What is the Maximum Load a Copper Wire Can Support?

In summary, the conversation discusses the breaking stress and maximum load of a copper wire, with a diameter of 0.37 mm. The formula for calculating stress in a wire under tension is mentioned, as well as the concept of strain in relation to load.
  • #1
CaptFormal
33
0

Homework Statement



(a) Copper has a breaking stress of about 3.00×108 N/m2. What is the maximum load that can be hung from a copper wire of diameter 0.37 mm?

(b) If 17 percent of this maximum load is hung from the copper wire, by what fraction of its original length will it stretch?

Homework Equations


The Attempt at a Solution



I know that this one is simple, I just can't find the correct formula to use. Anyone got any ideas?
 
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  • #2
(a) They give you the diameter of the wire, so you have cross sectional area. You can also assume the wire is only in tension. Do you know how to calculate stress in a wire under tension?

(b) Given the load, can you find strain on this particular wire?
 
  • #3


(a) To determine the maximum load that can be hung from a copper wire, we can use the formula for stress:

Stress = Force/Area

We are given the breaking stress of copper (3.00x10^8 N/m^2) and the diameter of the wire (0.37 mm). We can calculate the cross-sectional area of the wire using the formula:

Area = πr^2

Where r is the radius of the wire. Since the diameter is given, we first need to convert it to meters by dividing by 1000. So the radius would be 0.37/2000 = 0.000185 m.

Plugging this into the area formula, we get:

Area = π(0.000185)^2 = 2.697x10^-8 m^2

Now we can plug in the values into the stress formula:

3.00x10^8 N/m^2 = Force/2.697x10^-8 m^2

Rearranging for force, we get:

Force = 3.00x10^8 N/m^2 x 2.697x10^-8 m^2 = 8091 N

Therefore, the maximum load that can be hung from the copper wire is 8091 N.

(b) To determine the fraction of the original length that the wire will stretch, we can use the formula for strain:

Strain = Change in length/Original length

We are given that 17% of the maximum load is hung from the wire. This means that the force acting on the wire is 0.17 x 8091 = 1374.87 N.

Using the stress formula again, we can solve for the change in length:

3.00x10^8 N/m^2 = 1374.87 N/Area

Area = π(0.000185)^2 = 2.697x10^-8 m^2

Rearranging for the change in length, we get:

Change in length = (3.00x10^8 N/m^2 x 2.697x10^-8 m^2)/1374.87 N = 5.876x10^-6 m

Now we can plug in the values into the strain formula:

Strain = 5.876x10^-6 m/Original length

 

Related to What is the Maximum Load a Copper Wire Can Support?

What is the maximum load that a copper wire can handle?

The maximum load that a copper wire can handle depends on various factors such as its gauge, length, and temperature. Generally, copper wires can handle loads ranging from 15 amps to 200 amps.

How does the gauge of a copper wire affect its maximum load?

The gauge, or thickness, of a copper wire has a direct impact on its maximum load capacity. Thicker wires have a larger cross-sectional area, allowing them to carry more current without overheating. As a result, thicker gauge wires can handle higher loads compared to thinner wires.

Does the length of a copper wire affect its maximum load?

Yes, the length of a copper wire also plays a role in determining its maximum load capacity. Longer wires have higher resistance, which means they can handle less current before reaching their maximum load. In general, shorter wires can handle higher loads compared to longer wires of the same gauge.

What is the maximum temperature that a copper wire can handle?

The maximum temperature that a copper wire can handle depends on its insulation and the application it is being used in. In general, most copper wires have a maximum temperature rating of 90°C for general use and 105°C for high-temperature applications.

What happens if a copper wire exceeds its maximum load?

If a copper wire exceeds its maximum load, it will start to overheat and can potentially melt or catch fire. This can lead to damage to the wire, the surrounding equipment, and even pose a safety hazard. It is important to always use copper wires within their maximum load capacity to ensure safe and efficient operation.

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