Pressure caused by beam of molecular oxygen

[TheGreatExplainer]

Homework Statement

A beam of molecular oxygen containing 10¹⁰ molecules/cm³ and average speed of 500 m/s strikes (elastic collision) a plate at an angle of 30º with the normal direction.
Calculate the exerted pressure on the plate.

Homework Equations

P = Impluse x Flux

The Attempt at a Solution

I tried to use the equation in the attached file but in this case we have a constant angle so I can´t just simply integrate.

Any help would be appreciated.

 

[Charles Link]

Homework Statement

A beam of molecular oxygen containing 10¹⁰ molecules/cm³ and average speed of 500 m/s strikes (elastic collision) a plate at an angle of 30º with the normal direction.
Calculate the exerted pressure on the plate.

Homework Equations

P = Impluse x Flux

The Attempt at a Solution

I tried to use the equation in the attached file but in this case we have a constant angle so I can´t just simply integrate.

Any help would be appreciated.

The equation you have in the "link" looks like it is for the pressure that a gas has when it is inside a container. It does not apply here. In some ways this problem is easier, because the beam is only going in one direction, and every particle has the same velocity. $\\$ First of all, you need to compute $m$ for the molecule. $\\$ Next, the number of incident particles/unit time per unit area will be decreased from that of the normal direction because of the $30^o$ angle. The first thing you need though is the number of particles per second per unit area that cross the plane normal to the beam. Then find the number per second incident at the surface tilted at $30^o$. You then need to compute the momentum change of each particle. Once you have that, it should start to come together. $\\$ An additional input: Since Force is equal to the rate of change of momentum, the Pressure, which is force/area, should equal to the rate of change of momentum per unit area=you need to find how much the momentum is changing per second per unit area. $\\$ Suggestion: Draw a vector diagram to compute the momentum change of each molecule.