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

Answer:

Approximately $0.29\; {\rm m \cdot s^{-1}}$.

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:

• $4\; {\rm kg} \times 0.5\; {\rm m \cdot s^{-1}} = 2\; {\rm kg \cdot m \cdot s^{-1}}$.
• $3\; {\rm kg} \times 0\; {\rm m\cdot s^{-1}} = 0\; {\rm kg \cdot m \cdot s^{-1}}$.

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:

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