Final answer:
The acceleration of a piece of dried cement on the inside wall of the mixer is approximately 0.0395 m/s², and the net force on it is approximately 0.000395 N.
Step-by-step explanation:
To calculate the acceleration of a piece of dried cement inside a cement mixer, we need to find the centripetal acceleration which is given by the formula a = (v^2)/r, where v is the linear speed and r is the radius of the circular path.
First, let's find the linear speed v using the relationship v = 2πr / T, where T is the period of one revolution. Given the radius r = 2.5 m and T = 50 s, we get v = (2π * 2.5 m) / 50 s. Calculating this, v is 0.314 m/s. Now we can find the centripetal acceleration a = (0.314 m/s)² / 2.5 m, which is approximately 0.0395 m/s².
The net force F acting on the cement piece can be found using Newton's second law, F = ma, where m is the mass of the cement piece. Given m = 0.010 kg and the calculated acceleration, F = 0.010 kg * 0.0395 m/s², which is 0.000395 N.