Final answer:
The magnitude of the centripetal force required for a 0.5 kg ball to spin in uniform circular motion at 5.0 m/s on a 2.0 m string is 6.25 Newtons.
Step-by-step explanation:
To find the magnitude of the centripetal force, we can use the formula F = m × ac, where m is the mass of the object, and ac is the centripetal acceleration. Centripetal acceleration is given by the formula ac = v² / r, where v is the linear speed and r is the radius of the circular path.
Given the mass m = 0.5 kg, the speed v = 5.0 m/s, and the string length (radius) r = 2.0 m, we can calculate the centripetal acceleration as:
ac = v² / r = (5.0 m/s)² / 2.0 m = 25 m²/s² / 2.0 m = 12.5 m/s²
Now we can compute the centripetal force:
F = m × ac = 0.5 kg × 12.5 m/s² = 6.25 N
Thus, the centripetal force required is 6.25 Newtons.