eders, A 6595 h and B (350 2.are held together by a string which comprekes t not

Question

eders, A 6595 h and B (350 2.are held together by a string which comprekes t not so 35 K Two gliders,A (550 ai and 8 (a5o g, are held together by astring which compresses a spring Two gliders, A (550 g) and B (350 g), are held together by a string which compresses a spring between the gliders. As shown, the masses are traveling at 0.5 m/s. A very quick, but not so safety-conscious physics student burns the string between the masses after which mass B is seen to be traveling at 2.1 m/s. Find the final velocity of mass A. Did the kinetic energy of the system grow, shrink or stay the same during this process? If it grew, where did the energy come from? If it shrank, where did the energy go? Finally, stimate the spring constant of the spring. Finally, estimate the spring constant of the spring string 0.5 m/s

Explanation / Answer

This is solved using the momentum conservation principle

by the conservation of momentum

(M+m) V = Mv1 + mv2

(0.55+0.35)*0.5 = 0.55*2.1 + 0.35*v2

0.35v2 = -0.705

v2 = -2.01 m/s

so the block A moves with a velocity of 2.1 m/s in the opposite direction

KE of the system earlier = 0.5*(M+m)v^2

KE = 0.5*(0.55+0.35)*0.5^2

KE = 0.1125 J

KE after string is burned = 0.5 Mv1^2 + 0.5 mv2^2

KE = 0.5*0.55*2.1^2 + 0.5*0.35*(-2.01)^2

KE = 1.9197 J

The KE is inreased because the potential energy stored in the compressed spring is converted to the KE of the blocks and this provides an increase in the kinetic energy of the blocks

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