Question

The distance between the centers of two wheels on the belt pulley system of the tractor is 24 inches. The length of the belt between the wheel is 23.5 inches. Find the exact length of the radius of each wheel if the radius of the larger wheel is twice the radius of the smaller wheel

Answer 1

Answer:

R = 0.334 inches, and r = 0.167 inches

Step-by-step explanation:

The centers of the two pulleys are 24 inches apart. And a belt of length 23.5 inches is between the wheels.

Thus,

difference in length = 24 - 23.5

                                 = 0.5 inches

Let the radius of the larger wheel be represented by R, and that of the smaller wheel by r.

So that,

R = 2r

Thus,

R + r = difference in length

2r + r = 0.5

3r = 0.5

r = $\frac{0.5}{3}$

  = 0.166666666

r = 0.167 inches

Therefore:

R = 2r

  = 2 x 0.167

  = 0.334

R = 0.334 inches