Answer:
Step-by-step explanation:
Too much information.
At 60° the cord tension must have a vertical component to support the weight and a horizontal component to provide the required centripetal force
tan60 = (mv²/R) / mg = v²/Rg
tan60 = v² / (Lsin60)g
v² = Lgsin60tan60
v² = 2(9.8)sin60tan60
v² = 29.4
v = 5.42 m/s
The ball MUST be moving at 5.42 m/s for the string to make a 60° angle with the vertical.
Let's see if the string is strong enough to do the task
Vertical force requirement
Fy = mg = 0.400(9.8) = 3.92 N
Horizontal force requirement
Fx = mv²/R = 0.400(29.4)/(2sin60) = 6.7896 N
total tension in the cord
F = √(3.92² + 6.7896²) = 7.84 N
so the cord is strong enough and has a safety factor of 60 / 7.84 = 7.7
But the question is asking what is the highest speed the ball can achieve without breaking.
For this we MUST ignore the 60° limit. The cord will be much closer to 90° from the vertical.
We already know the tension must supply 3.92 N vertically.
So the cord on the verge of breaking is at an angle of
θ = arccos(3.92/60) = 86.25°
and has a centripetal force of
Fx = 60sin86.25 = 59.8715 N
Fx = mv²/R
v² = RFx/m = (Lsinθ)Fx / m
v = √(2sin86.25)(59.8715) / 0.400)
v = 17.28342...
v = 17 m/s