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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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Most popular questions from this chapter

A biologist is studying plant growth and wants to simulate a gravitational field twice as strong as Earth's. She places the plants on a horizontal rotating table in her laboratory on Earth at a distance of \(12.5 \mathrm{cm}\) from the axis of rotation. What angular speed will give the plants an effective gravitational field \(\overrightarrow{\mathrm{g}}_{\mathrm{eff}},\) whose magnitude is \(2.0 \mathrm{g} ?\) \([\) Hint: Remember to account for Earth's gravitational field as well as the artificial gravity when finding the apparent weight. \(]\)
The orbital speed of Earth about the Sun is $3.0 \times 10^{4} \mathrm{m} / \mathrm{s}\( and its distance from the Sun is \)1.5 \times 10^{11} \mathrm{m}$. The mass of Earth is approximately \(6.0 \times 10^{24} \mathrm{kg}\) and that of the Sun is \(2.0 \times 10^{30} \mathrm{kg} .\) What is the magnitude of the force exerted by the Sun on Earth? \([\) Hint: Two different methods are possible. Try both.\(]\)
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