| An air track glider of mass M is built, consisting of two smaller connected gliders with a small explosive charge located between them. The glider is traveling along a frictionless rail at 2 m/s to the right when the charge is detonated, causing the smaller glider with mass \[\frac{1}{4}M,\] At, to move off to the right at 5 m/s. What is the final velocity of the second small glider? |
 |
A) 4 m/s to the left
B) 2 m/s to the left
C) 1 m/s to the left
D) 1 m/s to the right
Correct Answer: D
Solution :
| This is a conservation of momentum problem, in which the total momentum of the glider at the beginning of the problem is equal to the sum of the momenta of the individual gliders at the end of the problem |
| \[Mv={{m}_{1}}{{v}_{1}}'+{{m}_{2}},{{v}_{2}}'\] |
| \[Mv=\frac{1}{4}M{{v}_{1}}'+\frac{3}{4}M{{v}_{2}}'\] |
| \[v=\frac{1}{4}{{v}_{1}}'+\frac{3}{4}{{v}_{2}}'\] |
| \[{{v}_{2}}'=\frac{4}{3}(v-\frac{1}{4}{{v}_{2}}')\] |
| \[{{v}_{2}}'=\frac{4}{3}(2-\frac{1}{4}5')=1\,\,m/s.\] |
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