How High Can Two Students Lift an Elephant Using a Hydraulic Lift?

[zuN]

Homework Statement

The 70kg student in the figure balances a 1200kg elephant on a hydraulic lift. A second 70kg student joins the first student. How high do they lift the elephant?
diameter of the piston elephant is on = 2.0m
diameter of the piston student is on = 0.48m
The liquid inside the lift is oil, therefore rho = 900 kg/m³
Out would be elephant, In would be the students

Homework Equations

Fout/Fin = Aout/Ain
F_out=A_out/A_in x F_in - $$\rho$$ghA_out

The Attempt at a Solution

I tried both equations
Fout/Fin = Aout/Ain
(rho x g x h x Aout) / (140 x 9.8) = (pi x 1²) / (pi x 0.24²)
which ended giving me h = 0.86m which was wrong.

When i tried it with the other equation i ended up with 0.44m which was wrong as well.

I am not sure if I'm using the wrong formula though so someone please give me some guidance.

 

[anathema]

it is important to always use the correct formula and units in order to accurately solve a problem. In this case, the correct formula to use would be the Pascal's principle which states that pressure applied to a confined fluid is transmitted equally in all directions. This principle can be applied to the hydraulic lift in order to determine the height at which the elephant is lifted.

The equation for Pascal's principle is P1 = P2, where P1 is the initial pressure and P2 is the final pressure. In this case, P1 is the pressure exerted by the students on the smaller piston and P2 is the pressure exerted by the oil on the larger piston.

Using the given information, we can calculate the pressure exerted by the students on the smaller piston. We know that the force exerted by the students is equal to the weight of the elephant, which is 1200kg x 9.8m/s^2 = 11760N. This force is spread over the area of the smaller piston, which is pi x (0.48/2)^2 = 0.18m^2. Therefore, the pressure exerted by the students is 11760N/0.18m^2 = 65333Pa.

Now, we can use Pascal's principle to calculate the final pressure exerted by the oil on the larger piston. We know that the area of the larger piston is pi x (2/2)^2 = 3.14m^2. Therefore, the final pressure exerted by the oil is 65333Pa/3.14m^2 = 20832Pa.

Finally, we can use the equation P = rho x g x h to calculate the height at which the elephant is lifted. Rearranging the equation, we get h = P/(rho x g) = 20832Pa/(900kg/m^3 x 9.8m/s^2) = 2.26m.

Therefore, the height at which the elephant is lifted is approximately 2.26m. It is important to always double check your units and make sure they are consistent throughout the calculation. I hope this helps and good luck with your studies!

 

[baba89]

Based on the information provided, it seems like you are using the correct equations to solve for the height that the students can lift the elephant. However, there may be a few factors that you are not taking into account.

Firstly, it is important to note that the equation you are using assumes that the lift is operating at maximum efficiency. This means that there is no loss of energy due to friction or other factors. In reality, there will always be some energy loss, so the actual height that the students can lift the elephant may be slightly lower than the calculated value.

Additionally, it is possible that the students may not be able to lift the elephant at all, depending on the strength and capabilities of the hydraulic lift system. The students may reach their maximum force output before they are able to lift the elephant to the desired height.

Furthermore, the diameter of the piston the elephant is on (2.0m) is significantly larger than the diameter of the piston the students are on (0.48m). This means that the force required to lift the elephant will be distributed over a larger area, making it more difficult for the students to lift the elephant.

Overall, while your calculations may be correct, there are other factors that need to be taken into consideration when determining the maximum height the students can lift the elephant. It is important to consider the capabilities of the hydraulic lift system and the physical limitations of the students.