Question

20 Two trolleys X and Y with momenta 20 Ns and 12 Ns respectively travel along a straight line in opposite directions before collision. After collision the directions of motion of both trolleys are reversed and the magnitude of the momentum of X is 2 Ns. What is the magnitude of the corresponding momentum of Y?
6 Ns
8 Ns
10 Ns
30 Ns

Answer 1

Answer on Question 58111, Physics, Other

Question:

20. Two trolleys $X$ and $Y$ with momenta $20\,Ns$ and $12\,Ns$, respectively, travel along a straight line in opposite directions before a collision. After the collision, the directions of motion of both trolleys are reversed and the magnitude of the momentum of $X$ is $2\,Ns$. What is the magnitude of the corresponding momentum of $Y$?

a) $6\,Ns$

b) $8\,Ns$

c) $10\,Ns$

d) $30\,Ns$

Solution:

From the Law of Conservation of Momentum we have:

$$p_{X\,(initial)} + p_{Y\,(initial)} = p_{X\,(final)} + p_{Y\,(final)}.$$

Let's assume that the trolley $X$ travels along a straight line to the right in positive direction. Then, the trolley $Y$ travels along a straight line in the opposite direction to the first one (to the left).

Then, from the last formula we can find the momentum of trolley $Y$ after collision:

$$\begin{array}{l} p_{X\,(initial)} - p_{Y\,(initial)} = -p_{X\,(final)} + p_{Y\,(final)}, \\ 20\,Ns - 12\,Ns = -2\,Ns + p_{Y\,(final)}, \\ p_{Y\,(final)} = 20\,Ns - 12\,Ns + 2\,Ns = 10\,Ns. \end{array}$$

Answer:

c) $10\,Ns$

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