Solving Static Equilibrium: Force at Support & Left End

[ehabmozart]

Homework Statement

A diving board of length 3.00 m is supported at a point 1.00 m from the end, and a diver weighing 490 N stands at the free end . The diving board is of uniform cross section and weighs 295 N. Find the force 1) by the support 2) at the left end

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Homework Equations

Static equllibrium equations

The Attempt at a Solution

I have a ONE big doubt. I understand that the support would point upwards since it is just like normal forces. What about the force at the left end. Where will it point and why?
Another general doubt is about equllibrium. When should we use tau net is equal to zero and when should we use the total net force is equal to zero and when should we use both .. Thanks for helping!

 

[Doc Al]

I have a ONE big doubt. I understand that the support would point upwards since it is just like normal forces. What about the force at the left end. Where will it point and why?

What do you think? If you replaced that structure with your hand, would you have to pull up or push down?

When in doubt GUESS. Then when you solve for the unknown force, you'll find out if you guessed the correct direction since you'll get a positive value.

Another general doubt is about equllibrium. When should we use tau net is equal to zero and when should we use the total net force is equal to zero and when should we use both ..

For equilibrium, both conditions must be met. The net torque equal to zero only applies with an extended body, such as a diving board.

 

[ehabmozart]

For the first part, why is there even a force at the end, there is a support. I mean the left hand could be either up or down.

 

[Doc Al]

For the first part, why is there even a force at the end, there is a support. I mean the left hand could be either up or down.

I don't understand what you mean. If you removed the structure, what do you think would happen to the board and diver?

 

[Nickie]

As a scientist, it is important to understand the concept of equilibrium and how it applies to this scenario. In this case, the diving board is in a state of static equilibrium, meaning that the forces acting on it are balanced and there is no net force or torque causing it to move. In order to solve for the force at the support and the left end, we can use the equations for static equilibrium.

First, we need to draw a free-body diagram of the diving board, showing all the forces acting on it. In this case, there are three forces: the weight of the diver (490 N) acting downwards at the free end, the weight of the diving board (295 N) acting downwards at the center of mass, and the reaction force from the support acting upwards at the support point.

To solve for the force at the support, we can use the equation for vertical equilibrium: ΣFy = 0. This means that the sum of all the vertical forces must equal zero. Since we know the weight of the diver and the diving board, we can plug those values in and solve for the reaction force from the support.

To solve for the force at the left end, we can use the equation for torque equilibrium: Στ = 0. This means that the sum of all the torques acting on the diving board must equal zero. Torque is calculated by multiplying the force by the distance from the pivot point (in this case, the support). We can set up an equation with the weight of the diver and the reaction force from the support as the two forces, and solve for the distance from the pivot point. This will give us the distance from the free end to the left end, where the force will be acting.

In terms of your general doubts, it is important to use both equations for equilibrium in different situations. In this scenario, we used the vertical equilibrium equation to solve for the force at the support, and the torque equilibrium equation to solve for the force at the left end. Both equations are necessary to fully understand the forces acting on the diving board in this static equilibrium scenario.