Final answer:
The effective spring stiffness constant, k, can be calculated using the formula: k = (4π²m/T²). To find the value of k for the web, substitute the mass of the fly and the period of oscillation into the formula. To calculate the frequency for a trapped insect of different mass, use the same formula and substitute the mass of the insect and the value of k.
Step-by-step explanation:
The effective spring stiffness constant, k, can be calculated using the formula:
k = (4π²m/T²)
Where m is the mass of the fly and T is the period of oscillation.
To convert the mass of the fly to kilograms, divide by 1000. So, the mass of the fly is 0.00022 kg (0.22 g / 1000). The period of oscillation is the reciprocal of the frequency, so T = 1 / 4.0 = 0.25 s.
Substituting the values into the formula, we get:
k = (4π²(0.00022)/(0.25)²)
Solving this equation gives us the value of the effective spring stiffness constant, k.
To calculate the frequency at which the web would oscillate if an insect of mass 0.44 g were trapped, we can use the same formula.
Again, convert the mass of the insect to kilograms, giving m = 0.00044 kg. Substitute the values into the formula, along with the value of k calculated in part (a), and solve for T to find the period of oscillation. The frequency is then the reciprocal of the period.