Sapling Learning A system of four particles moves along one dimension. The cente

Question

Sapling Learning A system of four particles moves along one dimension. The center of mass of th the particles do not interact with any objects outside of the system. Find the velocity, v4, of particle 4 at e system is at rest, and 2.59 s, given the following details for the motion of particles 1, 2 and 3 Particle 1 : m, = 1.69 kg, vi (r) = (6.75 m / s) + (0.343 mi /s, × , Particle 2: n":-329 kg, v2w-18.49 m/s) + (0.399 m/s2)st Particle 3: m,-4.13 kg, v3W-(6.33 m/s) + (0.237 m/s*)×t (6.33 m/s0.237 m/s x r Particle 3: m,-4.13 kg, v, Particle 4: m,-5.39 kg, Number m/s

Explanation / Answer

Given that

mass m1=1.69 kg

velocity V1=6.75+0.343*2.59=7.64 m/s

mass m2=3.29 kg

mass m3=4.13 kg

mass m4=5.39 kg

velocity V2=8.49+0.399*2.59=9.52 m/s

velocity v3=6.33+0.237*2.59=6.944 m/s

now we find the velocity

Vcm=m1v1+m2v2+m3v3+m4v4/(m1+m2+m3+m4)

0(m1+m2+m3+m4)=m1v1+m2v2+m3v3+m4v4

0=m1v1+m2v2+m3v3+m4v4

v4=-(m1v1+m2v2+m3v3)/m4

=-(1.69*7.64+3.29*9.52+4.13*6.944)/5.39

=-13.51 m/s

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