Easy pressure and fluid problemsi swear

[Dantes]

easy pressure and fluid problems..i swear :)

Got some (what I think) are easy pressure and fluid problems.

A 23.5 kg woman balances on one heel of a pair of high-heeled shoes.The acceleration of gravity is 9.8 m/s^2 :If the heel is circular with radius 0.225 cm,
what pressure does she exert on the floor? Answer in units of N/m^2.

On this one I been doing (23.5*9.8)/((.225 x 10^-2)^2*pi) and i get 1448.03 without the conversion to meters i get 14480348.99 which seems a little high. But 1448.03 is wrong..what am i doing wrong.

A Ping-Pong ball has a diameter of 1.79 cm and average density of 0.0377 g/cm^3.The acceleration of gravity is 9.8 m/s^2 :What force would be required to hold it completely submerged under water? Answerin units of N.

On this one I got the volume of the ping ball by 4/3*pi*(1.79/2)^3 which came out to be 3.003 cm^3 and when applying the bouyant force equation of B = p sub f * volume of the object * gravity I get 29429.4 N which comes out to be wrong. Do i need to take that number and multiply it by the area for the force? The numbers seem really high.

A homogeneous solid object floats on water with 69 percent of its volume below the surface. The same object when placed in a second liquid floats on that liquid with 66 percent of its volume below the surface. Find the density of the object. Answer in units of kg/m^3. Also what is the specific gravity of the liquid?

On this one i have no idea where to start since it doesn't give me any densities of the liquids other then water which i can only assume to be fresh water with 1.0 X 10^3.

Any help on these would be great sort of want to learn this stuff and not be doubt with the answers I get are right or not.

 

[Fermat]

Q1: you're out by a factor of 10. Ans is 14,480.35 N/m²

Q2: the density of water is 1 gm/cc. The volume of the displaced water is 3 cm^3. So the mass of the displaced water is about 3 gm. Convert that to kg and multiply by g to get the bouyant force

Q3: sorry, no time to answer.

 

[quicknote]

I would first like to commend you for taking the time to work through these problems and for seeking clarification on any areas where you may be unsure. It shows a dedication to learning and understanding the concepts, which is crucial in scientific research.

Regarding the first problem, you are correct in using the formula P = F/A, where P is pressure, F is force, and A is the area. However, it seems that you may have made an error in converting the units. The radius should be converted to meters (0.225 cm = 0.00225 m) and the mass should be converted to kg (23.5 kg). This will give you a pressure of 1448.03 N/m^2, which is the correct answer.

For the second problem, you have correctly calculated the volume of the ping-pong ball. However, the buoyant force equation you are using is not quite correct. The correct equation is B = pVg, where p is the density of the fluid, V is the volume of the object, and g is the acceleration due to gravity. Using the given density of the ball (0.0377 g/cm^3), the volume you calculated (3.003 cm^3), and the acceleration due to gravity (9.8 m/s^2), you should get a buoyant force of 0.111 N. This is the force required to hold the ball completely submerged under water.

For the third problem, you are correct in assuming that the density of water is 1.0 x 10^3 kg/m^3. To solve this problem, you can use the formula for specific gravity, which is the ratio of the density of the object to the density of the liquid. In this case, the specific gravity is equal to 0.69 for the first liquid and 0.66 for the second liquid. Using these values and the known density of water, you can solve for the density of the object and the specific gravity of the second liquid.

I hope this helps clarify any confusion and allows you to confidently solve these problems. Keep up the good work!