When a force of 50n is applied to the free end of an elastic cord ,an extensioncord,calculatethe work done on the cord
The work done on the cord can be calculated using the formula:
Work = Force x Distance x cos(theta)
where theta is the angle between the force and the displacement.
Since the cord is elastic, its extension will depend on its spring constant (k) and the displacement (x). The equation for the potential energy stored in a spring is:
Potential energy = 0.5*k*x^2
Therefore, the work done on the cord when a force F is applied and the cord is extended by x can be calculated as:
Work = Potential energy = 0.5*k*x^2
In this case, the force applied is 50N, but we need to know the extension of the cord to calculate the work done.
Assuming that the cord follows Hooke's Law and the spring constant is k = 10 N/m, we can use the equation:
F = k*x
to find the extension:
x = F/k = 50/10 = 5 meters
Now we can calculate the work done on the cord:
Work = 0.5*k*x^2 = 0.5*10*(5^2) = 125 J
Therefore, the work done on the cord when a force of 50N is applied is 125 Joules.
To calculate the work done on the cord, we need to know the extension of the cord. Work is defined as the product of force and displacement in the direction of the force. However, an elastic cord does not have a direct correlation between force and displacement. Instead, we need to consider the equation for elastic potential energy.
The elastic potential energy stored in a cord is given by the equation:
Elastic potential energy = (1/2) * k * x^2
Where:
- k is the spring constant of the cord (a measure of its stiffness)
- x is the extension of the cord from its natural length
In this case, without knowing the extension of the cord, we cannot determine the exact work done on the cord.