The mass of the blue puck shown below is 10.0% greater than the mass of the gree

Question

The mass of the blue puck shown below is 10.0% greater than the mass of the green puck. Before colliding, the pucks approach each other with momenta of equal magnitudes and opposite directions, and the green puck has an initial speed of 9.0 m/s. Find the speeds the pucks have after the collision if half the kinetic energy of the system becomes internal energy during the collision. V_green = Your response differs from the correct answer by more than 10%. Double check your calculations, m/s V_blue= Your response differs from the correct answer by more than 10%. Double check your calculations, m/s

Explanation / Answer

here,

let the mass of green puck be mg

mass of blue puck mb = 1.1 * mg

initial speed of green , ug = 9 m/s

as they have initial equal momenta

mg*ug = mb*ub

mg*9 = 1.1 * mg * ub

ub = 8.18 m/s

let the final velocity be vg and vb

using conservation of momentum about x axis

mg*ug + mb*ub = mg*vg * cos(30) + mb*vb * cos(30)

vg = 1.1 * vb ....(1)

and using conservation of kinetic energy

0.5 * (0.5*mg*ug^2 + 0.5*mb*ub^2 = 0.5*mg*vg^2 + 0.5*mb*vb^2

0.5 * (0.5*mg*ug^2 + 0.5*1.1*mg*ub^2 = 0.5*mg*vg^2 + 0.5*1.1*mg*vb^2

0.5 * (9^2 + 8.18^2 * 1.1 = vg^2 + 1.1*vb^2 ....(2)

from (1) and (2)

vg = 6.36 m/s

vb = 5.78 m/s

the final speed of the green puck is 6.36 m/s and the blue puck is 5.78 m/s

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