Questions tagged [statics]

Analysis of a system of bodies where all forces are in balance and there is no motion relative to a chosen reference frame.

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How non-collinear forces balance each other?

In the system of parallel forces , all the forces are non-colinear. So how to they balance each other?. Here in this case a wooden plank is supported at its end by two supports. All the forces here ...
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What curve does a rod form when bent to intersect 3 or more points?

Suppose that we have a sufficiently thin, flexible cylindrical rod of length $L$ made from a homogeneous, isotropic material, and that initially [at rest?] the central axis of the rod is a straight ...
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Equilibrium and constitutive partial and algebraic equations describing stresses and deformation of an axisymmetric elastic thin shell over a hole

I want to design a vacuum table to clamp down a very thin plate and I want to know the stresses and deformations due to the atmospheric pressure. Consider the simplified model below: ...
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How to calculate the distributed weight across multiple "scales" (points)

Intro As the title says, I'm looking for a way to calculate the weight (or even better, the percentage of weight) at multiple points on a rigid object. Long story short, I'm making a game and need to ...
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Is It true that If the angular momentum is zero with respect to any point then the system is at rest?

If the angular momentum is zero with respect to any point, surely the system is at rest. It is intuitive that this is the case but I would like to prove it. I guess supposing the opposite leads to ...
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Motionless chain in a tube

Good evening, I come to this site with doubts on some very basic concepts. I have started reading through Morin's Classical Mechanics. Among the problems on Chapter 2, Problem 3 says: A frictionless ...
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Truss Deflection Problem

Dear Readers, why doesnt the deflection formula depend on moment of inertia (I) or even the second momnet of area that are responsible for the cross-sectional shape of beam. Does that mean in the ...
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Critical point in 2D Potts model and duality equation

I have to prove, considering the limits of high and low temperatures, duality equation: $$ Z=q e^{2 N K} F\left(e^{-K}\right)=q^{-N}\left(e^{K}+q-1\right)^{2 N} F\left(\frac{e^{K}-1}{e^{K}+q-1}\right) ...
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What is the physics behind a TV wall mount? [closed]

As I was installing this wall mount, I began to wonder how exactly physics is at work with it. In other words, how does the design of the mount play a role in ensuring that the mount itself supports ...
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Why is lever in mechanical equilibrium?

Let's consider a lever with a fulcrum (see image below), such that it's load arm and load are $d_1$ and $F_1$, respectively, and it's effort arm and effort are $d_2$ and $F_2$, respectively. Now my ...
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Weight Suspended From A Springlike Belt [closed]

This situation is similar to the physics involved in a slack line, though I'm looking at it for some CNC applications. There is a 3meter belt, that is tightened to be under 200N of tension between two ...
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How to replace these two forces with one force?

Here, $P>Q$. $O$ is the center of mass of the rigid and uniform bar/stick. As $P>Q$, the resultant is situated to the right of $\vec{P}$ and is parallel to $\vec{P}$. The magnitude of the ...
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Static mechanics: I get two different forces in an equilibrium system [closed]

The problem comes from "Engineering Mechanics Statics Dynamics" by Russell Charles(newest edition), on page 97, f3-4. You can see it here: https://www.youtube.com/watch?v=Nw7iN4BnU44 The $x ...
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How does a gravity defying stand comes in equilibrium?

The gravity defying wine bottle stand are now becoming very common these days. Can someone explain in detail the physics involved here? Here is a video that gives details about its making.
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How will the force act outside the stick?

Scenario 1: Here, $P>Q$. $O$ is the center of mass of the rigid and uniform bar/stick. The resultant acts to the right of $\vec{P}$ as $P>Q$. Scenario 2: Here, $P>Q$ also. $O$ is the center ...
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What is the significance of sliding a force vector?

Scenario 1: Here $AB$ is the line of action of the force $\underline{u}$, and $AB$ passes through the center of mass of an infinitely long rigid and uniform bar. Here, $\vec{CD}=\underline{u}$. Now, ...
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Why is there no normal force acting at this pillar?

(I've tried to ask about the specific concept that's giving me trouble so as to not make this an illegal question) Question: A uniform plank $AB$ of $4m$ length and $15kg-wt$ weight rests horizontally ...
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How are force couples free vectors?

According to wiki, In rigid body mechanics, force couples are free vectors, meaning their effects on a body are independent of the point of application. I'm having some trouble understanding this ...
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How can a force vector be shifted laterally when it is a sliding or a bound vector? [closed]

Question: One end of a rope of length $l$ is attached to a vertical wall, the other end being attached to a point on the surface of a uniform sphere of radius $a$. If the weight of the sphere is $W$, ...
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Confusion about Hydrostatic Equilibrium

When deriving the hydrostatic equilibrium for a static fluid, it is said that the net force on a fluid element dV of the fluid must be 0 because it is at rest (on the average, of course). There is a ...
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2D statics problem with 5 unknowns? [closed]

In this problem there are 2 hinges (each one with 2 reaction) one at point C [$C_x$,$C_y$] and the other at point G [$G_x$,$G_y$] , Also there is a cable that Dc that has tension $T_{DC}$. Then how ...
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Static equilibrium of a small spring network [closed]

Three springs $AB$, $OB$ and $CB$ with equal spring constants are fixed at the nodes $A$, $O$ and $C$ respectively and attached to a common node $B$, as shown below. The springs are at rest in this ...
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Why do these 2 different methods of finding tension in a string give 2 different answers?

