Question

The ratio of the diameter of the two pistons of a hydraulic press is 16: 3 and the ratio of the two arms of its lever is 9: 4. What are the mechanical advantages of the press?

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Answer 1

Explanation:

Hydraulic press =16:3

Arms of its level = 9:4

Mechanical advantage = 16:3×9:4

= 4×3=12

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Answer 2

Given :

• The ratio of the diameter of the two pistons of a hydraulic press is 16: 3.
• The ratio of the two arms of its lever is 9: 4.

To find :

• Mechanical advantage of the press.

Solution :

Let the 1st diameter of the piston be 16x and the 2nd diameter of the piston be 3x.

• Radius of 1st piston(r)= 16x/2 = 8x.
• Radius of 2nd piston(r')=3x/2.

Let,

• 1st arm of its lever= 9y
• 2nd arm of its lever = 4y

So,

• Area of 1st piston = π × 8x × 8x
• Area of 2nd piston = $\sf{\pi\times\frac{3x}{2}\times\frac{3x}{2}}$

Formula Used :-

${\boxed{\bold{Mechanical\: advantage=\dfrac{y\beta}{x\alpha}}}}$

Where, y > x and ẞ > $\alpha$

• Terms identification :-
• y = 1st arm of its lever.
• x = 2nd arm of its lever.
• $\alpha$= Area of 2nd piston.
• ẞ = Area of 1st piston.

Here,

• y = 9y
• x = 4y
• ẞ = π × 8x × 8x
• $\sf{\alpha=\pi\times\frac{3x}{2}\times\frac{3x}{2}}$

Mechanical advantage,

$\implies\sf{\dfrac{y\beta}{x\alpha}}$

$\implies\sf{\dfrac{9y}{4y}\times\dfrac{\pi\times\:8x\times\:8x}{\pi\times\dfrac{3x}{2}\times\dfrac{3x}{2}}}$

$\implies\sf{64}$

Therefore, the mechanical advantage is 64.