Question

George Of The Jungle's wife, Mrs. Of The Jungle, has been pestering him to go on a diet. He should have listened. During his commute home last Thursday afternoon, the Number 8 vine upon which he was swinging (along a circular path) snapped.
At the time of the incident, George was at the bottom of his swing, moving at a peppy 14.1 m/s. Given that the maximum tension that the vine (length 7.3 m) was able to tolerate was 4150 N, determine George's mass.
A) 110 kg
B) 120 kg
C) 130 kg
D) 140 kg
E) 150 kg

Answer 1

Answer:

112.06 kg - Thats heavy !

Explanation:

Let's do force balance here. Let the object of our interest be George. The forces acting on him are the tension in  the upward direction, his weight in the downward direction and the centrifugal force in the downward direction. Considering the upward and downward directions on the y-axis and f=given the fact that George doesn't move up or down, the forces are balanced along the y-axis. Hence doing force balance:

magnitude of forces upward =magnitude of forces downward

i.e., Tension(T) = Weight(mg) + Centrifugal force (mv²/r)

where: 'm' is the mass of George, g is the acceleration due to gravity (9.8 m/s²). v is the speed with which George moves (14.1 m/s) and r is the radius of the circle in which he's moving at the instant (Here since he's swinging on the rope, he moves in a circle with radius as the length of the rope and hence r=7.3m).

therefore, T = m (9.8 + (14.1)²/7.3) = 4150 N

Therefore, m = 112.06 kg