The mass of the blue puck shown below is 40.0% greater than the mass of the gree

Question

The mass of the blue puck shown below is 40.0% 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 10.0 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.

vgreen =
vblue =
The mass of the blue puck shown below is 40.0% 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 10.0 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.

Explanation / Answer

first off, we know that they have equal magnitudes of momentabefore the colission

so we have
?green=m*10
?blue=m*1.4*v
setting them equal, we have m*10=m*1.4*v
canceling m, we obtain v=7.1428 m/s

so finding the initial kinetic energy we have
Kgreen+Kblue
1/2*m*10^2 + 1/2*m*1.4*7.1428^2 = m(85.71 ) J

we know that half the energy is converted into internal energy, andwe know that since they deflect at the same angle, that they willboth have the same momentum after the collision
so K=m(85.71/2)= 72.43m

so we have 1/2*m*Vgreen^2+1/2*m*1.4*Vblue^2=42.85m
1/2(Vgreen^2+1.4Vblue^2)=42.85
Vgreen^2+1.4Vblue^2=85.71

since they have the same momentum after the collision we know
m*Vgreen=m*1.4*Vblue
Vgreen=1.4Vblue

with these two equations, we can solve for both Vgreen and Vblue,obtaining
Vgreen=7.07m/s
Vblue=5.05 m/s

hope this helps, please rate

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