Answer:
m = 19.16 kg
Explanation:
from the question we have:
maximum tension (T) = 5.07 x 10^{2} N
angle formed (θ) = 58.6 degrees
acceleration due to gravity (g) = 9.8 m/s^{2}
length of the rope (r) = ?
maximum mass (m) =?
we can get the maximum height from the equation below
T - mg = \frac{mv^{2}}{r}
But we need to find the velocity, and we can do so by applying the conservation of energy
mgh = 0.5mv^{2}
gh =0.5v^{2}
h is the vertical height of the rope = r x sin 58.6
h = 0.85r
now we have
9.8 x 0.85r = 0.5 x v^{2}
v^{2} = 16.66r
now we can substitute the value of v^{2} into T - mg = \frac{mv^{2}}{r}
T - mg = \frac{m × 16.66r}{r}
(5.07 x 10^{2}) - 9.8m = m × 16.66
(5.07 x 10^{2}) = 9.8m + 16.66m
(5.07 x 10^{2}) = 26.46m
m = 19.16 kg
