Chapter 12: Problem 11

You're hanging a heavy picture on a wall, using wire attached to the top corners of the picture. Is the wire more likely to break if you run it tightly between the corners or if you give it some slack? Explain.

Short Answer

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A wire with some slack is less likely to break when hanging a heavy picture. This is because the tension gets evenly distributed across the wire rather than being concentrated at a single point as in the case of a tightly stretched wire.

Step by step solution

Understand the physics behind tension in a wire

When an object is hanging by a wire or rope, the weight of the object is causing a downward force due to gravity. This force applies a tension in the wire which is greatest at the points of attachment. Specifically, if the wire is directly attached from one point to another (a tight line), the entire tension caused by the weight of the object is concentrated in this one wire. Therefore, the tension is directly proportional to the weight.

Analysing the scenario of a wire with slack

When the wire has some slack or forms a 'V' shape, the scenario changes. Now the wire splits into two sections, each supporting half of the total weight of the picture.If we consider only one section of the wire, only half of the picture's weight is applying a downward force to this section, which reduces the tension at the point of attachment. As a result, the tension in the wire is distributed more evenly and it is less likely to break. This is a direct application of vector resolution of forces in physics.

Conclusion

Therefore, a wire with some slack is less likely to break while hanging a heavy picture because the tension gets distributed evenly across the wire. In contrast, a tightly stretched wire bears the entire weight of the picture and is consequently more likely to break.

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You're hanging a heavy picture on a wall, using wire attached to the top corners of the picture. Is the wire more likely to break if you run it tightly between the corners or if you give it some slack? Explain.

Short Answer

Step by step solution

Understand the physics behind tension in a wire

Analysing the scenario of a wire with slack

Conclusion

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