Spaceship

Classical Mechanics Level 1

An astronaut is accidentally separated from his small spaceship which is accelerating in inter stellar space at a constant rate of $100\text{ m/s}^2$ . What is the acceleration of the astronaut the instant after he is outside the spaceship?

Details

Assume that there are no nearby stars to exert gravitational force on him.

There is more net force acting on him, so he possesses more acceleration. The net force acting on him, once he is out of the spaceship is zero and acceleration is also zero. The instant he steps off the ship, he has half the acceleration of the ship. There is less net force acting on him, so he possesses less acceleration.

6 solutions

Robert Isabal
Aug 11, 2016

There is a force acting on him: the gravitational force exerted by the spaceship. That means that the astronaut will have less acceleration than the spaceship, but it won't be 0. The correct answer should be the last one.

Right, but at the same time, more force would be exerted the closer to earth he gets, and since acceleration is proportional, it should increase too , right ?

Lavann D Hoggard - 4 years, 7 months ago

Earth was never mentioned in the question so doesn't come into play.

Vikram Harinath - 2 years, 10 months ago

It is mentioned that it is interstellar space - far enough from Earth that the gravitational force is effectively zero. Ignore the picture.

Chris Sparke - 2 years, 5 months ago

I assumed that there are no stars nor planets, only the astronaut and the spaceship, but it's true :)

Robert Isabal - 4 years, 7 months ago

Good observation! First the masses of the astronaut and the spacecraft are so infinitesimal that the gravitational force between them would be practically indiscernible. The gravitational constant itself is infinitesimal at 6.674×10−11 N · (m/kg)2. The actual gravity is reduced even further because the force is inversely proportional to the square of the distance between their centers of gravity. Also, at such close distances and small masses, they must be treated as bodies with spacial extent rather than point masses, meaning that only the smallest mass of the ship closest to the smallest mass of the astronaut's closest extremity experiences any significant gravitational force, which quickly approaches a negligible magnitude because the ship is accelerating away from the astronaut. Finally, this infinitesimal gravitational force was completely negated by the force required to exit the ship, so that the NET force at exit is actually ZERO.

Here is an interesting aside. If the escape velocity of earth's gravitational field is about 11.186 km/s, what would the escape velocity of the ship's gravitational field be?

Scot Magann - 4 years, 5 months ago

Yeah.

I answered the last one and was surprised by the 'Incorrect'

A Former Brilliant Member - 3 years, 7 months ago

That is so miniscule that it is almost equal to zero

Arpan Das - 3 years, 2 months ago

What about acceleration due to earth, g

ishwar gowda - 2 years, 10 months ago

They are in interstellar space, so the Earth is a long, long way away.

Chris Sparke - 2 years, 5 months ago

They meant small ship, by default the g due to the ship is neglected... It's highly impossible to measure small force on him.

Hari Kumar - 1 year, 10 months ago

Parangav Dubey
May 13, 2015

the qustion is correct but the picture given is misleading since it shows the astronaut and the spaceship orbiting around the earth and in that case the astronaut will be under free fall along with the spaceship so it will have centrepetal acceleration.

I suppose it's just because we don't have many photos of astronauts in interstellar space? It is misleading, but it's also not claiming to be a picture of the problem. Given that the problem states 'interstellar space', I think its fine.

Chris Sparke - 2 years, 5 months ago

Arnab Bhattacharya
Aug 8, 2014

Without any kind of force you cannot accelerate be it external or internal. Even if u think you can accelerate using your own muscles you still need the frictional force to do so. In inter-stellar space the lack of gravity means you just float due to lack of boundaries without accelerating. Once the contact with a spaceship is lost, the driving force( jet fuel) is no longer there to accelerate. So, any object, be it living or non-living cannot accelerate.

Correct answer: The net force acting on him, once he is out of the spaceship is zero and acceleration is also zero. Your answer: There is not net force acting on him,so he has no acceleration.

This is confusing.

Ashish Bhatia - 6 years, 10 months ago

the reason he has no acceleration is because he has no net force once he is out of the spaceship! That's what i answered.

Arnab Bhattacharya - 6 years, 10 months ago

Your ans is correct Arnab, my claim is there are two correct ans will similar languages. Either I am misreading something or there are two correct solutions.

Ashish Bhatia - 6 years, 10 months ago

@Ashish Bhatia – there are two correct answers which differ a little only as far as the language is concerned. the meaning is the same.

Arnab Bhattacharya - 6 years, 10 months ago

The units in the question should read $ms^{-2}$ , not $ms^{-1}$ . Also, I agree with Arnab that the answers are a bit misleading - I don't think you can have two correct responses to a question?

Zarak K - 6 years, 10 months ago

Needs re-edit for at least 2 reasons.

Oussama Erraji - 6 years, 10 months ago

This is a very poorly phrased question with equally horrible answer options. Please edit.

Gaurav Verma - 6 years, 10 months ago

What about the gravitational force of attraction between the spaceship and the astronaut? That is a net force - no matter how miniscule. The acceleration will be very small - but NOT zero !!

Bob Kadylo - 5 years, 7 months ago

acceleration = Force / mass. Force = 0 (No Gravitational Force) implies acceleration = 0.

Anirudh Mathur - 6 years, 10 months ago

Is the qualifying characteristic "living or non-living" necessary for solution of the problem?

Ceazar Sunga - 6 years, 10 months ago

Difference between answers 3 and 4??

Oussama Erraji - 6 years, 10 months ago

Option 2 & 3 are very similar and misleading..... I gave option 3 as my answer but the correct answer turned out to be option 2..... Secondly, the unit of acceleration is m/s^2 and not m/s.

Nirmit Tripathii - 6 years, 10 months ago

This question has a couple of issues with it. The acceleration should be in correct units m/s is simply a velocity and secondly it doesn't state where the force is from!

Andy Cooper - 6 years, 10 months ago

I am much happy with all these problems .i solve and this is that as soon as he comes out ,heis in space.so no force can be there and so no acceleration prabir kumar ray India.

prabir ray - 6 years, 10 months ago

As a math teacher, I know that problems in a question arise when you try to trick your students... Boo to this problem.

Kai King - 6 years, 10 months ago

Doesn't he have a gravitational force applied to him by the spaceship he just left? Everything has a force acting upon two objects, therefore the space ship should be pulling him closer to it since there's no other forces acting on him.

jim smith - 4 years, 8 months ago

doesnt the astronaut get momentum from said frictions between him and the ship?

Vatea Tahiti - 3 years, 12 months ago

Mark Billingham
Aug 8, 2017

I don't believe the astronaut left the spacecraft accidentally. An acceleration of 100 m/s2 is over 10g and would be extremely uncomfortable to say the least. He/she obviously had enough and got out.

Deepak Kumar
Dec 28, 2015

According to the given question, there is not any external forces like gravitational force, friction force or any other contact forces acting on astronaut when he separate from his spaceship. Therefore there is not any acceleration of astronaut without any external force.

Aditya Paul
Mar 28, 2015

In the absence of any external force (outside space ship), net acceleration on the body is zero, by Newtons first Law and due to the bad luck of the astronaut.

Spaceship

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