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A small fly of mass 0.22 g is caught in a spider’s web. The web oscillates predominantly with a frequency of 4.0 Hz.

(a) What is the value of the effective spring stiffness constant k for the web?
(b) At what frequency would you expect the web to oscillate if an insect of mass 0.44 g were trapped?

1 Answer

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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.

User Peteorpeter
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