If a cart and a string are attached and there is a weight on the end of the string to pull the cart, and both the cart and the weight on the string were the same.. what would I expect acceleration to be using Newton's second law?

To determine the expected acceleration using Newton's second law, you need to know the forces acting on the system. In this case, there are two forces:

1. The force due to the weight of the cart, which we will call "F1".
2. The tension force in the string due to the weight at the end of the string, which we will call "F2".

According to Newton's second law, the net force acting on an object is equal to its mass multiplied by its acceleration (F = m * a). In this case, the net force is the sum of the two forces acting on the system.

Since the weight of the cart and the weight at the end of the string are the same, the magnitude of F1 and F2 would be equal. Let's assume the mass of the cart and the weight is "m" (in kg).

Therefore, the net force on the system would be F = F1 + F2 = m * a + m * a = 2 * m * a.

Since the mass of the system is 2m, the net force acting on the system is 2m * a.

Now, rearranging the equation F = m * a, we can solve for the acceleration:

2 * m * a = m * a

Canceling out the mass (m) from both sides, we get:

2 * a = a

Therefore, the acceleration of the system would be zero (0 m/s²), as both sides of the equation are equal.

This means that if the weights of the cart and the weight on the string are the same, and all other forces are negligible, the system would not accelerate and remain at rest.