Equilibrium of Objects: Finding Reactions of a Diving Board with Weights

[lukasz08]

Homework Statement

A_________B____________Wd_________Wp_
|--1.2m--|----1.2m------|---2.2m-----|

Above is a diving board with 2 weights on it. determine the reactions of A and B
wd= 36kg = weight of diving board
wp= 54kg = weight of person standing on diving board
point A = pin support
point B

Homework Equations

Ok so the sum of the forces in the x and y directions are as follows x = 0 because their are no x components. Y = -54gk(9.81m) + (-36kg(9.81m)) = 529.74 + 353.16 = -882.9N. After this i do not know what to do.

The Attempt at a Solution

Answers are Ax= 0, Ay = -1870N, By=2740N

 

[lukasz08]

Nevermind i have figured it out

 

[piercas]

it is important to approach problems like this with a systematic and logical approach. It seems like you have started off correctly by identifying the given values and setting up the sum of forces equations. However, it is important to also consider the moments of the forces acting on the diving board.

To find the reactions at points A and B, we can use the equations of static equilibrium, which state that the sum of forces and the sum of moments must both equal zero. In this case, we can set up the following equations:

Sum of forces in the x-direction: Ax + Bx = 0
Sum of forces in the y-direction: Ay + By - 54kg(9.81m/s^2) - 36kg(9.81m/s^2) = 0
Sum of moments about point A: By(2.2m) - 54kg(9.81m/s^2)(1.2m) = 0

Solving these equations simultaneously, we can find that Ax = 0, Ay = -1870N, and By = 2740N. It is important to note that the negative sign for Ay indicates that the reaction at point A is acting downwards, as expected for a pin support.

In addition, it is always a good idea to check your answer by plugging the values back into the original equations and making sure they equal zero. In this case, we can check that Ax + Bx = 0, Ay + By = 0, and By(2.2m) - 54kg(9.81m/s^2)(1.2m) = 0, confirming our solution.

Overall, it is important to approach equilibrium problems with a clear understanding of the principles involved and to carefully set up and solve the necessary equations.