Question

2.67 a 600 - lb crate is supported by several rope - and - pulley arrangements as shown. determine for each arrangement the tension in the rope. (see the hint for prob. 2.66.)

Explanation:

Step1: Recall pulley - system principle

In a rope - and - pulley system, the tension in the rope is related to the number of rope segments supporting the load. The weight of the crate \(W = 600\) lb. The formula for the tension \(T\) in the rope is \(T=\frac{W}{n}\), where \(n\) is the number of rope segments supporting the load.

Step2: Analyze case (a)

In case (a), there is 1 rope segment supporting the load. So, \(n = 1\). Then \(T=\frac{W}{n}=\frac{600}{1}=600\) lb.

Step3: Analyze case (b)

In case (b), there are 2 rope segments supporting the load. So, \(n = 2\). Then \(T=\frac{W}{n}=\frac{600}{2}=300\) lb.

Step4: Analyze case (c)

In case (c), there are 2 rope segments supporting the load. So, \(n = 2\). Then \(T=\frac{W}{n}=\frac{600}{2}=300\) lb.

Step5: Analyze case (d)

In case (d), there are 3 rope segments supporting the load. So, \(n = 3\). Then \(T=\frac{W}{n}=\frac{600}{3}=200\) lb.

Step6: Analyze case (e)

In case (e), there are 2 rope segments supporting the load. So, \(n = 2\). Then \(T=\frac{W}{n}=\frac{600}{2}=300\) lb.

Answer:

(a) 600 lb
(b) 300 lb
(c) 300 lb
(d) 200 lb
(e) 300 lb