A spring of 40 cm long is stretched to 45cm by a load of 50N. What will be it's length when stretched by load 100N. Assuming that the elastic limit is not reached
To solve this problem, we can use Hooke's Law, which states that the force applied to a spring is proportional to the extension or compression of the spring.
Hooke's Law can be written as:
F = k * x
Where F is the force applied to the spring, k is the spring constant, and x is the extension or compression of the spring.
First, we need to find the spring constant. We can use the given information that the spring is stretched from 40 cm to 45 cm by a load of 50 N.
Using the formula for extension:
x = ΔL = 45 cm - 40 cm = 5 cm = 0.05 m
Now we can rearrange Hooke's Law to solve for the spring constant, k:
k = F / x
Plugging in the values:
k = 50 N / 0.05 m
k = 1000 N/m
Now that we have the spring constant, we can use it to find the length of the spring when stretched by a load of 100 N.
Again, using Hooke's Law:
F = k * x
Plugging in the values:
100 N = 1000 N/m * x
Solving for x:
x = 100 N / 1000 N/m
x = 0.1 m
To find the length of the spring when stretched by 100 N, we need to add the extension to the original length of the spring:
Length = original length + extension
Length = 40 cm + 0.1 m = 40.1 cm
Therefore, when the spring is stretched by a load of 100 N, its length will be 40.1 cm.
An elastic cord can be stretched to it elastic limit by load of 4N. If a 40cm length of a 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 solve this problem, we need to first find the spring constant of the elastic cord using the given information.
Hooke's Law states that the force applied to a spring is proportional to its extension or compression. The equation is given as:
F = k * x,
Where F is the force applied to the cord, k is the spring constant, and x is the extension or compression of the cord.
We are given that the cord can be stretched to its elastic limit by a load of 4N. This means that at the elastic limit, the force applied is equal to 4N. At this point, the extension is not provided, but we can still find the spring constant by rearranging Hooke's Law:
k = F / x
Plugging in the values:
k = 4N / x
Next, we are given that a 40cm length of the cord is extended to 0.8cm by a force of 0.5N. This means that at this point, the force applied to the cord is equal to 0.5N, and the extension is 0.8cm. Again, we can use Hooke's Law to find the spring constant:
k = F / x,
k = 0.5N / 0.8cm
Convert the extension to meters (since we are working with the spring constant in N/m):
k = 0.5N / (0.008m)
k = 62.5 N/m
Now that we have the spring constant, we can find the length of the cord when stretched by a force of 2.5N. Let's call this extension x.
Using Hooke's Law:
F = k * x,
2.5N = 62.5 N/m * x
Solving for x:
x = 2.5N / 62.5 N/m
x = 0.04 m
To find the length of the cord when stretched by 2.5N, we need to add the extension to the original length of the cord:
Length = original length + extension
Length = 40 cm + 0.04 m
Length = 40.04 cm
Therefore, when the cord is stretched by a force of 2.5N, its length will be approximately 40.04 cm.
To calculate the length of the spring when stretched by a load of 100N, we can use Hooke's Law, which states that the force exerted on a spring is directly proportional to its extension (change in length).
Given:
Initial length of the spring (unstretched): 40 cm
Extension of the spring (change in length) when loaded with 50N: 45 cm - 40 cm = 5 cm
Load when the spring extends by 50N: 50N
To find the constant of proportionality, we can use Hooke's Law formula:
Force = k × extension
Where:
Force = Load applied on the spring
k = Constant of proportionality (spring constant)
Now, let's calculate the spring constant (k):
k = Force / Extension
k = 50N / 5cm
k = 10 N/cm
Using this constant, we can determine the extension of the spring when loaded with 100N:
Extension = Force / k
Extension = 100N / 10 N/cm
Extension = 10 cm
Finally, to find the length of the spring when stretched by a load of 100N, we add the extension to the initial length:
Final Length = Initial Length + Extension
Final Length = 40 cm + 10 cm
Final Length = 50 cm
Therefore, the length of the spring when stretched by a load of 100N will be 50 cm.