Can a Rocket Reach the Sound Barrier Without Breaking Internal Equipment?

[monikraw]

Homework Statement

A 2.45×10^4-kg rocket blasts off vertically from the Earth's surface with a constant acceleration. During the motion considered in the problem, assume that remains constant. Inside the rocket, a 13.1-N instrument hangs from a wire that can support a maximum tension of 33.9N .

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

Find the maximum vertical thrust of the rocket engines under these conditions.

How far is the rocket above the Earth's surface when it breaks the sound barrier?

Homework Equations

F = ma
w = ma
vx = v0x + axt

probably missing a couple

The Attempt at a Solution

The only thing I could think to do so far is to calculate the downward force acting on the rocket which would be weight?

so 24500 x 9.8 = 240100N acting downward

I don't know how to find the upward force.
I don't know what all this hanging instrument stuff is?

Help is much appreciated! Thanks c:

 

[SHISHKABOB]

well so imagine you're dragging some object along a frictionless surface (say, ice) and you're pulling it with a rope

let's say you can accelerate at will (like you've got a jetpack on or something)

so when you're pulling this object along, it will experience a force, yeah?

Same idea here. The hanging instrument is being pulled upwards by the same force that is pushing the rocket up into the air.

 

[monikraw]

so the string can handle 2.587 times the force it's handling right now right? but how do I incorporate that into an equation to find speed or acceleration?

 

[SHISHKABOB]

the string can support 33.9N, and is feeling 13.1N when the system is at rest. How much more force can be applied before it breaks?

 

[Nickie]

As a scientist, it is important to approach a problem like this with a systematic and analytical mindset. The first step would be to identify and understand all the given information and variables in the problem.

In this case, we have a rocket with a mass of 2.45×10^4 kg, a maximum tension of 33.9 N for the wire, and a desired speed of 330 m/s. The acceleration of the rocket is constant and we are asked to find the minimum time, maximum vertical thrust, and distance from Earth's surface when it reaches the sound barrier.

To solve for the minimum time, we can use the equation v = v0 + at, where v is the final velocity, v0 is the initial velocity (which is 0 m/s), a is the acceleration, and t is the time. We know the final velocity is 330 m/s and the acceleration is constant, so we can rearrange the equation to solve for t. This gives us t = v/a = 330/9.8 = 33.67 seconds.

Next, to find the maximum vertical thrust of the rocket engines, we can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the acceleration is also the same as the acceleration due to gravity, so we can use the weight of the rocket as the force. This gives us F = 2.45×10^4 kg x 9.8 m/s^2 = 240100 N. This is the maximum vertical thrust of the rocket engines.

To determine how far the rocket is from Earth's surface when it reaches the sound barrier, we can use the equation d = v0t + 1/2at^2, where d is the distance, v0 is the initial velocity, a is the acceleration, and t is the time. In this case, the initial velocity is 0 m/s and the acceleration is constant, so we can plug in the values we know to solve for d. This gives us d = 0 + 1/2 x 9.8 x (33.67)^2 = 5608.23 meters. Therefore, the rocket will be 5608.23 meters above Earth's surface when it reaches the sound barrier.

As for the hanging instrument, it is not relevant to the calculations, but it is important to consider in terms of the