153
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 ...
- 12.4k
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 ...
- 36.3k
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 ...
- 104k
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.
...
- 119k
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 ...
- 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 ...
- 2,234
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 ...
- 13.7k
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 ...
- 4,799
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 ...
- 38.9k
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 ...
- 51.7k
19
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 ...
- 27k
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 $\...
- 1,302
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....
- 36.3k
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) ...
- 57.6k
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 ...
- 10.2k
13
votes
Accepted
How does this tensegrity table work?
Stable mechanical equilibrium broadly means that any movement would incur a net energy penalty.
This is intuitive when we see a ball at rest in a dip, for example; it’s clear that any rolling would ...
- 27k
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 ...
- 16.4k
12
votes
How does this tensegrity table work?
What's confusing here is probably that the lifting is dose via the tensile force of the rubber band, which due to the placement on the arms pulls down the bottom and up the top part.
Mechanically, ...
- 4,497
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 ...
- 38.9k
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 ...
- 75.8k
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 ...
- 404
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 ...
- 60.2k
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 ...
- 12.7k
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 ...
- 359k
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 ...
- 38.9k
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 (...
- 119k
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 ...
- 35.7k
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 ...
- 98.6k
Only top scored, non community-wiki answers of a minimum length are eligible