A 32-u oxygen molecule (O2) moving in the +x direction at 580 m/s collides with an oxygen atom (mass 16 u) moving at 870 m/s at 27 degrees to the x axis. The particles stick together to form an ozone molecule. Find the velocity of the ozone. Express your answer in terms of the units vectors i and j.
I know my i is 645 and my J is 132 but for my answer do I just put fo my final velocity i=645m/s
In the x direction, conservation of momentum says
(32*580) + (16 cos27*870)= 48 Vx
Vx = 645
16 sin27*870 = 48 Vy
Vy = 132
Write the answer as
V(final) = 645i + 132j m/s
since they want both components.
Actually an O2 + O -> O3 reaction would not work in the manner described, but that would require a lesson in chemistry. The kinetic energy lost in the collision, together with chemical reaction energy, would cause the O3 molecule to break apart
I got this question also on mastering physics and i cant figure out how to enter it in properly... I got the same answer as you both got
Actually i figured this out on mastering physics, you need to use the extra key button that has the arrow pointing up at the top of the letter, then put i, in the main box.
Well, Mr. Smarty Pants, it seems like you've got your i and j components all figured out! Bravo! However, let's not be so hasty with our final answer.
Since the particles stick together to form an ozone molecule, we need to consider the conservation of momentum. The total momentum before the collision should equal the total momentum after the collision.
Now, let's break down everything into components. The momentum before the collision in the x-direction is given by:
Px_before = m1 * v1x + m2 * v2x
Where m1 is the mass of the oxygen molecule (O2), v1x is its velocity in the x-direction, m2 is the mass of the oxygen atom, and v2x is its velocity in the x-direction.
Using the given values, we have:
Px_before = (32 u) * (580 m/s) + (16 u) * (870 m/s * cos(27 degrees))
Do the math, and you'll find the x-component of the momentum before the collision.
Now, here comes the exciting part. Since momentum is conserved, the x-component of momentum after the collision will be the same as before:
Px_after = (32 u + 16 u) * Vx
Where Vx is the x-component of the velocity of the ozone molecule.
Now, we can solve for Vx using the equation:
Px_before = Px_after
Plug in the values for Px_before and solve for Vx. Trust me, it won't be as painful as stepping on a banana peel!
And once you've found Vx, you can express your final answer as:
The velocity of the ozone molecule in terms of the unit vectors i and j is Vx i + Vy j.
Remember, laughter is the best way to fight off the confusion!
To find the velocity of the ozone molecule, we can break down the problem into components along the x and y axes.
Given data:
Mass of the oxygen molecule (O2) = 32 u
Velocity of the oxygen molecule (O2) in the x-direction = 580 m/s
Mass of the oxygen atom = 16 u
Velocity of the oxygen atom in the x-direction = 870 m/s
Angle between the oxygen atom's velocity vector and the x-axis = 27 degrees
To solve the problem, we need to find the final velocity of the ozone molecule. Since the oxygen molecule and oxygen atom stick together, the final mass is the sum of the two (32u + 16u = 48u).
Now, let's find the x and y components of the final velocity of the ozone molecule.
X-component of the final velocity:
The x-component of the oxygen molecule's velocity is already given as 580 m/s. For the oxygen atom's velocity, we need to calculate its x-component using the given angle and magnitude of the velocity vector.
Velocity of the oxygen atom in the x-direction = (870 m/s) * cos(27°)
Y-component of the final velocity:
The y-component of the oxygen molecule's velocity is zero since it is moving only in the x-direction. Similarly, for the oxygen atom's velocity, we need to calculate its y-component using the given angle and magnitude of the velocity vector.
Velocity of the oxygen atom in the y-direction = (870 m/s) * sin(27°)
Now, let's calculate the x and y components:
X-component:
Oxygen molecule's x-component = 580 m/s
Oxygen atom's x-component = (870 m/s) * cos(27°)
Y-component:
Oxygen molecule's y-component = 0
Oxygen atom's y-component = (870 m/s) * sin(27°)
Next, we can simply add up the x and y components to get the final velocity of the ozone molecule.
X-component of ozone's velocity = Oxygen molecule's x-component + Oxygen atom's x-component
Y-component of ozone's velocity = Oxygen molecule's y-component + Oxygen atom's y-component
So, the final velocity of the ozone molecule is expressed as a vector sum:
Velocity of the ozone molecule = (X-component of ozone's velocity) * i + (Y-component of ozone's velocity) * j
Substituting the calculated x and y components for the ozone molecule, we get:
Velocity of the ozone molecule = (580 m/s + (870 m/s) * cos(27°)) * i + ((870 m/s) * sin(27°)) * j
Thus, the final velocity of the ozone molecule is expressed in terms of the unit vectors i and j as:
Velocity of the ozone molecule = (580 + (870 * cos(27°))) * i + (870 * sin(27°)) * j
Therefore, the final answer is the expression: (580 + (870 * cos(27°))) * i + (870 * sin(27°)) * j, where i and j are unit vectors denoting the x and y directions, respectively.