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

Th extra force exerted against the bottom is 5979.23 N

Step-by-step 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\\\\(F_1)/(A_1)=(F_)/(A_2)\\\\F_2=(A_2)/(A_1)F_1\\\\F_2=(d_2)/(d_1)F_1\\\\F_2=((12)/(1.7))^2* 120\\\\F_2=5979.23\ N`

Hence, this is the required solution.