Two carts collide elastically. The second cart is pushed horizontally in the positive direction on a frictionless surface with a force of F2. The carts have masses m1 and m2, respectively. What acceleration does the first cart feel during the collision? Remember it's a vector.

First of all, we notice that the collision is elastic: this means that there are no external forces acting on the system, as the total momentum and the total kinetic energy of the system are conserved.

The force acting on the cart 2 is

[tex]F_2[/tex]

According to Newton's third law of motion:

"When an object 1 exerts a force on another object 2, then object 2 exerts an equal and opposite force on object 1"

Therefore, if we call [tex]F_1[/tex] the force exerted on cart 1 during the collision, we can write

[tex]F_1=-F_2[/tex]

According to Newton's second law of motion, the net force acting on an object is equal to the product between its mass (m) and its acceleration (a):

[tex]F=ma[/tex]

So for cart 1 we have:

[tex]F_1=m_1 a_1[/tex]

And som the acceleration of cart 1 is

[tex]a_1=\frac{F_1}{m_1}=-\frac{F_2}{m_1}[/tex]

Where the negative sign means that the direction of the acceleration of cart 1 is opposite to the direction of the force F2.