A certain insect’s wing has been shown to deflect a distance 14.8 mm under a force of 0.19 N applied to the end of the wing.
(a)
If the wing is assumed to behave as an ideal spring, calculate the force constant in N/m.
(b)
At this deflection, how much energy is stored in the wing, in Joules?
(a) The force constant can be calculated using the equation F = kx, where F is the applied force, k is the force constant, and x is the deflection. Rearranging this equation to solve for k gives k = F/x, so the force constant is 0.19 N/14.8 mm = 0.0128 N/m.
(b) The energy stored in the wing can be calculated using the equation E = 1/2kx^2, where E is the energy stored, k is the force constant, and x is the deflection. Substituting in the values from part (a) gives E = 1/2(0.0128 N/m)(14.8 mm)^2 = 0.0044 J.
To calculate the force constant of the wing, we can use Hooke's Law, which states that the force applied on a spring is directly proportional to the displacement produced:
F = kx
Where:
F is the force applied (0.19 N),
k is the force constant (to be determined),
x is the displacement (14.8 mm = 0.0148 m).
(a) To find the force constant (k), we rearrange the equation:
k = F / x
Substituting the given values:
k = 0.19 N / 0.0148 m
k ≈ 12.84 N/m
Therefore, the force constant of the wing is approximately 12.84 N/m.
(b) To calculate the energy stored in the wing, we can use the formula for potential energy stored in a spring:
PE = (1/2) kx²
Where:
PE is the potential energy stored in the wing (to be determined),
k is the force constant (12.84 N/m),
x is the displacement (0.0148 m).
Substituting the given values:
PE = (1/2) * 12.84 N/m * (0.0148 m)²
PE ≈ 0.011 J
Therefore, at this deflection, approximately 0.011 Joules of energy is stored in the wing.
(a) To calculate the force constant (k) in N/m, we can use Hooke's Law, which states that the force applied to a spring is directly proportional to the displacement of the spring from its equilibrium position.
Hooke's Law equation is given by:
F = k * x
Where:
F is the force applied (0.19 N),
k is the force constant (unknown),
x is the displacement (14.8 mm = 0.0148 m).
Rearranging the equation, we can solve for k:
k = F / x
k = 0.19 N / 0.0148 m
k ≈ 12.838 N/m
Therefore, the force constant (k) of the wing is approximately 12.838 N/m.
(b) To find the energy stored in the wing, we can use the formula for potential energy stored in a spring:
Potential Energy (PE) = 0.5 * k * x^2
Where:
k is the force constant (12.838 N/m),
x is the displacement of the wing (0.0148 m).
Substituting the values, we get:
PE = 0.5 * 12.838 N/m * (0.0148 m)^2
PE ≈ 0.00536 J
Therefore, at this deflection, approximately 0.00536 Joules of energy is stored in the wing.