An elastic cord can be stretched to it elastic limit by a load of 2N if a 35cm length of cord is extend to 0.6cm by a force of 0.5N . What will be the length of the cord when it is stretching cord is 2.5N
To determine the relationship between the force applied to the cord and the amount of stretch, we can use Hooke's Law. Hooke's Law states that the force applied to a spring (or elastic cord) is directly proportional to the amount of stretch or compression.
In this case, we are given that a load of 2N stretches a 35cm length of cord to 0.6cm. We can use this information to find the proportionality constant, or the spring constant (k), using the formula:
k = (F / x)
where F is the force applied and x is the amount of stretch.
k = (2N / 0.6cm) = 3.33 N/cm
Now, we can use this spring constant to find the length of the cord when a force of 2.5N is applied. Let L1 be the original length of the cord and L2 be the stretched length of the cord when a force of 2.5N is applied.
k = (F / x)
3.33 N/cm = (2.5N / (L2 - L1))
We know the original length (L1) is 35cm and the force applied (F) is 2.5N. Plugging in these values, we can solve for L2:
3.33 N/cm = (2.5N / (L2 - 35cm))
Cross-multiplying, we get:
3.33 N/cm * (L2 - 35cm) = 2.5N
Dividing both sides by 3.33 N/cm:
(L2 - 35cm) = 2.5N / 3.33 N/cm
Simplifying, we have:
L2 - 35cm = 0.7515 cm
Adding 35cm to both sides:
L2 = 35.7515 cm
Therefore, the length of the cord when it is stretched by a force of 2.5N is approximately 35.7515 cm.
To solve this problem, we can use Hooke's law, which states that the extension of a spring or elastic cord is directly proportional to the force applied to it until it reaches its elastic limit.
Let's first determine the spring constant (k) of the elastic cord using the given information.
Using Hooke's law, we can write:
F = k * x
Where F is the force applied, k is the spring constant, and x is the extension.
Given:
Force (F1) = 0.5 N
Extension (x1) = 0.6 cm = 0.006 m
Rewriting the equation with the given values:
0.5 N = k * 0.006 m
Solving for k:
k = 0.5 N / 0.006 m
k ≈ 83.33 N/m
Now, we can use the spring constant to find the extension of the cord when a force of 2.5 N is applied.
Given:
Force (F2) = 2.5 N
Using Hooke's law again:
F2 = k * x2
Rearranging the equation to solve for x2:
x2 = F2 / k
Substituting the given values:
x2 = 2.5 N / 83.33 N/m
x2 ≈ 0.03 m
Finally, to find the length of the cord when it is stretched by a force of 2.5 N, we need to add the extension to the original length of the cord:
Length = original length + extension
Length = 35 cm + 0.03 m (converting to meters)
Length ≈ 35.03 cm
Therefore, the length of the cord when stretched by a force of 2.5 N will be approximately 35.03 cm.