To determine the force constant (k) of an ideal spring, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. In mathematical terms, this can be expressed as:
F = -kx
where F is the force applied to the spring, k is the force constant, and x is the displacement of the spring.
Given that 1.02 J of energy are stored in the spring when it is compressed by 0.22 m, we can use the formula for potential energy stored in a spring:
PE = (1/2)kx^2
where PE is the potential energy stored in the spring.
Setting the potential energy equal to 1.02 J and the displacement (x) equal to 0.22 m, we can solve for k:
1.02 J = (1/2)k(0.22 m)^2
1.02 J = (1/2)k(0.0484 m^2)
Simplifying:
1.02 J = 0.0242 k
k = 1.02 J / 0.0242
k ≈ 42.15 J/m
Therefore, the force constant of the ideal spring is approximately 42.15 J/m.
what is the force constant of an ideal spring if 1.02J are stored in the spring when it is compressed 0.22m
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