Question

An oxygen atom (mass 16 u) moving at 733 m/s at 15.0° with respect to the ˆi direction collides and sticks to an oxygen molecule (mass 32 u) moving at 528 m/s at 128° with respect to the ˆi direction. The two stick together to form ozone. What is the final velocity of the ozone molecule?

a) (578 m/s)^i + (432 m/s)^j
b) (387 m/s)^i - (285 m/s)^j
c) (197 m/s)^i + (158 m/s)^j
d) (0 m/s)^i + (0 m/s)^j

Answer 1

To determine the final velocity of the ozone molecule formed from the collision of an oxygen atom and molecule, one must use the conservation of momentum, calculate the components of velocity for both bodies, and combine them to find the resultant velocity vector.

Step-by-step explanation:

The collision and combination of an oxygen atom and an oxygen molecule to form ozone involve the conservation of momentum. To find the final velocity of the ozone molecule, we calculate the velocity components for both the atom and molecule, sum them according to the conservation of momentum, and then determine the resultant velocity vector.

First, we convert the angles to radians and calculate the velocity components of the oxygen atom in the î (horizontal) and î (vertical) directions:

• Vx_atom = 733 m/s * cos(15.0°)
• Vy_atom = 733 m/s * sin(15.0°)

Next, we do the same for the oxygen molecule:

• Vx_molecule = 528 m/s * cos(128°)
• Vy_molecule = 528 m/s * sin(128°)

After finding these components, we sum the x and y components of the velocities of the two objects separately and then calculate the final velocity vector of the ozone molecule:

• Vx_total = Vx_atom + Vx_molecule
• Vy_total = Vy_atom + Vy_molecule

Finally, we calculate the magnitude and direction of the resultant velocity vector to find the final velocity of the ozone molecule.