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Answer: Pyramid Builders. Ancient pyramid builders are
Chapter 11, Problem 86P(choose chapter or problem)
Pyramid Builders. Ancient pyramid builders are balancing a uniform rectangular slab of stone tipped at an angle \(\theta\) above the horizontal using a rope (Fig. P11.86). The rope is held by five workers who share the force equally.
(a) If \(\theta=20.0^{\circ}\) what force does each worker exert on the rope?
(b) As \(\theta\) increases, does each worker have to exert more or less force than in part (a), assuming they do not change the angle of the rope? Why?
(c) At what angle do the workers need to exert \(\text { no force }\) to balance the slab? What happens if \(\theta\) exceeds this value?
Equation Transcription:
°
Text Transcription:
\theta
\theta=20.0^\circ
\theta
no force
\theta
Questions & Answers
QUESTION:
Pyramid Builders. Ancient pyramid builders are balancing a uniform rectangular slab of stone tipped at an angle \(\theta\) above the horizontal using a rope (Fig. P11.86). The rope is held by five workers who share the force equally.
(a) If \(\theta=20.0^{\circ}\) what force does each worker exert on the rope?
(b) As \(\theta\) increases, does each worker have to exert more or less force than in part (a), assuming they do not change the angle of the rope? Why?
(c) At what angle do the workers need to exert \(\text { no force }\) to balance the slab? What happens if \(\theta\) exceeds this value?
Equation Transcription:
°
Text Transcription:
\theta
\theta=20.0^\circ
\theta
no force
\theta
ANSWER:Solution 86P
Introduction
First we have to calculate the tension of the rope. From the tension we can calculate the force exerted by each person. Then we have to discuss whether tension will increase or decrease with increase of angle . Then we have to find out at which angle at which the slab will balance and what happens to the tension if the angle increases further.
Step 1
The free body diagram of the stone is shown below.
The rock is rotating about the corner of the stone which is in contact with the ground (A, shown as big dot in the figure). To find the tension we have to find the moment of force about the axis of rotation for both the tension and the weight. Then, as we know that for equilibrium the total moment will be zero, we have to make total moment as zero and then find out the tension.