Statics of body in two dimensions

[togo]

Homework Statement

Homework Equations

A 50 lb force is applied to a corner plate as shown. Determine an equivalent system consisting of a 150 lb force at B and another force at A.

The Attempt at a Solution

There is an algebraic solution to the problem, but I was wondering if it was possible to solve this problem using a table of moments and forces?

the Fx = 25 lb and Fy = 43.3 lb.

Thanks

 

[Spinnor]

First write down what you know.

We have a force at B and a force at A with components,

Bx, By, Ax, Ay.

We know the magnitude of B is √(Bx^2 + By^2) = 150 lbs.

We are given a force F = Fx i + Fy j

You know Fx = Ax + Bx and Fy = Ay + By

And we can take moments about points A and B (and at the point where F acts) to get two (three) more equations.

Its just a lot of algebra after that?

 

[togo]

a table like this:

if course it wouldn't be measured in kips, it would be measured in lbs.

 

[togo]

Let's abandon the table idea. Can someone explain to me why, in the solution to this problem, (part b) they say "Having found the direction of the forces P and P', we complete the solution..."

when as you can see in the photo, there is no indication of the direction of the force P', although P was solved for. (the solution seems to come after this sentence which confuses me). Thanks.

this is the missing information. Please help; there are no tutors available for this course, the teacher isn't available, and its getting extremely hard to find help.

 

[rwisz]

for your question! I would like to point out that the use of tables of moments and forces is a common and effective approach to solving problems in statics. However, in this particular problem, it may not be the most efficient method.

To solve this problem using a table of moments and forces, we would first need to construct a free-body diagram and then apply the equations of equilibrium (sum of forces and sum of moments) to find the unknown forces at points A and B. This process can be time-consuming and may require multiple iterations to arrive at the correct solution.

On the other hand, the algebraic approach involves using basic trigonometry and vector addition to find the magnitudes and directions of the unknown forces at A and B. This method is often faster and more straightforward.

In conclusion, while it is possible to solve this problem using a table of moments and forces, the algebraic approach may be more efficient in this case. However, it is always beneficial to have multiple problem-solving techniques in your toolkit as different problems may require different approaches.