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The mechanical advantage of a wheel and axle is the radius of the wheel divided by the radius of the axle. On wheel and axle A, the wheel and axle are very close in size. On wheel and axle B, the radius of the wheel is much greater than the radius of the axle.

Answer :

MrRoyalgo

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

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