Answer:
The speed of the mass M is 7.2 meters per second
Explanation:
In this case because there aren't external forces on the system blocks-spring and the spring is light we should apply the conservation of linear momentum (P) that states:
[tex]\overrightarrow{p}_{f}+\overrightarrow{p}_{i}=0 [/tex] (1)
Momentum is mass (m) times velocity (v) ([tex] \overrightarrow{p}=m\overrightarrow{v}[/tex] (2)) and Initial momentum [tex] \overrightarrow{p}_{i} [/tex] is zero because the blocks are released form rest, so (1) is:
Using (2) on (1):
[tex]\overrightarrow{p}_{f}=M\overrightarrow{v_{M}}+3M\overrightarrow{v_{3M}}=0 [/tex] (3)
It's important to note that momentum and velocity are vector quantities so we should take care of directions, assuming right direction as positive, velocity of 3M mass is positive, and velocity of M mass is negative, (3) is:
[tex]M(-v_{M})+3M(v_{3M})=0 [/tex]
solving for [tex]v_{M}[/tex]
[tex] M(v_{M})=3M(v_{3M})[/tex]
[tex] v_{M}=\frac{3M(v_{3M})}{M}=\frac{3(2.4)}{1}[/tex]
[tex]v_{M}=7.2\frac{m}{s} [/tex]
