# Solving Static Equilibrium: Force at Support & Left End

• ehabmozart
In summary, the problem involves a 3.00 m diving board with a diver weighing 490 N standing at the free end, supported by a point 1.00 m from the end. The board itself weighs 295 N. The force at the support is pointing upwards and the force at the left end could be either up or down, depending on the direction of the applied force. Both the net torque and net force must be equal to zero for equilibrium to occur in an extended body like a diving board.
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

## 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!

ehabmozart said:
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.

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.

ehabmozart said:
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?

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.

## 1. What is static equilibrium?

Static equilibrium is a state in which all the forces acting on an object are balanced, resulting in no net force and no acceleration. This means that the object is either at rest or moving at a constant velocity.

## 2. How do you determine the force at the support in a static equilibrium scenario?

The force at the support can be determined by taking the sum of all the forces acting on the object and setting it equal to zero. This is known as the equation of static equilibrium. By solving this equation, the force at the support can be calculated.

## 3. What is the significance of solving for the force at the left end in a static equilibrium problem?

The force at the left end is important because it represents the external force acting on the object. This force can be used to determine the stability of the object and whether it will remain in static equilibrium or not.

## 4. What are some common mistakes when solving for static equilibrium?

One common mistake is forgetting to include all the forces acting on the object, including any external forces. Another mistake is not properly setting up the equation of static equilibrium, which can lead to incorrect calculations.

## 5. How can static equilibrium be applied in real-world scenarios?

Static equilibrium is commonly used in engineering and physics to analyze the stability of structures, such as bridges and buildings. It is also used in designing and balancing objects, such as see-saws and wheelbarrows, to ensure they remain in equilibrium.

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