Question: a pneumatic blaster is a device that launches a low...
A pneumatic “blaster” is a device that launches a low mass projectile from a cylindrical tube using pressurized air stored upstream of the projectile. The projectile is held in place while the pressurized air is introduced to the cylinder. After the trigger is released, the projectile accelerates down the tube, while the pressure upstream of the projectile drops according to the relation,
p = pi*(1-((x/d)^2)/30)
where pi is the initial (high) pressure in the tube before the trigger is release, x is the distance traveled by the projectile and d is the diameter of the tube. If we have a 5.0 cm diameter tube, with a projectile initially located 4.5 tube diameters upstream of the tube exit, and the initial pressure upstream of the projectile is 1.2 MPa, determine the work done by the air on the projectile during the time that projectile is in the tube, assuming there is no friction between the tube and the projectile.