Question

Two carts, one of mass 2m and one of mass m, approach each other with the same speed, v. When the carts collide, they hook together. Assume that positive momentum is to the right.

Which graph best represents the momentum of both carts over time, before and after the collision?

Answer 1

Second option

Step-by-step explanation:

Linear Momentum

The linear momentum of an object of mass m and speed v is

P=mv

If two or more objects are interacting in the same axis, the total momentum is

`P_t=m_1v_1+m_2v_2+...`

Where the speeds must be signed according to a fixed reference

The images show a cart of mass 2m moves to the left with speed v since our reference is positive to the right

`P_1=-2mv`

The second cart of mass m goes to the right at a speed v

`P_2=mv`

The total momentum before the impact is

`P_t=-2mv+mv=-mv`

The total momentum after the collision is negative, both carts will join and go to the left side

The first option shows both carts with the same momentum before the collision and therefore, zero momentum after. It's not correct as we have already proven

The third option shows the 2m cart has a positive greater momentum than the other one. We have proven the 2m car has negative momentum. This option is not correct either

The fourth option shows the two carts keep separated after the collision, which contradicts the condition of the question regarding "they hook together".

The second option is the correct one because the mass
`m_2` has a negative momentum and then the sum of both masses keeps being negative