Calculating Cork Volume for Child's Water Slide Float | Fluid Questions

[shadow2006]

Hey! I have been out of school sick for a week! I'm a little behind and having some trouble understanding some things. Here is a question that has me stumped.

An Amusement park is planning to build a water slide, and the park owners would like to use big giant corks (p= 0.28g/cm^3) as "floats" for young children. what volume of cork is need to keep 20 percent (by volume) of a 40kg child above water at the base of the slide(assume the density of the child is 1.01g/cm^3)?

I found that the 20% of 40kg = 8kg
and i found that the density of the child = 7.9207

 

[shadow2006]

Another that has me stumped in this section is:

when you take your car into the shop to have it worked on, a hydraulic lift is used. The diameter of the piston lifting your car and the base it sits on have a combined mass of 12000kg. the oil used in this lift has a density of 800kg/m^3.

A. How many apples would you need to place on the imput piston in order to hold up your car? A medium apple weighs approximately one Newton.
B. When the car reaches a height of 0.15m, how many apples will it take to support the car at that height?

I don't even know where to start,i don't even know what they are talking about??

 

[wais]

cm^3

Hi there! Sorry to hear that you've been sick, I hope you're feeling better now. Let's see if we can work through this question together.

First, let's clarify the information given. We know that the park wants to use corks with a density of 0.28g/cm^3 as floats for children. We also know that the child in question has a density of 1.01g/cm^3, and that the park wants 20% of the child's volume to be above water.

To calculate the volume of cork needed, we can use the formula: Volume = Mass/Density. We know that the mass of the child is 40kg, so the volume of the child is 40kg/1.01g/cm^3 = 39.6039 cm^3.

To keep 20% of the child's volume above water, we need to find 20% of 39.6039 cm^3, which is 7.9207 cm^3. This is the amount of cork needed to keep 20% of the child's volume above water.

Now, to find the total volume of cork needed, we need to divide 7.9207 cm^3 by the density of the cork (0.28g/cm^3). This gives us a total volume of 28.29 cm^3 of cork needed to keep 20% of the child's volume above water.

I hope this helps! Let me know if you have any other questions or need further clarification. Good luck!