154 votes
Accepted

Why is the shape of a hanging chain not a "V"?

The V shape makes sense for an ideal chain with all of its mass concentrated at the midpoint (with the rest of the chain being massless). But now consider a chain with its mass distributed over 3 ...
PM 2Ring's user avatar
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71 votes

Why is the shape of a hanging chain not a "V"?

Sorry to put in my contribution so late in the proceedings, but I don't think anyone has yet presented this simple argument based on forces… Suppose the chain did hang in a V shape. Consider a small ...
Philip Wood's user avatar
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64 votes

Why is the shape of a hanging chain not a "V"?

The V has a higher gravitational potential energy than the catenary does. To see this, consider pulling down at the center of the catenary very hard. As you pull down, the chain deforms into a V. But ...
knzhou's user avatar
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50 votes
Accepted

Why are arched bridges stronger than flat bridges?

Fracture happens under tension - that is, when you pull on something hard enough, it rips. The key to understanding the arc design hinges on understanding that it lowers the maximum tensile force. ...
Floris's user avatar
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37 votes

Plank overhanging off a building — where does the normal force go?

Adding to Chemomechanics' answer, the resulting forces is dependent also on the plank's geometry and material. Here's the behaviour of a particular material and geometry of a plank. Fine, it's ...
Passer By's user avatar
  • 506
33 votes
Accepted

Hanging a hammer from a table and a stick so that its midpoint is outside of the support of the table

The ruler is actually being supported by the handle of the hammer to provide two points of support so the downward force from the string lies between the two and the system balances. Moment on the ...
Lio Elbammalf's user avatar
24 votes
Accepted

Why does the curve of a hanging chain not minimize the area below it?

What is wrong with your argument is this paragraph: If we imagine the chain as having many small segments, then the potential energy of each segment is $E_p=mgh$. As the number of small segments ...
John Hunter's user avatar
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23 votes

Why does the curve of a hanging chain not minimize the area below it?

To put the accepted answer in mathematical terms, if you have a curve $y(x)$, hanging fixed at $x_0$ and $x_L$ at an height $h=y(x_0)=y(x_L)$, of total length $L$ and mass $M$ then then linear mass ...
JalfredP's user avatar
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22 votes

Hanging a hammer from a table and a stick so that its midpoint is outside of the support of the table

You can make two free body diagrams. One for the plank (with pink arrows), and one for the hammer (with blue arrows). Then examine if the forces can balance out. The reaction force on the plank from ...
John Alexiou's user avatar
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21 votes
Accepted

What holds up the lowest point of a rope following a catenary curve?

That lowest point is not exactly horizontally aligned with the neighboring points. It is slightly below. If it wasn't, then, as you describe, there would be a net vertical force downwards. If that ...
Steeven's user avatar
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20 votes
Accepted

Plank overhanging off a building — where does the normal force go?

Of the existing answers, one suggests that the reaction force can be represented by two forces, whereas the other says that the force is a distributed force. These aren't incorrect, but they aren't ...
Chemomechanics's user avatar
16 votes

Why is the normal contact force horizontal on an inclined ladder?

Think about how a ladder stands up in real life. Would the ladder stay in the orientation shown in your image if the ground were ice? No! The reason? Friction. The friction force, represented by $\...
Bunji's user avatar
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15 votes

Is the weight of something being dropped the same as the force of something being static?

Your foot brings the falling block rapidly to rest. Suppose the block has been dropped from a height of 0.90 m above the top of your foot. When it reaches the top of your foot it will be falling at 4....
Philip Wood's user avatar
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13 votes

Objects falling from table

If the centre of gravity of the object is vertically above the edge of the table then the object is in equilibrium. However, this equilibrium position is unstable (like a pencil balanced on its point) ...
gandalf61's user avatar
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13 votes

Plank overhanging off a building — where does the normal force go?

It is really a distribution of small force pieces across the entire plank-roof surface. But it can be simplified as two forces, one at the edge of the building, and the other at the other end of the ...
naturallyInconsistent's user avatar
12 votes
Accepted

What is the role of pillars in bridges?

There are three reasons: Moment of the forces In order for the structure to be stable, not only the vector sum of the forces must be zero $$\sum \vec F =0 \tag{1}$$ the total moment of the forces ...
valerio's user avatar
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10 votes

What holds up the lowest point of a rope following a catenary curve?

The rope is continuous and of uniform density. The amount of mass any small segment has depends on how long this segment is. At exactly the center you either have a segment of zero length and hence ...
John Alexiou's user avatar
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10 votes

Plank overhanging off a building — where does the normal force go?

For vertical equilibrium the normal reaction force must equal the weight of the plank. But that force is distributed over the length $L_2$ varying linearly from the ledge of the building to the other ...
Bob D's user avatar
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7 votes

Hanging a hammer from a table and a stick so that its midpoint is outside of the support of the table

I don't know what question other people are trying to answer, but the real answer is simple: yes, the center of mass is in the metal part, or in the few centimeters of wood that are still under the ...
milo's user avatar
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7 votes

How can we differentiate a statics and dynamics problem?

I will offer some general advice on how to handle ambiguity in a question, and how to tackle hard problems. First, if you think a question is ambiguous, meaning you think the words have more than one ...
Andrew Steane's user avatar
7 votes

Is weight distribution influenced by the location of the weight's attachment points (see drawing)?

Lets look at the equations Static equilibrium to obtain the unknows forces $~F_1~,F_2~$ you take the sum of the forces $~\sum F_i=0~$ and the sum of the torques about point A $~\sum_A\tau_i=0~$. you ...
Eli's user avatar
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7 votes
Accepted

Why can multiple eggs support more weight per egg when there are more of them?

With a fracture process the fracturing is usually caused by a local concentration of stress, that is there is some small region where a lot of force is concentrated in a small area and the resulting ...
John Rennie's user avatar
6 votes
Accepted

Where does the formula for bending of a rod come from?

A thin slender beam (rod) with length $\ell$, 2nd area moment $I = \frac{1}{12} b d^3$ and Young's modulus $E$ obeys the following differential equation $$ M(x) = E I \frac{\partial ^2 y(x)}{\partial ...
John Alexiou's user avatar
  • 38.4k
6 votes

Hanging a hammer from a table and a stick so that its midpoint is outside of the support of the table

When you use an object to strike another object, there is a place called the "center of percussion" where you don't get a "sting" in your hand. This is sometimes called the "sweet spot" in sports (...
Floris's user avatar
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6 votes

Why the dust on the wing cannot be cleaned by air flow?

There are two factors at play here: Static electricity causes dust to adhere to the wings of a plane. When a plane is in the air, there is nowhere to dissipate static charge buildup (as that usually ...
probably_someone's user avatar
6 votes
Accepted

How are force couples free vectors?

In rigid body mechanics, force couples are free vectors, meaning their effects on a body are independent of the point of application. You have misinterpreted the Wiki statement. Given a couple, two ...
Farcher's user avatar
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5 votes
Accepted

The Physics Behind the American Death Triangle

This is a great example of elementary physics concepts, which perhaps due to my lack of skill bring in some rather inelegant mathematics. The whole concept can be explained with a free body diagram. ...
Novice C's user avatar
  • 765
5 votes

What is the role of pillars in bridges?

The reason of having pillars in bridges is just pressure. You know that the pressure become less if the contact area is increased. And by increasing the number of pillars the surface area in contact ...
Harsh Kumar's user avatar

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