Final answer:
The centripetal force acting on a body can be calculated using the formula Fc = mac, where m is the mass of the body and a is the centripetal acceleration. In this case, the centripetal acceleration can be calculated using the formula ac = v²/r, where v is the tangential velocity and r is the radius of the circular path. By substituting the given values, we can find that the centripetal force is 128π²/5 N.
Step-by-step explanation:
The centripetal force acting on a body moving in a circular path can be computed using the formula Fc = mac, where m is the mass of the body, a is the centripetal acceleration, and c is the radius of the circular path.
First, we need to find the centripetal acceleration. We can use the formula ac = v²/r, where v is the tangential velocity and r is the radius of the circular path.
Given that the body makes one revolution every 10 seconds and the radius of the circular path is 8 meters, we can calculate the tangential velocity v as the circumference of the circle divided by the time to complete one revolution. The circumference is 2πr, so v = (2πr)/t.
Substituting the values, we get v = (2π * 8)/10 = 16π/10 m/s.
Now, we can substitute the centripetal acceleration into the formula ac = v²/r to find a. Substituting the values, we get a = (16π/10)²/8 = 8π²/5 m/s².
Finally, we can calculate the centripetal force Fc using the formula Fc = mac. Substituting the values, we get Fc = 8 * 8π²/5 = 128π²/5 N.