# Find maximum thrust of a rocket blasting off

1. Oct 16, 2015

### RUphysics3

1. The problem statement, all variables and given/known data

A 2.49×104-kg rocket blasts off vertically from the earth's surface with a constant acceleration. During the motion considered in the problem, assume thatg remains constant. Inside the rocket, a 14.5-N instrument hangs from a wire that can support a maximum tension of 37.3 N .

I found that :

Acceleration = 15.42 m/s^2

Find the minimum time for this rocket to reach the sound barrier (330m/s) without breaking the inside wire.

The answer to this was 21.4 .

How far is the rocket above the earth's surface when it breaks the sound barrier?
3530 m.

Now I have to find the maximum vertical thrust of the rocket engines under these conditions.

2. Relevant equations
I tried using F=ma and some basic kinematics.

3. The attempt at a solution

Using F=ma...
i tried F=(2.49x10^4) * 15.42 . This wasn't correct.

2. Oct 16, 2015

### Titan97

Tension acts on the instrument and on the rocket. (Downwards on rocket and upwards on the instrument) Let acceleration of rocket be $a$. Since the string is inextensible, the instrument will also have same acceleration. Write newtons law equation for both rocket and instrument.

3. Oct 16, 2015

### Mister T

Is this the net force on the rocket or the thrust force?

4. Oct 16, 2015

### RUphysics3

Well it's a vertical launch..So wouldn't it be the same thing? the only component is in the y direction.. I don't really understand thrust that well. I think it's something like thrust comes out the bottom of the rocket and propels it upwards so the thrust acts upwards? I really don't know

5. Oct 16, 2015

### RUphysics3

What do you mean?
So for the rocket it would be F=(2.49x10^4) * 15.42
For the instrument.. F=(14.5N/9.81) * 15.42 ? Now what?

6. Oct 16, 2015

### Mister T

Thrust is the exhaust gas pushing upward on the rocket. Gravitational force (weight) is Earth pulling downward on the rocket.

7. Oct 16, 2015

### RUphysics3

So weight would be the mass times 9.8. But i did mass * acceleration..Okay.. so should I find weight of the rocket and subtract that from the upward thrust?

8. Oct 18, 2015

### haruspex

To get the net force, yes.