An elastic cord can be stretched to its elastic limit by a load of 2N. If a 35cm length of the cord is extended 0.6cm by a force of 0.5N, what would be the length when the stretching force is 2.5N?
To find the length of the cord when the stretching force is 2.5N, we can use the concept of Hooke's Law.
Hooke's Law states that the force (F) applied to an elastic material is directly proportional to the extension (x) of the material, as long as the elastic limit is not exceeded.
Mathematically, this can be expressed as: F = k * x, where k is the spring constant.
In this case, when a load of 2N is applied, the cord is stretched to its elastic limit. Let's assume that the original length of the cord is L cm.
Given that a 35cm length of the cord is extended by 0.6cm with a force of 0.5N:
0.5N = k * 0.6cm
k = 0.5N / 0.6cm
k = 0.833 N/cm
Now, let's find the length of the cord when the force is 2.5N.
Using Hooke's Law, we can set up the following equation: 2.5N = 0.833 N/cm * x
Solving for x, we get:
x = 2.5N / 0.833 N/cm
x = 3 cm
Therefore, the length of the cord when the stretching force is 2.5N would be 3 cm.
To solve this problem, we can use Hooke's Law, which states that the extension of a spring or elastic material is directly proportional to the force applied. Mathematically, Hooke's Law is represented as:
F = k * ΔL
where F is the force applied, k is the spring constant, and ΔL is the change in length.
We are given that the elastic cord can be stretched to its elastic limit by a load of 2N. This means that when a load of 2N is applied, the extension will be at its maximum and the cord will not stretch further.
Let's find the spring constant, k, using the given information:
F = k * ΔL
2N = k * 0.6cm
To find k, divide both sides of the equation by 0.6cm:
k = 2N / 0.6cm
= 3.33 N/cm
Now we can use Hooke's Law to find the length when the stretching force is 2.5N:
F = k * ΔL
2.5N = 3.33 N/cm * ΔL
To find ΔL, divide both sides of the equation by 3.33 N/cm:
ΔL = 2.5N / 3.33 N/cm
≈ 0.75 cm
Finally, we can find the total length when the stretching force is 2.5N by adding the original length of the cord (35cm) and the change in length (0.75cm):
Total length = 35cm + 0.75cm
= 35.75cm
Therefore, the length of the cord when the stretching force is 2.5N would be approximately 35.75cm.