Final answer:
The tension in Spiderman's web at the lowest point is calculated by adding his weight to the centripetal force, and the time to reach the other side is found by calculating half the period of a full pendular swing using the formula involving the length of the web and acceleration due to gravity.
Step-by-step explanation:
We are asked to calculate the tension in Spiderman's web at the lowest point of his swing and determine how long it takes him to reach the other side. Let's approach each part of the question step-by-step.
(a) Tension in the Web at the Lowest Point
At the lowest point of his swing, Spiderman experiences two forces: the gravitational force (his weight) pulling him downward and the tension in the web pulling him upward. The tension in the web at the lowest point not only supports his weight but also provides the centripetal force necessary for circular motion. Using the formula for centripetal force (Fc = m * v2 / r) and Newton's second law, we can express the tension (T) in the web.
To find the tension, we use the following equation:
T = mg + m * v2 / r
Since we do not have Spiderman's speed (v) at the lowest part of the swing, we must first calculate it using conservation of energy from the point where he started the swing to the lowest point.
(b) Time to Reach the Other Side
The time to reach the other side can be found by calculating the period of a full swing (T) and then dividing by 2 since Spiderman is only completing half of the full circular path. The period of a pendulum-like swing is given by T = 2π * sqrt(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.