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 the stretching point is 2.5
To find the length of the cord when the stretching force is 2.5N, we can use the concept of the elastic limit.
We know that the elastic limit occurs when the load is 4N and the length is 0.8cm. So, the ratio of load to length is:
(4N / 0.8cm) = (2.5N / x)
Cross multiplying, we get:
4N * x = 0.8cm * 2.5N
4x = 0.8cm * 2.5
4x = 2cm
Dividing both sides by 4, we get:
x = 2cm / 4
x = 0.5cm
Therefore, when the stretching force is 2.5N, the length of the cord will be 0.5cm.
To solve this problem, we can use Hooke's Law, which states that the force applied to a spring is directly proportional to the displacement from its equilibrium position. The formula for Hooke's Law is:
F = k * x
Where:
F: Force applied to the cord
k: Spring constant (a measure of the stiffness of the cord)
x: Displacement or change in length of the cord
First, we need to find the spring constant (k) using the given information.
Given:
Force to stretch the cord to its elastic limit = 4N
Length of the cord when stretched by 0.8cm = 40cm
Using the formula, we can find the spring constant:
k = F / x
k = 4N / 0.8cm
Now, we can calculate the spring constant (k):
k = 5N/cm
Next, we need to find the change in length (x) when the stretching force is 2.5N.
Given:
Force to stretch the cord to 0.8cm = 0.5N
New stretching force = 2.5N
Length of the cord when stretched to 0.8cm = 40cm
Using the formula, we can find the change in length:
x = F / k
x = (2.5N - 0.5N) / 5N/cm
Now, we can calculate the change in length (x):
x = 0.4cm
Finally, we can calculate the length of the cord when the stretching point is 2.5N:
Length = Initial length + Change in length
Length = 40cm + 0.4cm
The length of the cord when the stretching force is 2.5N is 40.4cm.