Finding the change in length of the rope

[Arquon]

Homework Statement

a= 0.3 m / s²
k = 10 000 N / m
m = 1800 kg ( of the car that is being pulled)
Ignore friction.

A car is being pulled by another car by a rope ( stiffness = 10 000 N/m) with acceleration of 0.3 m/s^2.. Find the change in length of the rope.

Homework Equations

F = ma
F = kx (x is the change in length)

The Attempt at a Solution

x = F / k
I am having trouble at finding F. I have made a graph, which I have uploaded here, of the car that is being pulled in this situation and I don't know if it's correct. A hint would be appreciated.

 

[TomHart]

Welcome to Physics Forums.

Here is a hint: There is only one horizontal force acting on the car being towed and that force is what is causing it to accelerate. The weight of the car is a downward force and the normal force is upward. So use one of the "relevant equations" that you listed.

 

[Arquon]

So F should be 540 N ( since there is only one horizontal force, got it simply by F = ma) , or is there something else I'm not noticing ? Because I'm not getting a correct answer. It's supposed to be 0.011 m, but I get 0.0054 m, so F should be approximately 1100 N.

 

[TomHart]

Well, unless there's something I'm not noticing also, I don't see how you did anything wrong. But I got 0.054 m, instead of 0.0054 that you got. That may have just been a typo. Sometimes the "correct answers" are wrong.

 

[TomHart]

You may just want to check that you copied down all of the information from the problem correctly.

 

[Arquon]

I forgot one 0 for k: it's supposed to be 10⁵, my bad. And it seems I lost one bit of information while translating this exercise, so I will re-do it:

Car A is being towed by car B with a rope ( k = 10⁵) and acceleration of 0.3 m/s². Car A has a mass of 1800 kg. Ignore friction. Find the change in length of the rope.

 

[haruspex]

I forgot one 0 for k: it's supposed to be 10⁵, my bad. And it seems I lost one bit of information while translating this exercise, so I will re-do it:

Car A is being towed by car B with a rope ( k = 10⁵) and acceleration of 0.3 m/s². Car A has a mass of 1800 kg. Ignore friction. Find the change in length of the rope.

It's definitely 0.0054m, unless you forgot to mention it is going uphill.

 

[Arquon]

No, it's going horizontal. Maybe car B has something to do with it ? If I imagine right, car B has 2 horizontal forces: one in direction of the rope, and another one to the front of the car B.

Edit : Although, nevermind. That still got me back to F = ma. I guess the answer is 0.054 m then. Thanks for help !