Rectangular box tips over (or not)

In summary, the conversation discusses a problem involving a uniform rectangular wood block on an inclined plane with a coefficient of static friction. The question is to determine the relationship between the block's dimensions and the coefficient of friction in order for the block to tip over at a certain angle without slipping. The solution involves considering torque, normal force, and gravity.
  • #1
usamo42j
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0

Homework Statement


A uniform rectangular wood block of mass M, with length b and height a, rests on an incline as shown. The incline and the wood block have a coefficient of static friction, μs. The incline is moved upwards from an angle of zero through an angle θ. At some critical angle the block will either tip over or slip down the plane. Determine the relationship between a, b, and μs such that the block will tip over (and not slip) at the critical angle. The box is rectangular, and a ̸= b.


Homework Equations



Fs≤μs*F_n
τ=Fr*sinθ



The Attempt at a Solution



I'm assuming this has to do with torque. There is the normal force doing torque (right?) but that's all I could see. Perhaps gravity also does torque but I'm having trouble seeing how much the radius in the torque formula would be and where does the static friction coefficient come in?
 
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  • #2
Hi usamo,

Start with a picture, showing all the forces and torques.

ehild
 

1. Why does a rectangular box sometimes tip over?

A rectangular box may tip over due to an uneven distribution of weight or a shift in the center of gravity. If the weight is not evenly distributed, the box may become top-heavy and tip over. Similarly, if the center of gravity shifts outside of the base of the box, it can cause the box to lose balance and tip over.

2. How can I prevent a rectangular box from tipping over?

To prevent a rectangular box from tipping over, make sure the weight is evenly distributed inside the box. You can also try to increase the base of the box by adding support or using a wider box. Additionally, placing the heaviest items at the bottom of the box can help lower the center of gravity and prevent tipping.

3. Does the shape of the box affect its tendency to tip over?

Yes, the shape of the box can affect its tendency to tip over. A taller and narrower box is more likely to tip over compared to a wider and shorter box. This is because a taller box has a higher center of gravity, making it easier to lose balance.

4. Can the surface on which the box is placed affect its stability?

Yes, the surface on which the box is placed can affect its stability. A smooth and even surface can provide better support and stability compared to a rough or uneven surface. Additionally, a surface with a higher coefficient of friction can help prevent the box from sliding and tipping over.

5. Is there a maximum weight limit for a rectangular box to prevent it from tipping over?

The maximum weight limit for a rectangular box to prevent it from tipping over depends on various factors such as the size and shape of the box, the distribution of weight, and the surface on which it is placed. It is important to consider these factors to ensure the box can support the weight and maintain its stability.

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