An elastic cord can be stretched to it elastic limit by a load of 4N. If a 40cm length of the cord is extended to 0.8cm by a force of 0.5N, What will be the length of the cord when stretcher point is 2.5N.
To find the length of the cord when stretched by a force of 2.5N, we need to use the concept of Hooke's Law.
Hooke's Law states that the force required to stretch or compress a spring by a distance x is directly proportional to the distance x and the spring constant k.
In this case, the elastic cord obeys Hooke's Law. We are given that the cord can be stretched to its elastic limit by a load of 4N, giving us the force and displacement information as follows:
Force (F) = 4N
Initial length (L0) = 40cm = 0.40m
Final length (L) = 0.8cm = 0.008m
Using Hooke's Law equation:
F = k * x
where F is the force, k is the spring constant, and x is the displacement.
We need to find the spring constant k by rearranging the formula:
k = F / x
Now we can calculate the spring constant:
k = 4N / 0.008m = 500 N/m
We can now use the spring constant to find the length of the cord when stretched by a force of 2.5N.
Force (F) = 2.5N
k = 500 N/m
Using the rearranged formula:
F = k * x
Rearranging for x:
x = F / k
x = 2.5N / 500 N/m = 0.005m
Finally, we can calculate the final length (L) of the cord when stretched by a force of 2.5N:
L = L0 + x
L = 0.40m + 0.005m = 0.405m
Therefore, the final length of the cord will be 0.405m when stretched by a force of 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 extension of an elastic material is directly proportional to the force applied, as long as it remains within its elastic limit. Mathematically, it can be written as:
F = k * x
Where:
F is the force applied
k is the spring constant (a measure of the stiffness of the material)
x is the extension produced
To solve this, we need to find the spring constant (k) using the given information:
Given:
Load at elastic limit (F) = 4N
Length of the cord when extended by 0.8cm (x) = 0.8cm = 0.008m
Force applied to produce this extension = 0.5N
Using Hooke's Law, we can write the equation as:
0.5N = k * 0.008m
Simplifying the equation, we can find the value of k:
k = 0.5N / 0.008m
k = 62.5N/m
Now, we can use this value of k to find the extension (x) when the stretching force is 2.5N:
2.5N = 62.5N/m * x
Simplifying the equation, we can find the value of x:
x = 2.5N / 62.5N/m
x = 0.04m = 4cm
Therefore, the length of the cord when the stretching force is 2.5N will be 40cm + 4cm = 44cm.