# Two Carts attached to a string

• B3NR4Y
In summary, the problem involves two carts on a low-friction track, with one being pushed by a constant force of 2.0N and the other being connected to it by a spring of spring constant k=300 N/m. The first part of the problem asks for the acceleration of the center of mass of the system without the spring, which is found to be 2.5 m/s/s. The second part asks for the acceleration with the spring, but it is found that the spring only provides an internal force and does not affect the acceleration of the center of mass. Therefore, the acceleration remains the same as without the spring.
B3NR4Y
Gold Member

## Homework Statement

Two 0.400-kg carts are 100 mm apart on a low-friction track. You push one of the carts with a constant force of 2.0N directed so that the cart you push moves away from the other cart.
Determine the acceleration of the center of mass of the two-cart system when the carts are connected by a spring of spring constant k = 300 N/m.

## Homework Equations

$F_{x} (x) = -k(x-x_{0})$ for the force of the spring
$COM = \frac{\sum_n x_{n} m_{n}}{\sum_{n} m_{n}}$ for the center of mass, initially is at 50 mm or 0.05 m
$a_{cm} = \frac{\sum F(x)}{\sum m}$ for the acceleration of the center of mass

## The Attempt at a Solution

So the first part of the problem had me find the acceleration of the center of mass without the spring, which I did by summing the forces (which was easy, 2+0) and dividing by the sum of the masses, so without the spring the acceleration of the center of mass was 2.5 m/s/s. The second part of the problem I don't understand what it is attempting to say. If you push the right most cart 2 N, it will have a force acting in the other direction that is equal to -k(x-x0), but I don't know what the change in x is or anything like that so I am confused on where to begin.

And what is going to be the force on the other cart? What acceleration is it going to have?

The force on the other cart should be k(x-x0) because the spring is pulling it, if I am not wrong. Which is equal and opposite the the force the spring is exerting on the other cart, right?

Yes, so how are the accelerations of the carts changed by this? How does it affect the center of mass acceleration?

Orodruin said:
Yes, so how are the accelerations of the carts changed by this? How does it affect the center of mass acceleration?
I can't believe the solution was so simple, the spring part just cancels and you get the same exact answer as without the spring. Astounding, this is why I love physics. Thank you for your help, you're my favorite volcano :P

B3NR4Y said:
I can't believe the solution was so simple, the spring part just cancels and you get the same exact answer as without the spring.

Precisely. What matters for the acceleration of the CoM of a system is only its total mass and the external forces acting on it. In this case, the spring only provides an internal force and therefore need not be considered.

Astounding, this is why I love physics. Thank you for your help, you're my favorite volcano :p

You're welcome. Also, most people seem to blame me for helping in the creation of a certain piece of jewelry. They always conveniently forget that I was also instrumental in its destruction too! :p

B3NR4Y

## 1. What is the concept of "Two Carts attached to a string"?

The concept of "Two Carts attached to a string" involves two carts connected by a string or rope, where one cart is placed on a horizontal surface and the other is suspended vertically. When the string is pulled, the carts move in opposite directions due to the tension in the string.

## 2. What is the purpose of studying "Two Carts attached to a string"?

Studying "Two Carts attached to a string" allows scientists to better understand the concepts of tension, forces, and motion. It can also be used to demonstrate and explore the principles of Newton's laws of motion.

## 3. How does the mass of the carts affect their movement in "Two Carts attached to a string"?

The mass of the carts does not affect their movement in "Two Carts attached to a string" as long as the string remains taut. The carts will move at the same rate regardless of their individual masses.

## 4. Can "Two Carts attached to a string" be used to demonstrate other scientific principles?

Yes, "Two Carts attached to a string" can be used to demonstrate other principles such as conservation of energy, potential and kinetic energy, and the relationship between force and acceleration.

## 5. Are there any real-world applications of "Two Carts attached to a string"?

Yes, the concept of "Two Carts attached to a string" can be seen in various real-world applications such as elevators, pulley systems, and even in the movement of molecules in a cell.

• Introductory Physics Homework Help
Replies
24
Views
3K
• Introductory Physics Homework Help
Replies
8
Views
5K
• Introductory Physics Homework Help
Replies
7
Views
3K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
16
Views
2K
• Introductory Physics Homework Help
Replies
20
Views
2K
• Introductory Physics Homework Help
Replies
29
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
341
• Introductory Physics Homework Help
Replies
6
Views
247
• Introductory Physics Homework Help
Replies
1
Views
3K