a 20N force is required to stretch a spring by 0.5 m.
a) what is the spring constant?
b)how much energy is stored in the spring ?
a) To find the spring constant, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to its displacement. Hooke's Law can be represented by the equation:
F = kx
where F is the force, k is the spring constant, and x is the displacement.
Given that a 20N force is required to stretch the spring by 0.5m, we can substitute these values into the equation and solve for k:
20N = k * 0.5m
To find k, we divide both sides of the equation by 0.5m:
k = 20N / 0.5m
k = 40 N/m
Therefore, the spring constant is 40 N/m.
b) The energy stored in a spring can be calculated using the formula for potential energy:
U = (1/2) * k * x^2
where U is the potential energy, k is the spring constant, and x is the displacement.
We've already found the spring constant to be 40 N/m, and the displacement is given as 0.5 m. Substituting these values into the formula, we get:
U = (1/2) * 40 N/m * (0.5 m)^2
U = 10 N * 0.25 m^2
U = 2.5 Nm or Joules (J)
Therefore, the energy stored in the spring is 2.5 Joules (J).
To answer both parts of the question, we can use Hooke's law which states that the force required to stretch or compress a spring is directly proportional to the displacement.
a) To find the spring constant (k), we can use the formula for Hooke's law:
F = k * x
where F is the force applied, k is the spring constant, and x is the displacement.
Given that a 20N force is required to stretch the spring by 0.5m, we can plug these values into the formula and solve for k:
20N = k * 0.5m
To find k, divide both sides of the equation by 0.5m:
k = 20N / 0.5m
k = 40 N/m
So, the spring constant is 40 N/m.
b) To find the energy stored in the spring, we can use the formula for potential energy stored in a spring:
PE = (1/2) * k * x^2
where PE is the potential energy, k is the spring constant, and x is the displacement.
Given that the displacement (x) is 0.5m and the spring constant (k) is 40 N/m, we can plug these values into the formula and solve for the potential energy:
PE = (1/2) * 40 N/m * (0.5m)^2
PE = (1/2) * 40 N/m * (0.25m^2)
PE = 5 J
Therefore, the energy stored in the spring is 5 Joules.