Answer:
The wheel and axle B has a greater mechanical advantage than wheel and axle B
Explanation:
Given
Let
[tex]R_W = Radius\ of\ the\ wheel[/tex]
[tex]R_A = Radius\ of\ the\ axle[/tex]
[tex]MA = \frac{R_w}{R_A}[/tex]
Required
Which wheel and axle has the greater mechanical advantage? (Missing Information)
For Wheel and Axle A:
[tex]R_w[/tex] is close to [tex]R_A[/tex]
For calculation purpose, we can assume that:
[tex]R_W \approx\ R_A[/tex]
So:
[tex]MA = \frac{R_w}{R_A}[/tex]
[tex]MA = \frac{R_A}{R_A}[/tex] or [tex]MA = \frac{R_W}{R_W}[/tex]
[tex]MA = 1[/tex]
For Wheel and Axle B:
[tex]R_w[/tex] far from [tex]R_A[/tex]
For calculation purpose, we can assume that:
[tex]R_W > R_A[/tex]
and
[tex]R_A = nR_A[/tex]
Where:
[tex]n > 1[/tex]
So:
[tex]MA = \frac{R_w}{R_A}[/tex]
[tex]MA = \frac{nR_A}{R_A}[/tex]
[tex]MA = n\frac{R_A}{R_A}[/tex]
[tex]MA = n * 1[/tex]
[tex]MA = n[/tex]
Since: [tex]n > 1[/tex]
Then
[tex]MA > 1[/tex]
So, we have:
[tex]MA = 1[/tex] ---> For Wheel and Axle A
[tex]MA > 1[/tex] ---> For Wheel and Axle B
By comparison, the wheel and axle B has a greater mechanical advantage than wheel and axle B
