of mass 1.2 x 10^4 kg, given an initial upward force (thrust) of 2.7 x 10^5 N and taking into account the gravitational force. Using the equation ΣF = ma, the net force in the upward direction can be found by subtracting the force of gravity, which is equal to the mass of the rocket multiplied by the acceleration due to gravity (9.8 m/s^2). Solving for acceleration, we get an initial upward acceleration of 210.7 m/s^2. However, this answer is incorrect because we neglected to include the gravitational force. When the gravitational force is
  • #1
bewger
6
0

Homework Statement



Compute the initial upward acceleration of a rocket of mass 1.2 multiplied by [tex] 10^4 [/tex] kg if the initial upward force produced by its engine (the thrust) is 2.7 multiplied by [tex] 10^5 [/tex] N. Do not neglect the gravitational force on the rocket.


Homework Equations



F = ma

The Attempt at a Solution



I tried doing [tex] \frac{9.8(Thrust - mass)}{mass} = a [/tex]

I get a = 210.7 m/s^2

but that's wrong.

Can anybody tell me what I'm doing wrong?
 
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  • #2
bewger said:
I tried doing [tex] \frac{9.8(Thrust - mass)}{mass} = a [/tex]
Not sure how you got that one.

Stick with ΣF = ma. What forces act on the rocket? What's the net force?
 
  • #3
So, if a = F/m, then is that also the initial acceleration also?

It stated not to neglect gravity, do I multiply gravity by the mass into the equation?
 
  • #4
Your formula is correct, except for the gravity factor which you are missing.
Think about forces, gravity is downward, the thrust is upward. You'll want the net force upward for the acceleration. So that should be everything you need.
 
  • #5
bewger said:
So, if a = F/m, then is that also the initial acceleration also?
Yes.
It stated not to neglect gravity, do I multiply gravity by the mass into the equation?
In order to get the force due to gravity--which is the rocket's weight--you would multiply the mass by g = 9.8 m/s^2.
 
  • #6
Sum the forces, draw a free body diagram if you need to
[PLAIN]http://img411.imageshack.us/img411/2641/blockb.png

Fg = force of gravity = mass * gravity
Ft = thrust of rocket

sum of the forces in Y = Ft - Fg = ma;

solve for a
 
Last edited by a moderator:
  • #7
Thank you everyone for your help.
Much appreciated.
 
  • #8
fizzynoob said:
Sum the forces, draw a free body diagram if you need to
[PLAIN]http://img411.imageshack.us/img411/2641/blockb.png

Fg = force of gravity = mass * gravity
Ft = thrust of rocket

sum of the forces in Y = Ft - Fg = ma;

solve for a

wait, is this a variable weight problem, like the fuel has a burn rate so mass decreases as time goes on?
 
Last edited by a moderator:
  • #9
They just want the initial acceleration of the rocket. Therefore you don't need to know the rate at which the fuel is being burned. Just sum the forces, and solve for A
 

Related to How Do You Calculate a Rocket's Initial Upward Acceleration?

1. What is initial upward acceleration?

Initial upward acceleration refers to the rate at which an object initially increases its upward velocity. It is typically measured in meters per second squared (m/s^2) and is a key factor in understanding an object's motion.

2. How is initial upward acceleration calculated?

Initial upward acceleration is calculated by dividing the change in upward velocity by the change in time. This can be represented by the formula a = (vf - vi)/t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time taken.

3. What factors affect initial upward acceleration?

The main factors that affect initial upward acceleration are the force applied to the object and the mass of the object. The greater the force or the lighter the object, the higher the initial upward acceleration will be.

4. How does initial upward acceleration differ from constant upward acceleration?

Initial upward acceleration is the acceleration at the beginning of an object's motion, whereas constant upward acceleration refers to a situation where the upward acceleration remains the same over time. In other words, initial upward acceleration is the starting point for an object's motion, while constant upward acceleration is a sustained acceleration.

5. Why is initial upward acceleration important in physics?

Initial upward acceleration is important in physics because it helps us understand and predict the motion of objects. By knowing the initial upward acceleration, we can calculate an object's velocity and position at any given time, and make predictions about its future motion based on the laws of physics.

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