Collision kinematics; center of mass. Two particles of mass M1=100 g and M2=40 g have initial

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Collision kinematics; center of mass. Two particles of mass $M_{1}=100 \mathrm{~g}$ and $M_{2}=40 \mathrm{~g}$ have initial velocities $\mathrm{v}_{1}=2.8 \hat{\mathrm{x}}-$ $3.0 \hat{\mathrm{y}} \mathrm{cm} / \mathrm{s}$ and $\mathbf{v}_{2}=7.5 \hat{\mathrm{y}} \mathrm{cm} / \mathrm{s}$. They collide, and after the collision the velocities are $\mathbf{v}_{1}^{\prime}=1.2 \hat{\mathbf{x}}-2.0 \hat{\mathbf{y}} \mathrm{cm} / \mathrm{s} \quad$ and $\mathbf{v}_{2}^{\prime}=4.0 \hat{\mathbf{x}}+5.0 \hat{\mathrm{y}} \mathrm{cm} / \mathrm{s}$ (a) Find the total momentum. (b) Find the velocity of a reference frame in which the total momentum (before collision) is zero. This is called the center-of-mass frame. (c) Show that the momentum is zero in this frame after the collision. (d) What fraction of the initial kinetic energy is not present as kinetic energy after the collision? Is the collision elastic?

          Collision kinematics; center of mass. Two particles of mass $M_{1}=100 \mathrm{~g}$ and $M_{2}=40 \mathrm{~g}$ have initial velocities $\mathrm{v}_{1}=2.8 \hat{\mathrm{x}}-$
$3.0 \hat{\mathrm{y}} \mathrm{cm} / \mathrm{s}$ and $\mathbf{v}_{2}=7.5 \hat{\mathrm{y}} \mathrm{cm} / \mathrm{s}$. They collide, and after the
collision the velocities are $\mathbf{v}_{1}^{\prime}=1.2 \hat{\mathbf{x}}-2.0 \hat{\mathbf{y}} \mathrm{cm} / \mathrm{s} \quad$ and
$\mathbf{v}_{2}^{\prime}=4.0 \hat{\mathbf{x}}+5.0 \hat{\mathrm{y}} \mathrm{cm} / \mathrm{s}$
(a) Find the total momentum.
(b) Find the velocity of a reference frame in which the total momentum (before collision) is zero. This is called the center-of-mass frame.
(c) Show that the momentum is zero in this frame after the collision.
(d) What fraction of the initial kinetic energy is not present as kinetic energy after the collision? Is the collision elastic?

Added by Laura N.

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