1. A small fly of mass 0.26 g is caught in a spider's web. The web vibrates predominately with a frequency of 4.2 Hz. Find the effective spring stiffness constant k for the web. Hint: use natural frequency of oscillations formula.

Question

N/m

2. At what frequency would you expect the web to vibrate if an insect of mass 0.52 g were trapped? Hint: use stiffness constant found in part 1. Hint: after the insect is trapped, the mass of the oscillator has increases by insect's mass, so the mass in the formula for natural frequency also has changed.

Hz

3. A spring scale being used to measure the weight of an object reads 12.8 N when it is used on earth. The spring stretches 4.95 cm under the load. The same object is weighed on the moon, where gravitational acceleration is
1/6g.

Find the reading of the spring scale on the moon.


Find the period for vertical oscillations of the spring on the moon.

Answer 1

(1) f = [1/(2 pi)]*(k/m)^1/2
Rearrange for k.

(2) With k staying the same, f drops a factor sqrt2 if the mass increases by a factor of 2.

(3) Spring scales measure weight, and weight = M g.

The scale reading decreases by a factor of 6. M stays the same and g decreases to 1/6 the value on Earth