Calculating Cork Volumes for Amusement Park Water Slide

[tiz_07]

An amusement park is planning to build a water slide, and the park owners would like to use giant corks with density 0.28 g/cm^3 as "floats" for young children. What volume of cork is needed to keep 20% (by volume) of a 40 kg child above the water at the base of the slide (assuming the density of the child is 1.01 g/cm^3).:yuck:

 

[Pyrrhus]

This is an Archimedes principle problem. What have you done?

 

[quicknote]

I would first like to commend the amusement park owners for considering the safety of young children on their water slide. Using giant corks as floats is a creative and potentially effective solution.

To calculate the volume of cork needed, we can use the formula V = m/d, where V is the volume, m is the mass, and d is the density. In this case, we are looking for the volume of cork needed to keep 20% of a 40 kg child above the water at the base of the slide.

First, we need to determine the mass of the child that needs to be supported by the cork. We can do this by multiplying the density of the child (1.01 g/cm^3) by the volume of the child (which we will represent as Vc). This gives us the equation: m = 1.01 g/cm^3 * Vc.

Next, we can calculate the total mass of cork needed by multiplying the mass of the child by the desired percentage (20%). This gives us the equation: mc = 0.2 * m = 0.2 * (1.01 g/cm^3 * Vc) = 0.202 g/cm^3 * Vc.

Finally, we can use the formula V = m/d to solve for the volume of cork needed (Vc). Plugging in the values we have calculated, we get the equation: Vc = mc / dc = (0.202 g/cm^3 * Vc) / (0.28 g/cm^3) = 0.725 cm^3.

Therefore, the amusement park will need approximately 0.725 cm^3 of cork to keep 20% of a 40 kg child above the water at the base of the slide. It is important to note that this is a rough estimate and may vary depending on the shape and size of the cork used. I would also recommend conducting further tests and calculations to ensure the safety and effectiveness of using giant corks as floats on the water slide.