Two particles, m 1 = 2 m and m 2 = m , are suspended on massless cords of the sa

Question

Two particles, m1 = 2m and m2 = m, are suspended on massless cords of the same length l = 1.00 m so that they touch each other (see Fig. below). Particle 1 is displaced to an angle of 30

Two particles, m1 = 2m and m2 = m, are suspended on massless cords of the same length l = 1.00 m so that they touch each other (see Fig. below). Particle 1 is displaced to an angle of 30A degree with the vertical and let go. After the particles collide, the cord attached to particle 2 comes to a maximum angle of 45A degree. Find the speed of mass m1 before the collision. (10 pts) Find the speed of mass m1 and m2 after the collision. (10 pts) Find the relative change of kinetic energy during the collision (DK/Ki). (5 pts)

Explanation / Answer

given,

m1 = 2m

m2 = m

length of chord = 1m

first particle displaced by 30 degree

so its height = 1-L * cos(30)

height = 1 - cos(30)

height = 0.134 m

potential energy of particle = mgh

potential energy of particle = 2m * 9.8 * 0.134

potential energy of particle = 2.6264m

kinetic energy of first particle just before collision = 0.5 * m * v^2

by conservation of energy

2.6264m = 0.5 * m * v^2

2.6264 = 0.5 * v^2

v = 2.2919 m/s

speed of mass m1 before the collision = 2.2919 m/s

second particle is displaced by 45 degree so

so its height = 1-L * cos(45)

height = 1- cos(45)

height = 0.293 m

potential energy of particle = mgh

potential energy of particle = m * 9.8 * 0.293

potential energy of particle = 2.871m

kinetic energy of first particle just after collision = 0.5 * m * v^2

by conservation of energy

2.871m = 0.5 * m * v^2

2.871 = 0.5 * v^2

v = 2.396 m/s

speed of m2 after collision = 2.396 m/s

by conservation of momentum

m2 * vi = m1v1 + m2v2

2m * 2.2919 = m * 2.396 + 2mv2

2 * 2.2919 = 2.396 + 2v2

v2 = 1.094 m/s

speed of m1 after collision = 1.094 m/s

relative change in KE = 0.5 * 2m * 2.2919^2 - (0.5 * m * 2.396^2 + 0.5 * 2m1.094^2) / 0.5 * 2m * 2.2919^2

relative change in KE = 0.5 * 2 * 2.2919^2 - (0.5 * 2.396^2 + 0.5 * 2*1.094^2) / 0.5 * 2 * 2.2919^2

relative change in KE = 0.2257

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