# Acceleration due to gravity of a rocket

• AlphaA
In summary: Here, the signs show you the directions of the vectors.If you rearrange the above to solve for t, you get the equation in your book.The book simply went straight for the rearranged equation.

#### AlphaA

If an object say a rocket is thrown up in the sky with an additional acceleration say ' x ' , then why do we add the value of acceleration due to gravity i.e 9.8 m/s^2 to the acceleration ' x' in order to find the total acceleration...
Since vector of acceleration due to gravity is directed downwards...so we consider it - 9.8 m/s^2 . So in accordance to this, if we find total acceleration then we should subtract 9.8 m/s^2 from 'x ' m/s^2 because...firstly, gravity is -9.8 m/s^2 and secondly, acceleration due to gravity will constantly decrease if the rocket or object will continue going up int he sky with that X acceleration. So why should 9.8 m/s^2 be added to X m/s^2 and not subtracted ?

If you add a negative value you're subtracting it, no?
##a+(-b)=a-b##

Bandersnatch said:
If you add a negative value you're subtracting it, no?
##a+(-b)=a-b##
But as the bookish explanation says, we add the positive value of acceleration due to gravity and not the negative one...
That's why I am confused...
Need some help and guidance

That doesn't seem right. Can you provide more context for the question? Perhaps a verbatim description of the problem as stated in your book? (a picture will do)

Bandersnatch said:
That doesn't seem right. Can you provide more context for the question? Perhaps a verbatim description of the problem as stated in your book? (a picture will do)
The example goes on like this :

A rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of 5.0 m/s^2 . Find the initial thrust(force) of the blast.
Take g=9.8 m/s^2

Solution (as given in my book) :
The rocket moves up against gravity with an acceleration of 5.0 m/s^2 .
Hence the blast produces a total acceleration of =
a=9.8+ 5.0 =14.8 m/s^2
By Newton's II law, the initial thrust(force) of the blast is =
F=ma = 20,000 kg x 14.8 m/s^2 =2.96 x 10^5 N.
Therefore, answer is 2.96 x 10^5 N

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AlphaA said:
The example goes on like this :

A rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of 5.0 m/s^2 . Find the initial thrust(force) of the blast.
Take g=9.8 m/s^2

Solution (as given in my book) :
The rocket moves up against gravity with an acceleration of 5.0 m/s^2 .
Hence the blast produces a total acceleration of =
a=9.8+ 5.0 =14.8 m/s^2
By Newton's II law, the initial thrust(force) of the blast is =
F=ma = 20,000 kg x 14.8 m/s^2 =2.96 x 10^5 N.
My doubt is the underlined portion only. If the rocket moves against gravity then why should acceleration due to gravity be added to the initial acceleration?

That could be written more clearly to show what's going on.

Try this:
##a=g+t##
where a is the net acceleration (5m/s^2, positive is up), g is the gravitational acceleration (-9.8m/s^2) and t is the thrust you want to find. Here, the signs show you the directions of the vectors.

If you rearrange the above to solve for t, you get the equation in your book.
The book simply went straight for the rearranged equation.

Note that the acceleration due to gravity is not
AlphaA said:
but is deducted from the net (initial) acceleration. ##-(-9.8) = +9.8##

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AlphaA said:
My doubt is the underlined portion only. If the rocket moves against gravity then why should acceleration due to gravity be added to the initial acceleration?
To get the proper acceleration, relative to free fall. That's what the engine must provide to cancel gravity and accelerate up.

Bandersnatch said:
That could be written more clearly to show what's going on.

Try this:
##a=g+t##
where a is the net acceleration (5m/s^2, positive is up), g is the gravitational acceleration (-9.8m/s^2) and t is the thrust you want to find. Here, the signs show you the directions of the vectors.

If you rearrange the above to solve for t, you get the equation in your book.
The book simply went straight for the rearranged equation.

Not that the acceleration due to gravity is not

but is deducted from the net (initial) acceleration. ##-(-9.8) = +9.8##

Oh...THANKYOU soooooooooooooooo much...
I got it!
I can now see it clearly...yaa...I've undersood it now...
Once again...THANKS A LOT !
It was really very sweet of you to guide me ...
Gratitude.

5 - (-9.8)=14.8

Chet

Chestermiller said:
5 - (-9.8)=14.8

Chet
Thank you so much .. Sir...
I got it !...
It was really simple and I was stuck at it like anything...
Thank you so much for helping me out.

AlphaA said:
Thank you so much .. Sir...
I got it !...
It was really simple and I was stuck at it like anything...
Thank you so much for helping me out.
It would have been much easier if you had drawn a free body diagram of the rocket, and then, based on the free body diagram, written the force balance:

F - mg = ma

Chet

If the rocket moves against gravity then why should acceleration due to gravity be added to the initial acceleration?

Perhaps think like this...

How much thrust would the rocket have to produce so that it only just manages to lift off the ground without accelerating upwards?

Then how much more does it have to produce to accelerate upwards at "a"?

What's the total?

## What is the definition of acceleration due to gravity of a rocket?

Acceleration due to gravity of a rocket is the force of gravity acting on a rocket as it accelerates through the Earth's atmosphere.

## How is the acceleration due to gravity of a rocket calculated?

The acceleration due to gravity of a rocket can be calculated using the equation a = G * (m1 + m2)/r^2, where a is the acceleration due to gravity, G is the gravitational constant, m1 and m2 are the masses of the rocket and the Earth, and r is the distance between them.

## What factors affect the acceleration due to gravity of a rocket?

The acceleration due to gravity of a rocket is affected by the mass of the rocket, the mass of the Earth, and the distance between them. It is also affected by any external forces acting on the rocket, such as air resistance.

## How does the acceleration due to gravity of a rocket change as it moves away from the Earth?

The acceleration due to gravity of a rocket decreases as it moves away from the Earth. This is because the gravitational force between the rocket and the Earth decreases as the distance between them increases.

## Why is the acceleration due to gravity of a rocket important in space exploration?

The acceleration due to gravity of a rocket is important in space exploration because it affects the trajectory and speed of a rocket as it travels through space. Understanding and calculating this acceleration is crucial in successfully launching and navigating a rocket to its desired destination.