# Force on a sphere

Hey people, first post, I'm sorry if I'm posting this in the wrong place.

How do you calculate the force exerted on a sphere? I'm building a pneumatic air rifle, and I'm trying to figure out how fast an airsoft bb accellerates with a certain pressure.

The projectile is 6mm in diameter, so that makes the surface on which the air pressure works 1/2 * (4 * pi * 3^2) = 1/2 * 113.1 = 56.5 mm^2 = 5.65 * 10^ -5 m^2.

What is the force on the projectile if the difference in pressure is 1 bar?

## Answers and Replies

Bystander
Science Advisor
Homework Helper
Gold Member
surface on which the air pressure works 1/2 * (4 * pi * 3^2) = 1/2 * 113.1 = 56.5 mm^2 = 5.65 * 10^ -5 m^2.
It's an attractive notion to use the area of the hemisphere, an it's also incorrect. The area on which the pressure acts is the cross-sectional area of the projectile, period. Force then is pressure times area of the bore.

Thanks, that makes things a whole lot easier!

Nathanael
Homework Helper
Just in case you're curious:
The force from the pressure acts perpendicular to the surface, so if you were to use the surface area of the hemisphere, you would have to use only the component of force that acts along the barrel. If you do the math it reduces to using the cross-sectional area.