# What is the magnitude of the force exerted by the water on the bottom of a bottle?

1. Nov 30, 2009

### jayced

1. The problem statement, all variables and given/known data
A container has a large cylindrical lower part with a long thin cylindrical neck. The lower part of the container holds 12.5 m3 of water and the surface area of the bottom of the container is 4.68 m2. The height of the lower part of the container is h1 = 3.30 m and the neck contains a column of water h2 = 8.20 m high. The total volume of the column of water in the neck is 0.200 m3. What is the magnitude of the force exerted by the water on the bottom of the container?

2. Relevant equations
F = PA
= (ρgh + P0)(4.68 m²)
ρ = density of water=1000kg/m^3
g = acceleration due to gravity = 9.8 m/sec²
h = height of water column = 3.30m + 8.20m = 11.50 m
P0 = air pressure at top of column = 1 atmosphere.

3. The attempt at a solution
F = PA
= (ρgh + P0)(4.68 m²)
= (1000kg/m^3)(9.8m/s^2)(11.50m) + 1 atm.)(4.65 m²)=527440.68N need to convert to MN

Is my formula correct?
Are my units for force correct that it comes out in Newtons?

2. Nov 30, 2009

### ideasrule

Re: What is the magnitude of the force exerted by the water on the bottom of a bottle

It's correct, but the question asks for the pressure the water exerts. The pressure exerted by the air above is not usually taken into consideration.

3. Nov 30, 2009

### ApexOfDE

Re: What is the magnitude of the force exerted by the water on the bottom of a bottle

I think the contribution of force exerting on bottom of container includes force by neck and force by lower part.

F = F_neck + F_low
The text passage contains a physics problem that involves calculating the force exerted by water on the bottom of a container with a specific geometry. The problem is presented with a detailed attempt at a solution, and there are comments from other users regarding the correctness of the approach.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# What is the magnitude of the force exerted by the water on the bottom of a bottle?

1. Nov 30, 2009

### jayced

1. The problem statement, all variables and given/known data
A container has a large cylindrical lower part with a long thin cylindrical neck. The lower part of the container holds 12.5 m3 of water and the surface area of the bottom of the container is 4.68 m2. The height of the lower part of the container is h1 = 3.30 m and the neck contains a column of water h2 = 8.20 m high. The total volume of the column of water in the neck is 0.200 m3. What is the magnitude of the force exerted by the water on the bottom of the container?

2. Relevant equations
F = PA
= (ρgh + P0)(4.68 m²)
ρ = density of water=1000kg/m^3
g = acceleration due to gravity = 9.8 m/sec²
h = height of water column = 3.30m + 8.20m = 11.50 m
P0 = air pressure at top of column = 1 atmosphere.

3. The attempt at a solution
F = PA
= (ρgh + P0)(4.68 m²)
= (1000kg/m^3)(9.8m/s^2)(11.50m) + 1 atm.)(4.65 m²)=527440.68N need to convert to MN

Is my formula correct?
Are my units for force correct that it comes out in Newtons?

2. Nov 30, 2009

### ideasrule

Re: What is the magnitude of the force exerted by the water on the bottom of a bottle

It's correct, but the question asks for the pressure the water exerts. The pressure exerted by the air above is not usually taken into consideration.

3. Nov 30, 2009

### ApexOfDE

Re: What is the magnitude of the force exerted by the water on the bottom of a bottle

I think the contribution of force exerting on bottom of container includes force by neck and force by lower part.

F = F_neck + F_low
user
The text passage contains a physics problem that involves calculating the force exerted by water on the bottom of a container with a specific geometry. The problem is presented with a detailed attempt at a solution, and there are comments from other users regarding the correctness of the approach.

TYPE: SINGLE_QUESTION_WITH_ANSWER