Final answer:
The question involves calculating the mass of a spider by using the wave speed on a silk thread, the silk's density, and the silk's radius to find the tension and hence the spider's weight.
Step-by-step explanation:
The question deals with the physics of wave motion and tension in a spider silk thread. We know the radius of the strand and its density, and we're given that the weight of the silk is negligible compared to the tension. Since the waves travel at a speed of 280 m/s, we can use the formula for wave speed on a string, which is v = √(T/μ), where v is the speed of the wave, T is the tension in the string, and μ is the linear mass density of the string.
First, we calculate the linear mass density of the silk as μ = (density of the silk) * (cross-sectional area of the silk). The cross-sectional area can be found using the radius (r = 3.97e-6 m) and the formula for the area of a circle, πr². Next, we rearrange the wave speed formula to solve for the tension T since we have the value for μ and the wave speed (v).
Once we have the tension, we can equate it to the weight of the spider, which is its mass (m) times the acceleration due to gravity (g), i.e., T = mg. Solving for m gives us the mass of the spider. Remember that the value for g is approximately 9.8 m/s².