Answer to Question #171708 in Physics for RHYLYN

Question

A10.0-g marble slides to the left with a velocity of magnitude on the frictionless, horizontal surface of an icy New York sidewalk and has a head-on, elastic collision with a larger 30.0-g marble sliding to the right with a velocity of magnitude (see figure below).

a) Find the velocity of each marble (magnitude and direction) after the collision. (Since the collision is head-on, all the motion is along a line.)

b) Calculate the change in momentum (that is, the momentum after the collision minus the momentum before the collision) for each marble. Compare the values you get for each marble.

c) Calculate the change in kinetic energy (that is, the kinetic energy after the collision minus the kinetic energy before the collision) for each marble. Compare the values you get for each marble.

Answer 1

a) Conservation of momentum gives

$$0.03(0.2)+0.01(-0.4)=0.03v_{A2}+0.01v_{B2}\\3v_{A2}+v_{B2}=0.2\\v_{B2}-v_{A2}=-(-0.4-0.2)=0.6$$

$$v_{A2}=-0.1\frac{m}{s}\\v_{B2}=0.5\frac{m}{s}$$

The 30.0 g marble is moving to the left and the 10.0 g marble is moving to the right.

b)

$$\Delta P_A=0.03(-0.1-0.2)=-0.009\frac{kgm}{s}\\\Delta P_b=0.01(0.5-(-0.4))=0.009\frac{kgm}{s}$$

The changes in momentum have the same magnitude and opposite sign.

c)

$$\Delta K_A=0.5(0.03((-0.1)^2-0.2^2))=-4.5\cdot10^{-4}\ J\\\Delta K_b=0.5(0.01(0.5^2-(-0.4)^2))=4.5\cdot10^{-4}\ J$$

The changes in kinetic energy have the same magnitude and opposite sign.