An adventurous archaeologist crosses between two rock cliffs by slowly going han

Question

An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle or the rope (Figure 1). The rope will break it the tension in it exceeds 2 55 times 10^4 N, and our hero's mass is 81 2 kg. Part A If the angle between the rope and the horizontal is theta = 11.9 degree, find the tension in the rope. _____ Part B What is the smallest value the angle theta can have it the rope is not to break? ________

Explanation / Answer

here,

mass of hero , m = 81.2 kg

A)

theta = 11.9 degree

let the tension in the rope be t

equating the forces vertically

2 * t * sin(theta) = m * g

2 * t * sin(11.9) = 81.2 * 9.8

t = 1929.5 N

the tension in the string is 1.9 * 10^3 N

B)

let the smallest angle be theta

maximum tension , t = 2.55 * 10^4 N

equating the forces vertically

2 * t * sin(theta) = m * g

2 * 2.55 * 10^4 * sin(theta) = 81.2 * 9.8

theta = 0.89 degree

the smallest value of angle is 0.89 degree

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