You are designing a hydraulic lift for an automobile garage. It will consist of two oil-filled cylindrical pipes of different diameters. A worker pushes down on a piston at one end, raising the car on a platform at the other end. To handle a full range of jobs, you must be able to lift cars up to 4000kg, plus the 600 kg platform on which they are parked. To avoid injury to your workers, the maximum amount of force a worker should need to exert is 100N.What should be the diameter of the pipe under the platform?
Can someone please explain how i should do this problem I have no idea
The maximum weight that has to be lifted is (4000 + 600) g = 45,080 N. The force applied to the other piston must must not exceed 100 N. The ratio of the diameters of the two pistons must be sqrt (45080/100) = 21.2
You seem to be missing an important piece of information: the diameter of the smaller piston that is "pushed" by the operator.
Then multiply that diameter by 21.2 to get the diameter of the piston that lifts the car and platform..
25cm is the other operator
Well, let's start by breaking down the problem. The lift consists of two pipes, one smaller in diameter than the other. The worker pushes down on a piston at one end, which raises the car on a platform at the other end. We need to find the diameter of the pipe under the platform.
To find the diameter, we can use the concept of pressure. Pressure is the force per unit area, and it can be calculated using the formula:
Pressure = Force / Area
In this case, we want to find the maximum force the worker needs to exert, so we can rearrange the formula to:
Force = Pressure * Area
Since the maximum force the worker should exert is 100N, we can replace "Force" in the formula with 100N:
100N = Pressure * Area
Now, let's consider the situation when the lift is lifting the maximum load. The maximum load consists of the weight of the car (4000kg) plus the weight of the platform (600kg).
Total Weight = 4000kg + 600kg
To find the pressure exerted on the piston, we can divide this total weight by the area of the smaller pipe. The area of a cylinder can be calculated using the formula:
Area = π * radius^2
Let's assume the radius of the smaller pipe is "r". So, the area of the smaller pipe is:
Area = π * r^2
Now, we can substitute this into the equation:
100N = (Total Weight) / (π * r^2)
We can simplify this equation to:
r^2 = (Total Weight) / (100N * π)
And then solve for r:
r = √((Total Weight) / (100N * π))
Finally, to find the diameter of the pipe, we double the radius:
Diameter = 2 * r = 2 * √((Total Weight) / (100N * π))
Now, plug in the values for the weights, the maximum force, and the value of π, and you should be able to calculate the diameter of the pipe under the platform.
Hope this helps you lift those cars safely!
To determine the diameter of the pipe under the platform, we can use Pascal's law, which states that the pressure applied to a fluid in a closed system is transmitted equally in all directions. In this case, the pressure exerted by the worker pushing down on the piston will be transmitted through the fluid to lift the car and the platform.
First, let's calculate the weight of the car and the platform combined. Given that the car weighs 4000 kg and the platform weighs 600 kg, the total weight is 4000 kg + 600 kg = 4600 kg.
Next, we need to calculate the force required to lift this weight. Since force is equal to mass multiplied by acceleration due to gravity (F = m * g), and the acceleration due to gravity is approximately 9.8 m/s^2, the force required to lift the weight is F = 4600 kg * 9.8 m/s^2 = 45,080 N.
Now, since the maximum force a worker should exert is 100 N, we have to find a way to multiply the worker's force by a certain factor to achieve the required 45,080 N force to lift the weight.
By using Pascal's law, we know that pressure is directly proportional to force applied and inversely proportional to the surface area on which the force is exerted. Therefore, if we have a smaller diameter pipe, the pressure will be higher, requiring less force from the worker.
Now, we can calculate the surface area required on the pipe under the platform, using the formula A = F / P, where A is the area, F is the force, and P is the pressure exerted.
So, A = 45,080 N / 100 N = 450.8 m^2.
Finally, we can calculate the diameter of the pipe using the formula A = πr^2, where A is the area and r is the radius of the pipe.
By rearranging the formula, r = √(A / π), we can solve for the radius.
Substituting the calculated area, r = √(450.8 m^2 / π) = √(143.6 m^2) ≈ 11.99 m.
Since the diameter is equal to twice the radius, the diameter of the pipe should be approximately 2 * 11.99 m = 23.98 m or rounded to 24 m.
Therefore, the diameter of the pipe under the platform should be approximately 24 meters.