Katya is training for an upcoming gymnastics competition and needs to improve her upper body strength. At the moment, she can on
ly support at most 180% of her body weight when she’s hanging off of equipment. Misha, a close friend and circus performer, suggests that she train on a swinging trapeze. Katya grabs onto the trapeze which hangs off a pair of cables of length ` that initially make an angle of 60.0◦ with the vertical. She steps off the platform and swings forward. To what height will she fall/rise as she swings? Will Katya swing back to the platform?
she will fall to an height of 21.09° only, beyond such an height ; the spring will break.
Katya will not be able to swing to the platform because the angle will be between -21.09° and 21.09° from vertical
Explanation:
If the distance is from the point of angle A to angle B , partitioned by a perpendicular line in the middle then, The conservation of energy between A and B can be expressed as :
where ; the height h =
T = mg(3 cos θ - 1)
Given that:
T = 180 % = 1.8 mg
Then:
1.8 mg = mg(3 cos θ - 1)
2.8 mg = (3 cos θ - 1)
cos θ =
θ = cos ⁻¹ (0.933)
θ = 21.09°
Therefore, she will fall to an height of 21.09° only, beyond such an height ; the spring will break.
Katya will not be able to swing to the platform because the angle will be between -21.09° and 21.09° from vertical