Question

A trolley of mass 4 kg moves with a velocity of 0.5 meter per second It colides with a stationary trolley of mass 3 kg. If the trolleys stick together after collision, find the velocity that they of with move

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Answer 1

Approximately
`0.29\; {\rm m \cdot s^(-1)}`.

Step-by-step explanation:

Make use of the fact that total momentum is conserved in collisions.

The momentum of an object of mass
`m` and velocity
`v` is
`p = m\, v`.

The momentum of the two trolleys before the collision would be:

• 
  `4\; {\rm kg} * 0.5\; {\rm m \cdot s^(-1)} = 2\; {\rm kg \cdot m \cdot s^(-1)}`.
• 
  `3\; {\rm kg} * 0\; {\rm m\cdot s^(-1)} = 0\; {\rm kg \cdot m \cdot s^(-1)}`.

Thus, the total momentum of the two trolleys right before the collision would be
`2\; {\rm kg \cdot m \cdot s^(-1)}`.

Since the two trolleys are stuck to one another after the collision, they could modelled as one big trolley of mass
`m = 3\; {\rm kg} + 4\; {\rm kg} = 7\; {\rm kg}`.

The momentum of the two trolleys, combined, is conserved during the collision. Thus, the total momentum of the new trolley of mass
`m = 7\; {\rm kg}` would continue to be
`v = 2\; {\rm kg \cdot m \cdot s^(-1)}` shortly after the collision.

Rearrange the equation
`p = m\, v` to find the velocity of the two trolleys combined:

`\begin{aligned}v &= (p)/(m) \\ &= \frac{2\; {\rm kg \cdot m \cdot s^(-1)}}{7\; {\rm kg}} \\ &\approx 0.29\; {\rm m \cdot s^(-1)}\end{aligned}`.