a. The rope's angle with the vertical when released is 90 degrees. b. The tension in the rope when released is 539 N. c. The max tension in the rope over the course of the girl's ride is 572 N.
a. What is the rope's angle with the vertical when released?
When the student releases the rope, her velocity is zero. At this point, the rope is at its lowest point, so the angle it makes with the vertical is 90 degrees.
b. What is the tension in the rope when released?
When the student releases the rope, the tension in the rope is equal to her weight. The weight can be calculated using the formula weight = mass * gravity. In this case, the weight is 55 kg * 9.8 m/s^2 = 539 N.
c. What is the max tension in the rope over the course of the girl's ride?
The maximum tension in the rope occurs when the student is at the highest point of her swing. At this point, the tension in the rope is equal to the sum of her weight and the centripetal force acting on her. The centripetal force can be calculated using the formula centripetal force = mass * velocity^2 / radius. In this case, the centripetal force is 55 kg * (4.5 m/s)^2 / 15 m = 33 N. So the maximum tension in the rope is 539 N + 33 N = 572 N.