What is the upward force exerted on the board by the support?

[alfredo24pr]

Homework Statement

A long uniform board weighs 62.6 N (12.5 lbs) rests on a support at its mid point. Two children weighing 317.0 N (63.4 lbs) and 500.0 N (100.0 lbs) stand on the board so that the board is balanced. What is the upward force exerted on the board by the support?

Homework Equations

F=ma

The Attempt at a Solution

I do not know even where to start. This is confusing

 

[AC130Nav]

Is there a reason why you wouldn't believe the equal and opposite force on the fulcrum wouldn't be the force of the sum of the weights (including the board)?

 

[alfredo24pr]

Is there a reason why you wouldn't believe the equal and opposite force on the fulcrum wouldn't be the force of the sum of the weights (including the board)?

lol! Is it really that simple?

 

[alfredo24pr]

lol! Is it really that simple?

yes it was the sum! I did not believe it was that simple. Thanks!

 

[rwisz]

and I do not know what to do.

The upward force exerted on the board by the support can be calculated using Newton's second law, which states that force is equal to mass multiplied by acceleration (F=ma). In this case, the board is not accelerating, so the net force on the board must be zero. This means that the upward force exerted by the support must be equal in magnitude to the downward forces exerted by the children.

To calculate the downward forces, we can use the weight of each child (mg), where g is the acceleration due to gravity (9.8 m/s^2). So the downward force exerted by the first child is 317.0 N and the downward force exerted by the second child is 500.0 N. Since the board is balanced, these two forces must be equal, so the upward force exerted by the support must also be 317.0 N and 500.0 N.

To find the total upward force exerted by the support, we simply add these two forces together: 317.0 N + 500.0 N = 817.0 N. So the upward force exerted by the support is 817.0 N.