Question

The end of the cutter cord of an electric grass trimmer measures a length of 0.21. If the motor rotates at a speed of 20 rev / s, what is the tangential speed of the end of the cable?

Answer 1

The tangential speed of the end of the cable on an electric grass trimmer with a length of 0.21 m and motor rotating at 20 rev/s is approximately 26.39 meters per second.

Step-by-step explanation:

To find the tangential speed of the end of the cable on an electric grass trimmer, we can use the relationship between the linear speed (tangential speed) and the angular speed. The formula to determine tangential speed (v) is v = r × ω, where r is the radius and ω (omega) is the angular speed. The angular speed can be calculated by taking the motor rotation speed and converting it from revolutions per second to radians per second (since 1 revolution equals 2π radians). Therefore, if the motor rotates at 20 rev / s and the length of the cutter cord is 0.21 m, we have:

ω = 20 rev/s × 2π rad/rev = 40π rad/s

Now, tangential speed v = r × ω = 0.21 m × 40π rad/s = 8.4π m/s.

Therefore, the tangential speed is 8.4π meters per second, which is approximately 26.39 meters per second.