Question

When an insect ventures onto a spider web a slight vibration is set up, alerting the spider. The density of spider silk is approximately 1.3 g/cm^3, and its diameter varies considerably depending on the type of spider, but 3.0 mm is typical.

If the web is under a tension of 0.60 N when a small beetle crawls onto it 23 cm from the spider, how long will it take for the spider to receive the first waves from the beetle? Express your answer to two significant figures in milliseconds.
t= ms

Answer 1

To calculate the time it takes for the spider to receive the first waves from the beetle, we need to find the speed at which the waves travel through the spider web. The linear mass density of the spider silk can be calculated by dividing its density by its cross-sectional area. Using the linear mass density and the tension in the web, we can find the speed of the waves. Finally, we can calculate the time it takes for the waves to travel a certain distance.

Step-by-step explanation:

To calculate the time it takes for the spider to receive the first waves from the beetle, we need to find the speed at which the waves travel through the spider web.

Since the density of the spider silk is given as 1.3 g/cm^3 and its diameter is 3.0 mm, we can calculate the linear mass density of the silk by dividing its density by its cross-sectional area.

Linear mass density = density / cross-sectional area = (1.3 g/cm^3) / (π * (1.5 mm)^2) = 0.18 g/cm

Next, we can use the linear mass density and the tension in the web to find the speed of the waves using the formula v = sqrt(tension / linear mass density).

Speed = sqrt(0.60 N / 0.18 g/cm) = 2.45 m/s

Finally, we can calculate the time it takes for the waves to travel 23 cm from the beetle to the spider using the formula t = distance / speed.

Time = 23 cm / 2.45 m/s = 9.39 ms