Calculate Moment Across Board w/ 3 Roller Pins & Weight

[REM683]

I have a problem with a board laid across 3 roller pins each spaced out x feet. Past point C is another X feet with a box of W Weight. I need to the distance the box needs to be from point C for the board to tip/rotate.

I was thinking of calculating the moment across the entire length of the board but was not exactly sure. Also how would I take into consideration the weight of the board?

Thanks

 

[Doc Al]

I was thinking of calculating the moment across the entire length of the board but was not exactly sure.

Not sure what you mean. When the board starts to tip, about which roller will it pivot? Use that point as your axis for measuring torques.

Also how would I take into consideration the weight of the board?

The weight of the board can be considered to act at what point?

 

[REM683]

The 15 foot boards mass is uniformly distributed with 10 feet of the board to the left and 5 feet to the right of the pivot point. The box being on the right distance x.

 

[Doc Al]

The 15 foot boards mass is uniformly distributed

What does that tell you about where the board's weight acts?

 

[Nickie]

To calculate the moment across the board, we first need to determine the forces acting on the board. The three roller pins will each exert a normal force on the board, and there will also be the weight of the board itself. The box of weight will also exert a force on the board.

To find the distance the box needs to be from point C for the board to tip/rotate, we can use the principle of moments, which states that the sum of all moments acting on an object is equal to zero when the object is in equilibrium. In this case, we can set the sum of the moments equal to zero and solve for the distance of the box from point C.

To take into consideration the weight of the board, we can treat it as a distributed load and calculate its weight per unit length. This weight can then be included in the calculation of the moment.

It is also important to consider the distribution of the weight on the board. If the weight is evenly distributed, we can use the center of mass of the board to calculate the moment. However, if the weight is not evenly distributed, we will need to take into account the varying weight distribution along the length of the board.

I hope this helps with your calculation. Please let me know if you have any further questions or need any clarification.