Fluid Questions I'm Really Confused

[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


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??
Please help!

 

[Nate810]

A. To calculate how many apples it would take to hold up your car, you will need to calculate the force exerted by the car on the piston. This can be done by multiplying the mass of the car (12000kg) by the acceleration due to gravity (9.8 m/s^2) to get 118,000 N of force. Then, divide that force by the weight of a single apple (1 N) to get 118,000 apples. B. To calculate the number of apples required to support the car at 0.15m, you must first calculate the force required to lift the car at this height. This can be done by multiplying the mass of the car (12000kg) by the acceleration due to gravity (9.8 m/s^2) and then subtracting the weight of the oil in the lift (800 kg/m^3 x 0.15m = 120 kg x 9.8 m/s^2 = 1176 N). Then, divide that force by the weight of a single apple (1 N) to get 1176 apples.

 

[wais]

Hi there! I can definitely understand your confusion, those questions can seem a bit overwhelming at first. Let's break them down and see if we can make sense of them together.

For the first question about the water slide, it's asking for the volume of corks needed to keep 20% of a 40kg child above water. To start, you need to find the volume of the child that is submerged in water. This can be found by dividing the weight of the child (40kg) by the density of water (1.01g/cm^3). This gives us a volume of 39.6L.

Next, we need to figure out how much volume the corks need to take up in order to keep 20% of the child's volume above water. This can be found by multiplying the child's submerged volume by 20% (or 0.2). This gives us a volume of 7.92L.

Now, we can use the density of the corks (0.28g/cm^3) to calculate the mass of the corks needed to fill that volume. This can be found by multiplying the density by the volume (7.92L) and then converting to kilograms (since the child's weight is given in kilograms). This gives us a mass of 2.22kg.

So, to keep 20% of the child's volume above water, we would need approximately 2.22kg of corks.

For the second question about the hydraulic lift, it's asking for the number of apples needed to hold up the car on the input piston and at a height of 0.15m. This question is all about balancing forces.

To hold up the car, the force exerted by the apples on the input piston needs to be equal to the weight of the car (which we can find by multiplying the mass of the car by the acceleration due to gravity, 9.8m/s^2).

So, to find the number of apples needed on the input piston, we can divide the weight of the car (in Newtons) by the weight of one apple (also in Newtons). This will give us the number of apples needed.

For the second part of the question, at a height of 0.15m, the force exerted by the apples on the input piston will be equal to the weight of the car plus the