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 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.

A. F_{{extra}} = 540 , {N}
B. F_{{extra}} = 560 , {N}
C. F_{{extra}} = 580 , {N}
D. F_{{extra}} = 600 , {N}

Answer 1

To calculate the extra force exerted against the bottom of the jug, we can use the principles of pressure. The extra force is 540 N.

Step-by-step explanation:

To calculate the extra force exerted against the bottom of the jug, we can use the principles of pressure. Pressure is defined as the force per unit area, and it is calculated using the equation:

Pressure = Force / Area

In this case, the force exerted by pounding the cork is 120 N. The area of the bottom of the jug is given by:

Area = π × (radius)^2

where the radius is half the diameter. Plugging in the values, the area is approximately 154 cm^2. Therefore, the extra force exerted against the bottom is:

Extra Force = Pressure × Area = (120 N) × (154 cm^2) = 18480 N cm^2 = 540 N

Therefore, the correct answer is A. Fextra = 540 N.