Final answer:
To find the pressure exerted on the material by the ball bearings, calculate the total force exerted by the bearings during collision and divide it by the area of the tested material. The force is found by using the change in momentum formula and considering the mass and velocity of the bearings, the number of bearings, and the time interval of the collisions.
Step-by-step explanation:
To calculate the pressure exerted on the material by the ball bearings, first determine the total force exerted. This is done by multiplying the change in momentum of each bearing by the number of bearings and dividing by the time interval. The change in momentum (∆p) of each bearing caused by the collision is given by ∆p = 2mv since the bearings come to a stop and then move in the opposite direction upon elastic collision, thus reversing their velocity. With each bearing having a mass (m) of 8.3 g (which is 0.0083 kg) and a velocity (v) of 412.7 m/s, and with 138 bearings over a time (τ) of 0.755 minutes (which is 45.3 seconds), the total force (F) is F = 138 × 2 × 0.0083 kg × 412.7 m/s / 45.3 s.
Pressure (P) is the force applied perpendicularly over an area (A), so P = F / A. With the area (A) given as 0.79 m², we plug in the total force to find the pressure. The final step is simple division to get the pressure in Pascals (Pa).