A swing is made from a rope that will tolerate a maximum tension of 5.07 x 102 N without breaking. Initially, the swing hangs vertically. The swing is then pulled back at an angle of 58.6 ° with respect to the vertical and released from rest. What is the mass of the heaviest person who can ride the swing?

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