An elastic cord can be stretched to it's elastic limit by a load of 2newton.if a 35cm length when the cord is extended 0.6m by a force of 0.5newton,what will be the length of the cord when the stretched force is 2.5newton?
To find the length of the cord when the stretched force is 2.5 newtons, we can use the concept of Hooke's law, which states that the extension of an elastic material is directly proportional to the applied force.
Let L1 be the original length of the cord when the load of 2 newtons stretches it to its elastic limit, and L2 be the length of the cord when it is extended by a force of 0.5 newtons.
Applying Hooke's law, we can write:
L2 = L1 + x
where x is the extension of the cord due to the 0.5 newton force.
Given that L1 = 35 cm and x = 0.6 m (since the cord is extended by 0.6 m), we can convert the length and extension to meters:
L1 = 35 cm = 0.35 m
x = 0.6 m
Now we can solve for L2:
L2 = 0.35 m + 0.6 m = 0.95 m
So, the length of the cord when the stretched force is 2.5 newtons would be 0.95 meters.
To solve this problem, we can use Hooke's law, which states that the force required to extend or compress a spring is directly proportional to the distance it is stretched or compressed. Mathematically, it can be represented as F = k * x, where F is the force, k is the spring constant, and x is the extension or compression.
Given:
Initial length of the cord (L1) = 35 cm = 0.35 m
Extension of the cord (x1) = 0.6 m
Force applied (F1) = 0.5 N
Load at the elastic limit (F2) = 2 N
To find the spring constant (k), we can use the formula F = k * x and rearrange it to k = F / x.
k = F1 / x1
k = 0.5 N / 0.6 m
k = 0.8333 N/m
Now, we can use the spring constant (k) to find the length of the cord (L2) when the stretched force (F3) is 2.5 N.
Using the formula F = k * x, we rearrange it to x = F / k.
Extension of the cord (x2) = F3 / k
x2 = 2.5 N / 0.8333 N/m
x2 = 3 m
Finally, we can find the length of the cord (L2) when the stretched force is 2.5 N by adding the extension to the initial length.
L2 = L1 + x2
L2 = 0.35 m + 3 m
L2 = 3.35 m
Therefore, the length of the cord when the stretched force is 2.5 N will be 3.35 meters.