Question

A crass host pours the remnants of several bottles of wine into a jug after a party. He then inserts a cork with a 1.70 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 12.0 cm diameter) breaks away. Calculate the extra force (in N) exerted against the bottom if he pounded the cork with a 120 N force.

Answer 1

Answer:

Th extra force exerted against the bottom is 5979.23 N

Explanation:

Given that,

Initial diameter of the cork, $d_1=1.7\ cm$

Final diameter of the cork, $d_2=12\ cm$

Initial force, $F_1=120\ N$

We need to find the extra force in second condition. The pressure at both condition will remains the same.

$P_1=P_2\\\\\dfrac{F_1}{A_1}=\dfrac{F_}{A_2}\\\\F_2=\dfrac{A_2}{A_1}F_1\\\\F_2=\dfrac{d_2}{d_1}F_1\\\\F_2=(\dfrac{12}{1.7})^2\times 120\\\\F_2=5979.23\ N$

Hence, this is the required solution.