# Problem: A crass host pours the remnants of several bottles of wine into a jug after a party. He then inserts a cork with a 2.00-cm diameter into the bottle, placing it in direct contact with the wine. He is amazed when he pounds the cork into place and the bottom of the jug (with a 14.0-cm diameter) breaks away. Calculate the extra force exerted against the bottom if he pounded the cork with a 120-N force.

###### FREE Expert Solution

Let's consider the situation of a hydraulic lift.

In a hydraulic lift, the pressure on the master cylinder is equal to the pressure on the slave cylinder.

However, force changes with the change in cross-section.

Pressure:

$\overline{){\mathbf{P}}{\mathbf{=}}\frac{\mathbf{F}}{\mathbf{A}}}$

We now have:

$\overline{)\frac{{\mathbf{F}}_{\mathbf{1}}}{{\mathbf{A}}_{\mathbf{1}}}{\mathbf{=}}\frac{{\mathbf{F}}_{\mathbf{2}}}{{\mathbf{A}}_{\mathbf{2}}}}$, where F1 is the force applied to the master cylinder, A1 is the cross-sectional area of the master cylinder, F2 is the force created at each slave cylinder, and A2 is the cross-sectional area of slave cylinder.

We consider the cork as the master cylinder and the jug as the slave cylinder.

F1 = 120 N

A1 = πr12

r1 = 2.00/2 = 1.00 × 10-2m

A1 = π(1.00 × 10-2)2 = 3.142 × 10-4 m2

90% (123 ratings) ###### Problem Details

A crass host pours the remnants of several bottles of wine into a jug after a party. He then inserts a cork with a 2.00-cm diameter into the bottle, placing it in direct contact with the wine. He is amazed when he pounds the cork into place and the bottom of the jug (with a 14.0-cm diameter) breaks away. Calculate the extra force exerted against the bottom if he pounded the cork with a 120-N force.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Pascal's Law & Hydraulic Lift concept. You can view video lessons to learn Pascal's Law & Hydraulic Lift. Or if you need more Pascal's Law & Hydraulic Lift practice, you can also practice Pascal's Law & Hydraulic Lift practice problems.

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Based on our data, we think this problem is relevant for Professor Reichl's class at TEXAS.