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 will be the length of the cord when the stretching force is 2.5N
We can use the concept of Hooke's Law to solve this problem.
Hooke's Law states that the extension of an elastic material is directly proportional to the force applied to it, as long as the force is within the elastic limit. This can be represented by the equation:
F = kx
where F is the force applied, x is the extension, and k is the spring constant of the elastic material.
In this problem, we know that the cord can be stretched to its elastic limit by a load of 2N. This means that the spring constant of the cord is:
k = F/x = 2N / 0.6cm = 3.33 N/cm
We also know that when a force of 0.5N is applied, the cord extends by 0.6cm. Using Hooke's Law, we can find the extension of the cord when a force of 2.5N is applied:
F = kx
2.5N = 3.33 N/cm * (x - 0.6cm)
Solving for x, we get:
x = 1.80 cm
Therefore, the length of the cord when the stretching force is 2.5N will be:
35cm + 1.80cm = 36.80cm
To solve this problem, we can use the concept of Hooke's Law, which states that the force applied to a spring is directly proportional to the extension or compression of the spring.
First, let's find the spring constant, k, using the given information. We know that the elastic cord can be stretched to its elastic limit by a load of 2N, and a 35cm length of the cord is extended 0.6cm by a force of 0.5N.
Using Hooke's Law, we can write the equation:
F = k * x
where F is the force applied to the spring, k is the spring constant, and x is the extension or compression of the spring.
Given that F = 0.5N and x = 0.6cm (or 0.006m), we can substitute these values into the equation to find k.
0.5N = k * 0.006m
Now, let's solve for k:
k = 0.5N / 0.006m
k = 83.33 N/m
Now that we have the spring constant, we can use it to find the length of the cord when the stretching force is 2.5N.
Again, we can use Hooke's Law to write the equation:
F = k * x
Given that F = 2.5N, we can substitute this value into the equation and solve for x, which represents the extension of the cord.
2.5N = 83.33 N/m * x
Now, let's solve for x:
x = 2.5N / 83.33 N/m
x = 0.03m or 3cm
Therefore, when the stretching force is 2.5N, the length of the cord will be 35cm + 3cm = 38cm.