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Chapter 5: Problem 65

A trimmer for cutting weeds and grass near trees and borders has a nylon cord of 0.23 -m length that whirls about an axle at 660 rad/s. What is the linear speed of the tip of the nylon cord?

Short Answer

Expert verified
Answer: The linear speed of the tip of the nylon cord is approximately 151.8 m/s.

Step by step solution

01

Identify the given information

We are provided with the following information: - Length of the nylon cord (radius of the circular path), r = 0.23 m - Angular speed of the nylon cord, ω = 660 rad/s
02

Apply the formula to find the linear speed

Now, we will use the formula that relates linear speed (v) and angular speed (ω): v = rω
03

Substitute the given values and calculate the linear speed

Let's substitute the values of r and ω into our formula: v = (0.23 m)(660 rad/s) Now, calculate the product: v ≈ 151.8 m/s
04

State the final answer

The linear speed of the tip of the nylon cord is approximately 151.8 m/s.

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