Breaking Down of a Force into Equally Distributed Component Forces

The Idea

You are hanging a sign for your café that weighs 50 pounds. You have one cable that is 4 feet long and another cable that is 5 feet long. Which one supports more of the weight?

Angles complicate how forces are distributed. This project explores a simple situation similar to hanging a sign with two different length cables.

What You Need

• 2 spring scales
• mass—(should give close to a full-scale reading in the vertical position on your spring scales)
• string
• 2 ring stands with clamps or comparable support
• key ring
• protractor

Method

Symmetrical sign

1. Place the ring stands about 18 inches apart.
2. Cut two equal-length sections of string. The strings should be 8 inches, leaving a couple of inches on each side for attaching to the support and the weight.
3. Set the spring scales to read zero (in the position they are being used), with no weight hanging from them.
4. Hook both of the spring scales to each of the ring stands.
5. Attach each string—one side to the key ring and the other side to the clamp on the ring strand.
6. The apparatus should be as shown in Figure 34-1.
7. Hang the mass on the key ring.
8. Record the reading on each of the spring scales.
9. Repeat, using different masses and different string lengths.

Asymmetric sign

1. Repeat the previous steps, using different string lengths.
2. Based on your evaluation, can you answer the question posed at the beginning of this section?

Expected Results

In the case of the symmetric supports, the two scales will read the same.

If the strings are different lengths, the shorter of the two strings will bear more of the weight.

Why It Works

The force in a cable is the combination of the various forces present. The overall force depends on how large each of the forces is and its direction. The method of combining these forces is called vector addition.

Other Things to Try

Tension is the force in a rope or cable that can change direction without losses by going around a pulley. How do you think the force in each of the cases in Figure 34-2 compares? Test it out with weights and pulleys.

Each spring scale should read 9.8 newtons, which is the amount of force exerted by gravity on a 1 kg mass.

Tug of war. It is almost impossible to pull a rope supporting a moderate weight tight enough to be perfectly horizontal. The experimental setup is shown in Figure 34-3. A gallon milk container filled with water makes a good 4 kg mass to try this with.

To bring the rope to within 5 degrees of horizontal with a 4 kg weight in the middle, you need to pull with a force of 560 newtons (or over 125 pounds). To bring the rope to within 1 degree of horizontal, you need to apply a force of about 2300 newtons (or over 500 pounds).

The Point

This exercise shows how a force can be broken down into or resolved into a pair of component forces. The downward force from the suspended sign is supported by cables of various lengths in various directions. This is the type of thinking civil engineers apply on a daily basis—to oversimplify, how strong something (like a bridge cable) needs to be to support a load (like the road surface with cars).

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