To find the maximum speed of the ball, we can use the concept of centripetal force.
Centripetal force (Fc) is the force that keeps an object moving in a circular path and is given by the formula:
Fc = (m * v^2) / r
where:
m = mass of the ball (4 kg)
v = speed of the ball (unknown, to be determined)
r = radius of the circular path (10 m)
The tension in the string is the maximum centripetal force it can withstand without breaking. Therefore, the maximum tension (Tmax) is equal to the centripetal force:
Tmax = Fc
Now, we can solve for the maximum speed (v):
Tmax = (m * v^2) / r
52 N = (4 kg * v^2) / 10 m
To find v^2, first, multiply both sides by 10 m:
520 Nm = 4 kg * v^2
Now, divide both sides by 4 kg:
v^2 = 520 Nm / 4 kg
v^2 = 130 Nm/kg
Finally, take the square root of both sides to find v:
v = √(130 Nm/kg)
v ≈ 11.4 m/s
So, the maximum speed of the ball is approximately 11.4 meters per second.