Evidence that the ship had its engine turned on

[JessicaHelena]

Homework Statement

Homework Equations

a = v/t
p=mv(?)

The Attempt at a Solution

If an engine is turned on, that means that the ships are accelerating since the engine pushes back on air with a force and air pushes back to propel the ships forward, so I thought (A) would be the answer, even though I was confused with other answers. However, the answer turns out to be (B)... Could someone explain why?

 

[kuruman]

Does the velocity of the center of mass change or does it stay the same? BTW, there is no air in deep space, but that's not important to the question.

 

[JessicaHelena]

@kuruman — From the graph (if I'm doing it right), I think it's increasing a little.

 

[kuruman]

@kuruman — From the graph (if I'm doing it right), I think it's increasing a little.

Can you be more precise? What is the velocity of the CM at t = 0 and then at t = 10 s? There is an equation for it.

 

[JessicaHelena]

@kuruman — At t=10 the v = 8005 m/s and at t=0 v= 8000 m/s .

Since the given graphs are pretty linear, the graph of CM velocity could be given by v=8000 + 1/2(t) ?

 

[kuruman]

It could but you don't need the approximation. Have you seen the equation $$V_{CM}=\frac{m_1v_1+m_2v_2}{m_1+m_2}~?$$ If so, use it. You can read the velocity values off the plot.

 

[JessicaHelena]

@kuruman

I think I actually get the same values using the equation you gave me above though... am I missing something? But now that I see the formula, it does involve momentum...

 

[kuruman]

@kuruman

I think I actually get the same values using the equation you gave me above though... am I missing something? But now that I see the formula, it does involve momentum...

You are not missing anything. Yes, the velocity of the CM in this case is given by the formula that you quoted. So what conclusion can be drawn from the fact that the velocity of the CM depends on time? What does this have to do with the engine being turned on?

 

[haruspex]

thought (A) would be the answer,

Kuruman is leading you to why B is a valid answer, but for completeness it is also important to rule out A.
Is it possible for ship 2 to be speeding up even if neither has its engine on?

 

[JessicaHelena]

@haruspex — I don't know about the first ship, but ship 2 could speed up if the first ship pulls in the cable?

 

[JessicaHelena]

Also, for justifying (B), I was wondering if I could say, "because there's a net force acting on the system the momentum is not conserved"?

 

[haruspex]

@haruspex — I don't know about the first ship, but ship 2 could speed up if the first ship pulls in the cable?

Right, so is A a valid reason for saying that at least one engine is on?

 

[haruspex]

Also, for justifying (B), I was wondering if I could say, "because there's a net force acting on the system the momentum is not conserved"?

Yes, but that is backwards from what you need. You want to show there is a net force.

 

[JessicaHelena]

@haruspex — Since CM has velocity that's increasing, it's got a positive (constant) acceleration and so it has F (because F=ma), is that right?

 

[haruspex]

@haruspex — Since CM has velocity that's increasing, it's got a positive (constant) acceleration and so it has F (because F=ma), is that right?

Yes.