Two skaters are placed on a smooth horizontal surface. The masses of the left an

Question

Two skaters are placed on a smooth horizontal surface. The masses of the left and right skater are 50kg and 70kg respectively. A spring whose spring constant is 500N/m is compressed 0.40m and placed between them. Initially at rest, the spring expands and each skater begins to move. a)The velocity of the center of mass after the spring has expandedb)The kinetic energy of the two skaters after the spring has expanded c) The velocity of the rightmost skater after the spring has expanded d)The velocity of the leftmost skater after the spring has expanded

Explanation / Answer

A) apply law of conservation of energy

0.5*(m1+m2)*Vcm^2 = 0.5*k*x^2 = 0.5*500*0.4*0.4 = 40 J

Vcm = 40/(0.5*(50+70)) = 0.667 m/s

B) 0.5*(m1+m2)*Vcm^2 = 0.5*k*x^2 = 0.5*500*0.4*0.4 = 40 J

C)

kinetic energy of the right skater is 40*7/12 = 23.34 J

then 0.5*m2*v2^2 = 23.34

v2 = sqrt(23.34*2/70) = 0.816 m/s

0.5*m1*v1^2 = 16.67 J

v1 = sqrt(16.67*2/50) = 0.816 m/s

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