A elastic cord can be stretched to its elastic limit by a load of 2N if a 35 cm length of the cord is extended 0.6cm by a force of 0.5N what will be the length if 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 a spring or elastic cord is directly proportional to the stretching force, as long as the elastic limit is not exceeded. Mathematically, we can write:
F = kx
where F is the stretching force, x is the extension, and k is the spring constant (a measure of the stiffness of the cord). To find the length of the cord for a given stretching force, we need to first determine the spring constant.
For the given cord, we know that it can be stretched to its elastic limit by a load of 2N. This means that the maximum stretching force F_max = 2N. At this force, the extension x_max = 0.6cm. We can use these values to find the spring constant:
k = F_max / x_max
k = 2N / 0.6cm
k = 3.33 N/cm
Now we can use this value of k to find the length of the cord for a different stretching force. Let's say we want to find the length of the cord when the stretching force is 2.5N. We can again use Hooke's law:
F = kx
Solving for x, we get:
x = F / k
Plugging in the values, we get:
x = 2.5N / 3.33 N/cm
x = 0.75 cm
Therefore, the length of the cord when the stretching force is 2.5N will be 35 cm + 0.75 cm = 35.75 cm.
To find the new 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 needed to stretch or compress a spring or elastic object is directly proportional to the displacement of the object from its equilibrium position.
In this case, we can use the formula:
F = k * ΔL
Where:
F is the stretching force,
k is the spring constant, and
ΔL is the change in length of the cord.
First, let's find the spring constant, k:
k = F / ΔL
Given:
Load = 2N
Length = 0.6cm
k = 2N / 0.6cm = 3.33 N/cm
Now, we can find the change in length, ΔL when the stretching force is 2.5N:
F = k * ΔL
Rearranging the formula, we can solve for ΔL:
ΔL = F / k
ΔL = 2.5N / 3.33 N/cm
ΔL ≈ 0.75 cm
Finally, we can find the new length:
New length = Initial length + ΔL
Given:
Initial length = 35 cm
New length = 35 cm + 0.75 cm
New length ≈ 35.75 cm
Therefore, when the stretching force is 2.5N, the length of the cord will be approximately 35.75 cm.