Minimum force to tip the bin over

In summary, the minimum force required to tip a bin over depends on several factors, including the bin's height, weight distribution, and the point of application of the force. To calculate the tipping point, one must consider the center of gravity, the base of support, and the angle at which the force is applied. By applying force at the right height and direction, the bin can be tipped over with the least amount of effort.
  • #1
sdfsfasdfasf
75
12
Homework Statement
x
Relevant Equations
M = F x D
1713800647166.png

I am stuck on part b) i). I understand that there is no normal force from the ground as the bin is on the point of being lifted off the ground, that is all fine. That leaves R, F and W.

I know W is 40g, and I am required to calculate F, therefore it makes most sense to take moments about the wheel such that the force R is ignored. I want to find the force F such that the total moment is 0. I do not know the perpendicular distance from the line of action of F to the wheel, nor do I know the perpendicular distance from the line of action of the vertical component of F to the wheel. All I know is the perpendicular distance from the line of action of the horizontal component, which is clearly 1.3.

Are we meant to ignore the vertical component and just write 40g(0.3) = Fcos(20)(1.3)? This gives me the correct answer but I do not see why we should ignore the vertical component.

Thank you all so much!
 
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  • #2
You are correct. Ignoring the vertical component is wrong based on the image and you would need the horizontal moment arm to account for it correctly.
 
  • #3
1713803228888.png

This is the markscheme provided, does it provide any insight as to what the author has done?
 
  • #4
Yes, the author is simply wrong.
 
  • #5
I suppose they have assumed that the handle is vertically above the wheel? Such that the line of action of the vertical component goes through the wheel itself and therefore doesn't provide any moment?
 
  • #6
Most likely, but this is clearly not the case based on the picture and there is no mention of this assumption in the problem statement. That makes it wrong in my opinion. Particularly as an image is provided where this is not the case.
 
  • #7
This is taken straight from an A-Level Physics Examination which is the highest level of examination in the UK you can take before university. :mad:
 
  • #8
Whoever constructed that clearly had a slip of mind and it should obviously not have passed quality control. Alternatively a case of the illustrator taking liberties to make the picture more realistic…
 

FAQ: Minimum force to tip the bin over

What factors determine the minimum force required to tip a bin over?

The minimum force required to tip a bin over is influenced by several factors, including the bin's height, width, weight, center of mass, and the friction between the bin and the surface it rests on. The tipping point occurs when the applied force creates a moment about the pivot point that exceeds the restoring moment due to gravity.

How is the center of mass related to tipping a bin?

The center of mass is the point where the mass of the bin is concentrated. When a force is applied, it creates a torque about the pivot point (usually the edge of the base). If the applied torque exceeds the torque due to the weight of the bin acting through its center of mass, the bin will tip over. Thus, a higher center of mass makes it easier to tip the bin.

Does the surface type affect the minimum force needed to tip the bin?

Yes, the surface type affects the friction between the bin and the ground, which in turn influences the minimum force required to tip it over. A rough surface increases friction, making it harder to tip the bin, while a smooth surface reduces friction, requiring less force to achieve the tipping point.

How can I calculate the minimum force required to tip a bin?

To calculate the minimum force required to tip a bin, you can use the formula: F = (W * d) / h, where F is the force, W is the weight of the bin, d is the distance from the pivot point to the center of mass, and h is the height of the center of mass above the pivot point. This formula helps determine the force needed to create a moment that will tip the bin.

Is there a difference in tipping a full bin versus an empty one?

Yes, there is a difference. A full bin typically has a greater weight, which increases the force required to tip it over. However, the distribution of weight and the position of the center of mass may also change depending on the contents, which can affect the overall stability and tipping point of the bin.

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