# Force Required to Tip a Block of wood?

• melancholy2
In summary, a person had good results pulling tablecloths out from under objects and noticed a wooden block would tip and stand up if pulled with enough force. They asked for help calculating the minimum force needed for this effect and the best pivot point to use. Another person suggested using a non-inertial frame and adding a pseudoforce at the block's center of mass to analyze the motion. The original person was still unsure of how to find the force needed and where to place the pivot. The second person clarified that the imaginary force would be equal to the accelerating force and suggested using the lower left edge as the pivot point.
melancholy2
Hi everyone,

Please refer to the attached diagram.

I was playing around with pulling tablecloths out from the bottom of plates and objects resting on it, and was getting good results. I also happened to have a cuboid wooden paperweight which was on the table cloth and I noticed that that wooden block would tip and stand up if I didn't pull hard enough (but enough to make it tip).

This got me thinking how I would calculate the force required to be exerted on the block in order to achieve this effect. I haven't been able to figure out anything yet, so I would like some inputs. I reformed the effect in the form of a question:

A block of wood with mass M, height h and length l is placed on a smooth frictionless surface. A force F is applied at the bottom left edge of the wooden block, causing it to pivot at that edge, counter-clockwise upwards till it is standing up. Find the minimum force required.

If one were to consider moments, where would one use as a pivot? If it were at the bottom edge, then F wouldn't generate a torque, and it wouldn't tip. Anywhere else on the cube and the pivot will also rise (will that cause any problems?).

#### Attachments

• forcerequired.JPG
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Realize that as soon as you apply the force F, the block will accelerate. The easiest way to analyze the motion is from the view of the non-inertial frame co-moving with the block. In that frame you need to add a pseudoforce that acts at the block's center of mass. In effect you'll have two forces exerting a torque about the lower left hand corner (a fine pivot point)--figure out when one is great enough to overcome the other.

Doc Al said:
Realize that as soon as you apply the force F, the block will accelerate. The easiest way to analyze the motion is from the view of the non-inertial frame co-moving with the block. In that frame you need to add a pseudoforce that acts at the block's center of mass. In effect you'll have two forces exerting a torque about the lower left hand corner (a fine pivot point)--figure out when one is great enough to overcome the other.

Thanks for the help but I still can't figure out how much that imaginary force would be. Will taking the view of the non-inertial frame comoving with the block, would that also affect how I find force F (which I have to minus the accelerating force?). I have no clue where to place the pivot given that it will rise when the block starts tipping.

Viewed from a non-inertial frame that accelerates to the right, there will be an imaginary force to the left equal to ma. Since F is the accelerating force, the imaginary force will equal F. As I said before, use the lower left edge as your pivot.

## 1. What factors affect the force required to tip a block of wood?

The force required to tip a block of wood depends on several factors, such as the weight and size of the block, the surface it is resting on, and the angle at which the force is applied. The location of the force also plays a role, as pushing closer to the edge of the block requires less force than pushing at the center.

## 2. How can I calculate the force required to tip a block of wood?

The force required to tip a block of wood can be calculated using the formula: Force = Weight x Distance x sin(θ), where θ is the angle at which the force is applied. The weight can be measured in pounds or kilograms, and the distance can be measured in feet or meters.

## 3. Can the force required to tip a block of wood be affected by its shape?

Yes, the shape of the block of wood can affect the force required to tip it. A block with a wider base and a lower center of gravity will require more force to tip than a taller and narrower block with the same weight. This is because the wider base provides more stability.

## 4. What is the minimum force required to tip a block of wood?

The minimum force required to tip a block of wood will vary depending on the factors mentioned earlier. However, in general, a force equal to or greater than the weight of the block will be required to tip it. This is known as the tipping point, where the force applied overcomes the block's weight and center of gravity.

## 5. Can the force required to tip a block of wood be reduced?

Yes, the force required to tip a block of wood can be reduced by increasing the block's stability. This can be achieved by increasing the weight of the block, increasing the size of its base, or lowering its center of gravity. Additionally, applying the force closer to the base of the block rather than the top can also reduce the required force.

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