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Chapter 3: Problem 25

How could a 100-lb object be lowered from a roof using a cord with a breaking strength of \(87 \mathrm{lb}\) without breaking the cord?

Short Answer

Expert verified
A 100 lb object can be lowered from a roof using an 87 lb cord by using a two-pulley system to distribute the weight evenly across both pulleys. This will ensure that neither pulley is supporting more than the maximum weight that the cord can handle.

Step by step solution

01

Analyze the Problem

We have an object that weighs 100 lb. This is more than our cord can handle. The cord can only support a maximum of 87 lb.
02

Formulate a Strategy

We should think of a way to reduce the effective weight of the object on the cord. One way of doing this is by using a simple machine such as a pulley. By redirecting the force through a pulley, we can reduce the effective weight on the cord.
03

Calculate Pulley Configuration

To figure out how many pulleys we would require, we can divide the weight of the object by the breaking strength of the cord. That gives us \(100 \, \mathrm{lb} \, / \, 87 \, \mathrm{lb} = 1.15\). So, we would need at least two pulleys to share the load, as one can handle less than the weight but two can handle more than the weight. With two pulleys, every pulley supports approximately half of the load.
04

Implement the Solution

We would use the two-pulley configuration to lower the object. Make sure to distribute the load evenly across both pulleys to prevent either from getting overloaded.

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