Question

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

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

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.

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.

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.

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.

Key concepts

Mechanics

Mechanics plays a significant role in understanding how systems work and analyzing forces and motions. In the context of a pulley system, mechanics helps us comprehend how objects can be moved using force. Here, the primary concern is the weight of the object we want to lower. The mechanics of this problem requires us to recognize that the 100 lb weight will exert a downward force due to gravity.

The mechanics principle helps identify how this force interacts with the pulley system. Using mechanics, we break down the problem into manageable parts: identifying the forces, understanding their directions, and calculating how these forces interact in the system. Mechanics provides us with the framework to assess when a cord might break under tension and how to intelligently distribute weight to prevent this. By knowing the cord’s breaking strength and the object’s weight, we're setting the stage for solving the problem accurately.

Force Distribution

Force distribution is a crucial concept when working with pulley systems. In essence, it involves how force is shared or distributed through different parts of the system to achieve an effortless movement or to prevent overloading any component.

When lowering the 100-lb object using the given 87-lb breaking strength cord, proper force distribution is our savior. By employing pulleys, the total force is divided among multiple points, ensuring no single section bears the entire load. The formula for calculating force distribution in such cases involves dividing the total weight of the object by the number of pulleys used.

• This action means the effective load on each cord segment is reduced.
• In practice, for this problem, two pulleys supporting the object mean each part of the cord carries roughly half the load.
• This distributed force ensures that neither section of the cord exceeds the 87-lb limit.

Simple Machines

Simple machines, like pulleys, are fundamental tools in physics and engineering that allow us to perform tasks with less effort. They work by redistributing the required work to move an object, making manual labor safer and more efficient.

In our case, a pulley system makes it possible to lower a heavy object without exceeding the cord's breaking strength. Using two pulleys transforms the system into a double pulley setup, also known as a block and tackle arrangement.

• This means the force necessary to lift or lower an object is split between the length of cord around each pulley.
• The key feature is that it not only changes the direction of force but also proportionately reduces the load on each section of the cord.
• Thus, the simple machine enables even a weak cord to handle loads greater than its maximum specified strength, simply by smartly arranging the components involved.

Simple machines like this demonstrate the power of physics to make tasks that seem impossible entirely feasible.