P7-2 Zartan of the jungle crosses a river by grabbing an 8m long vine, convenien

Question

P7-2 Zartan of the jungle crosses a river by grabbing an 8m long vine, conveniently hanging from a strong branch, and swinging over the water. Knowing Zartan has a mass of 85 kg and achieves a speed of 4 m/s at the lowest point on the arc of the swing, find A) his acceleration and B) the tension in the vine.
Please show the algebraic manipulation of any formula used to solve! Also, the inclusion of a free body diagram would also greatly help me understand the problem! P7-2 Zartan of the jungle crosses a river by grabbing an 8m long vine, conveniently hanging from a strong branch, and swinging over the water. Knowing Zartan has a mass of 85 kg and achieves a speed of 4 m/s at the lowest point on the arc of the swing, find A) his acceleration and B) the tension in the vine.
Please show the algebraic manipulation of any formula used to solve! Also, the inclusion of a free body diagram would also greatly help me understand the problem! P7-2 Zartan of the jungle crosses a river by grabbing an 8m long vine, conveniently hanging from a strong branch, and swinging over the water. Knowing Zartan has a mass of 85 kg and achieves a speed of 4 m/s at the lowest point on the arc of the swing, find A) his acceleration and B) the tension in the vine.
Please show the algebraic manipulation of any formula used to solve! Also, the inclusion of a free body diagram would also greatly help me understand the problem!

Explanation / Answer

A.

Centripetal accelration is given by:

ac = V^2/R

ac = 4^2/8 = 2 m/sec^2

B.

Tension at the bottom is given by

T = mg + mV^2/R

T = m(g + V^2/R)

T = 85*(9.81 + 4^2/8)

T = 1003.85 N

For the FBD part

you can see that at the lowest point mg will be always downward and Tension in the vine will be upward so using newton's second law:

Total force = m*a

here acceleration will be centripetal acceleration

T - mg = mV^2/R

T = mg + mV^2/R

Comment below if you have any doubt.

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