Problem 5.56 Part A An adventurous archaeologist crosses between two rock cliffs

Question

Problem 5.56 Part A 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 of the rope (Figure 1). The rope will break if the tension in it exceeds 2.90x104 N, and our hero's mass is 91.5 kg If the angle between the rope and the horizontal is = 11.1 , find the tension in the rope Submit My Answers Give Up Part B What is the smallest value the angle can have if the rope is not to break? Figure 1 of 1 Submit My Answers Give Up rovide Feedba Continue

Explanation / Answer

Given

mass of hero m = 91.5 kg

the maximum tension the rope can have is tmax = 2.90*10^4 N

Part A

the angle theta = 11.1 degrees

here the hero stops at the center so that the forces acting on him zero (vertically)

the force is T sin theta+T sin theta = weight  

2T sin theta = mg

T = mg /(2 sin theta)

T = (91.5*9.8)/(2 sin(11.1)) N

T = 2328.82 N

Part B

the smallest value of theta so that the rope does not break , with maximum tnesion is  

2T sin theta = mg

sin theta = mg /2T

theta = arc sin (mg/2T)

= arc sin (91.5*9.8/(2*2.90*10^4))

= 0.88585 degrees

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---