Question

the end of the cutting cord on a gas-powered weed cutter is 0.15 m in length. if the motor rotates at the rate of 20 rev/s, what is the tangential speed of the end of the cord?

Answer 1

To find the tangential speed of the end of the cord, we need to multiply the rotational speed by the circumference of the circular path traced by the end of the cord.

Given:

Rotational speed (ω) = 20 rev/s

Length of the cutting cord (L) = 0.15 m

The circumference of a circle is given by the formula: C = 2πr, where r is the radius of the circle.

In this case, the radius of the circular path traced by the end of the cord is equal to the length of the cord (L), since the cord extends radially from the center of rotation.

So, the circumference of the circular path is: C = 2πL

The tangential speed (v) can be calculated using the formula: v = ω * C

Substituting the values:

C = 2π * 0.15

C ≈ 0.94248 m

v = 20 rev/s * 0.94248 m/rev

v ≈ 18.8496 m/s

Therefore, the tangential speed of the end of the cord is approximately 18.85 m/s.