An elastic string of length 20cm extends to 24cm when it supports a weight of 50N. Calculate the energy stored in the string.
k = 50/.04 N/m
E = 1/2 kx^2 J
Extension= final length- original length
Extension=24cm-20cm
Extension=4cm
Remember F = Ke
Therefore 50N = K ×4
Then K = 50/4 =12.5N/m
Then finally energy stored in a spring = 1/2Ke*2
Energy=1/2×12.5 ×4×4
Energy= 100 joules
Well, aren't you just full of energy? Let's calculate the energy stored in your stretchy string.
The energy stored in an elastic string can be calculated using the equation:
Elastic Potential Energy = 0.5 * k * x^2
where k is the spring constant and x is the extension of the string.
First, we need to find the spring constant. The spring constant (k) can be calculated using Hooke's Law:
k = F / x
where F is the force applied and x is the extension.
In your case, the force applied (F) is 50N and the extension (x) is 24cm - 20cm = 4cm = 0.04m.
So, k = 50N / 0.04m = 1250 N/m.
Now, let's get back to the equation we mentioned earlier:
Elastic Potential Energy = 0.5 * k * x^2
Plugging in the values, we have:
Elastic Potential Energy = 0.5 * 1250 N/m * (0.04m)^2
Calculating this expression, we find that the energy stored in your string is approximately 1 Joule.
So, that's the energy stored in your elastic string! Keep it stretchy!
To calculate the energy stored in the string, we can use Hooke's Law, which states that the force required to extend or compress a spring is directly proportional to the displacement.
The formula for calculating the energy stored in a spring is given by:
E = (1/2) * k * x^2
Where:
E - Energy stored in the spring
k - Spring constant
x - Displacement
In this case, the length of the string extends from 20 cm to 24 cm, which represents a displacement of 4 cm or 0.04 m.
Now, we can find the spring constant using Hooke's Law:
F = k * x
Rearranging the equation:
k = F / x
Substituting the given values:
k = 50 N / 0.04 m
k = 1250 N/m
Now, we can calculate the energy stored in the string:
E = (1/2) * k * x^2
E = (1/2) * 1250 N/m * (0.04 m)^2
E = 0.5 * 1250 N/m * 0.0016 m^2
E = 1.25 J
Therefore, the energy stored in the string is 1.25 Joules (J).
To calculate the energy stored in the string, we need to use Hooke's Law, which states that the force exerted by an elastic object is directly proportional to the extension or compression of the object. The energy stored in the string can be calculated using the formula:
E = (1/2) * k * x^2
Where:
E is the energy stored in the string
k is the spring constant
x is the extension or compression of the string
In this case, the extension of the string is given by the difference between the extended length (24 cm) and the original length (20 cm), which is 24 cm - 20 cm = 4 cm.
To find the spring constant, we use Hooke's Law:
F = k * x
Where:
F is the force exerted on the string (50 N in this case)
k is the spring constant
x is the extension or compression of the string (4 cm in this case)
Rearranging the equation, we can solve for k:
k = F / x
Substituting the values, we have:
k = 50 N / 4 cm
To calculate the energy stored in the string, we can now substitute the values of k and x into the formula:
E = (1/2) * k * x^2
E = (1/2) * (50 N / 4 cm) * (4 cm)^2
E = (1/2) * (50 N / 4 cm) * 16 cm^2
E = 200 N cm
Therefore, the energy stored in the string is 200 N cm.