Two carts connected with a spring -- working with forces and acceleration

[Jaccobtw]

Homework Statement

A 2.0 kg cart and an 8 kg cart are connected by a relaxed, horizontal spring of spring constant 300 N/m. You pull the 8 kg cart with some constant horizontal force. The separation between the carts increases for a short time interval, then remains constant as you continue to pull and the spring is stretched by 0.1 m. (a) What pulling force did you exert? (b) If you instead pull the 2.0 kg cart, what forces must you exert to get the same stretch in the spring?

Relevant Equations

F = -kd
F = ma

Problem Statement: A 2.0 kg cart and an 8 kg cart are connected by a relaxed, horizontal spring of spring constant 300 N/m. You pull the 8 kg cart with some constant horizontal force. The separation between the carts increases for a short time interval, then remains constant as you continue to pull and the spring is stretched by 0.1 m. (a) What pulling force did you exert? (b) If you instead pull the 2.0 kg cart, what forces must you exert to get the same stretch in the spring?
Relevant Equations: F = -kd
F = ma

I'm not sure how to execute the problem.

 

[.Scott]

How much force is the spring exerting once it has been stretched?

 

[berkeman]

Welcome to the PF.

I'm not sure how to execute the problem.

You need to show some effort before we can be of tutorial help. Please use the Relevant Equations to set up the equations for both cases. Draw the Free Body Diagrams (FBDs) for each case, and show all of the forces involved. Please show us your work...

 

[Jaccobtw]

How do you draw a freebody diagram on here?

 

[Jaccobtw]

How much force is the spring exerting once it has been stretched?

F = -kd
(-300)(-0.1) = 30 N

 

[berkeman]

How do you draw a freebody diagram on here?

We don't have any built-in drawing tools (yet), but you can make a hand sketch and attache it to a post with the Attach Files button below the Edit window. Try to take a good quality picture of the sketch, or better yet scan it with a scanner/copier.

 

[Jaccobtw]

How much force is the spring exerting once it has been stretched?

Ok, here is my understanding: Because (technically) the only thing exerting a force on the 2 kg car is the spring we can do this:

-kd = ma

and solve for acceleration (15m/s^2)

Now, because the 2kg cart and the 8 kilogram cart are a single moving system, the 8 kg cart must also be accelerating at the same rate. Also, we still have the spring pulling in the opposite direction as the car:

F = ma - kd
(8kg)(15m/s) - (300)(0.1)

F = 1.5 x 10^2 N

but technically this doesn't make sense because it means the cart was never accelerating at 15m/s^2 because the spring was pulling against it. I don't know, this is why I'm confused

 

[.Scott]

Now, because the 2kg cart and the 8 kilogram cart are a single moving system ...

And this system is how much more massive that the cart being pulled at 30N?

 

[Jaccobtw]

And this system is how much more massive that the cart being pulled at 30N?

8N right?

 

[.Scott]

8N right?

Let's try that again:
This system is how much more massive that the cart being pulled at 30N?
That is, what is the ratio of the total mass of both carts to the mass of the one being pulled by 30N?

 

[Jaccobtw]

Let's try that again:
This system is how much more massive that the cart being pulled at 30N?
That is, what is the ratio of the total mass of both carts to the mass of the one being pulled by 30N?

Sorry, I meant 6 kg (8kg - 2kg) = 6kg. The ratio is 5kg to 1 kg (8 + 2 / 2)

 

[.Scott]

Sorry, I meant 6 kg (8kg - 2kg) = 6kg. The ratio is 5kg to 1 kg (8 + 2 / 2)

Can we call that a factor of five?
Think - what force will be required to pull that entire mass at the same rate as the smaller one?

 

[Jaccobtw]

Can we call that a factor of five?
Think - what force will be required to pull that entire mass at the same rate as the smaller one?

10kg x 15m/s^2 = 150 N

 

[.Scott]

Yup. It was 30N for the 2Kg cart - so it would be 5 times the force for 5 times the mass. 5x30N.

 

[Jaccobtw]

Thank you so much...haha that went over my head at first