Frame/Machines- Statics Question

[megr_ftw]

Homework Statement

A floor jack is used to support a 2000 lbf load. Calculate the pressure exerted on the hydraulic fluid by the piston H if the piston has a diameter of 2 in. SHOW ALL WORK AND FBDs. Note: CDE is a solid, continuous member.
*I attached the diagram****

Homework Equations

F=ma

The Attempt at a Solution

I am unsure if there are any 2 force members. I really just need to know where to start because there are a lot of members in this problem. Do i need a FBD for all of them?
thanks

 

[KataKoniK]

for the help.



Thank you for your question. I am happy to assist you with solving this problem. To start, let's break down the problem into smaller steps and focus on the key components.

First, we need to determine the force exerted by the 2000 lbf load on the piston H. This can be calculated using the formula F=ma, where F is the force, m is the mass, and a is the acceleration. In this case, we can assume that the acceleration is 0 since the load is not moving, so the force exerted is simply 2000 lbf.

Next, we need to consider the pressure exerted on the hydraulic fluid by the piston. Pressure is defined as force per unit area, so we need to calculate the area of the piston to determine the pressure. The formula for area of a circle is A=πr^2, where r is the radius. In this case, the diameter of the piston is given as 2 inches, so the radius is 1 inch. Thus, the area of the piston is π(1 in)^2 = π in^2.

Now, we can use the formula for pressure, P=F/A, to calculate the pressure exerted by the piston. Plugging in our values, we get P=2000 lbf / π in^2 = 637.5 lbf/in^2. This is the pressure exerted on the hydraulic fluid by the piston H.

To show this visually, we can create a free body diagram (FBD) for the piston H. The FBD will include the force exerted by the 2000 lbf load, as well as the reaction force from the hydraulic fluid pushing back on the piston. The FBD will also show the area of the piston, which we have already calculated.

I have attached a diagram to help explain this solution. I hope this helps you understand the problem better. Please let me know if you have any further questions or need clarification on any of the steps.
Scientist

 

[Mene]

I would first start by identifying the main components of the problem and drawing a free body diagram for each one. In this case, the main components are the floor jack, the 2000 lbf load, and the hydraulic piston.

For the floor jack, the forces acting on it are the reaction forces from the ground and the force from the hydraulic piston pushing down. The free body diagram for the floor jack would show these forces acting on it.

For the 2000 lbf load, the only force acting on it would be its weight, which can be calculated using the equation F=ma, where m is the mass and a is the acceleration due to gravity.

For the hydraulic piston, the forces acting on it are the pressure from the hydraulic fluid and the reaction force from the load. The free body diagram for the piston would show these forces acting on it.

To solve for the pressure exerted on the hydraulic fluid, we can use the equation P=F/A, where P is pressure, F is force, and A is area. In this case, the force is the reaction force from the load, which can be calculated using F=ma, and the area is the cross-sectional area of the piston, which is given as 2 in. We would need to convert this to square inches (in^2) to use in the equation.

Once we have all the necessary information from the free body diagrams and equations, we can plug them in and solve for the pressure exerted on the hydraulic fluid by the piston H. It is important to show all the work and calculations to ensure accuracy and understanding of the problem.

In conclusion, as a scientist, I would approach this problem by breaking it down into smaller components, drawing free body diagrams for each one, and using relevant equations to solve for the desired quantity.