A uniform rod BC of length $L$ and weight $W_1$ is hinged to a fixed point at $B$. A particle of weight $W_2$ is attached to the rod at $C$. The system is in equilibrium by a light elastic string in ...
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Torque considering the mass of the lever arm [closed]

Consider a mass pulling on a lever. The well known formula for torque is: $\vec{M}=\vec{r} \times \vec{F} \space$ Is there a general formula that also considers the mass and geometry of the lever ...
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Gravitational forces of a building

In trying to understand the gravitational forces of a building, I have devised a thought experiment: A building is floating in space. The building's mass is asymmetrically distributed. Inside it also ...
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How to calculate force required to push down on a supported wooden cylinder (arrow shaft), a distance of exactly 12.7mm (0.5″)?

trying to find out how many newtons do I need to push down an arrow shaft a distance of 0.5″ in order to measure the spine factor. the diameter of the wooden arrow is 7.9375mm (5/16") stiff ...
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Is it possible for rigid objects to slip before friction is saturated everywhere?

A common technique in statics problems is to assume that static friction is saturated everywhere. Consider, for example, the following problem: A thin, uniform bar of mass $m$ lies on a uniform floor,...
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A question on static physics (equilibirium) [closed]

I have a question about static physics which includes multiple pullies and parts. I have tried to solve it but I have a problem which prevents me from solving the whole question. so I started from ...
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How does a rope's tension work?

A problem I encountered is as follows: A pulley consists of a circle of radius $R$ is pivoted about a point a distance $R/2$ from the circle’s center. A string attaches to a block hanging from the ...
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Mass Distribution to turn Hanging Chain into Parabola

I've learned recently about how a uniform chain hanging between two points will form a catenary curve (of the form $a \cdot \cosh (\frac{x}{a})$), and I reflected on the fact that this is only because ...
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How can we differentiate a statics and dynamics problem?

Here is the problem I confused a lot. A uniform rod of mass m and length l is hanging vertically from the pivot O. A horizontal force F acts at the lower end of the rod. If F always remains ...
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1 vote
2 answers
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Why same force acts on two different strings?

Let us take two different strings and arrange them vertically. The first string is attached to the ceiling and connected in series with the second string and a mass $m$ is connected at the bottom of ...
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Calculating the bending moment in 3D [closed]

I'm studying for exam week, and I met this problem in my text book. I thought it was quite cool, however, I couldn't arrive at the correct result according to my text book. Hence, I want to present my ...
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What should the direction (a.ka sign) of torque be on this problem? [closed]

Ok, two sticks on a wall (Morin, 2.36), same mass density, let $F_x$ be horizontal component of the force on the upper hinge and $F_y$ it's vertical component, we could from there calculate what these ...
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Tensions caused by a force in a system of 3 static pillars

I was trying to analyze a system like this, which is in static equilibrium. I have used Newton's first law for forward and rotational motion, and ended up with a peculiar result, where T1 = 0. I was ...
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Balancing smartphone on corner of table

Today when I saw my phone on table some of its part was off the table, so I wondered what will be the arrangement of phone to balance it on corner of table such that it's minimum area (of screen) is ...
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Tools for analyzing forces in 3D structures

I'm trying to analyze ball towers like the one below. The problem is that the force vectors are pointing in many directions and it's difficult to draw 3D free body diagrams. Are there any tools that ...
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Statics question: Free body diagram help for garage construction project

I'm building a climbing training apparatus in my garage that both rests on the ground and hangs by a rope from a hook attached to a ceiling joist. Here are some pictures of builds similar to what I'm ...
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1 answer
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Why does the cable at point B carry no weight? [closed]

Roughly translated from Dutch; "The engine has a weight of 4250 N. Determine the forces in each of the chains (in point A, B and C) the engine is hanging from. The measurements of the hooks can ...
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3 answers
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The non-doubling of forces from compression/tension, is it just convention?

I drew 2 diagrams. A 10-kg ball rests on the ground or is suspended from a rope. Everything is in static equilibrium. (I drew the first one twice just to illustrate that the gravity force acts at the ...
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Which force component is $F_{N3}$ on figure (2)?

Here's a diagram of a man standing on a ladder that's currently fixed in position. Forces are in equilibrium, and the ladder is static. There are two figures illustrating the forces acting on the ...
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What's the Difference between Lattice Dynamics and Lattice Statics?

I understand that one involves movement of atoms, and the other one doesn't, but where would something like structural optimisation via energy minimisation fall? Is that Lattice Statics or Lattice ...
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Masses connected with a string, one mass in unifom circular motion

A light inextensible string of length $a$ is threaded through a fixed smooth ring $R$. One end of the string is attached to a particle $A$ of mass $3m$. The other end of the string is attached to a ...
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1 answer
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Tension force transmitted to 4 attachment points

I have a given 3D vector of tension force ($\vec{T}$) and I want to find a way to transmit it through 4 strings that connect the attachment points $\vec{a}, \vec{b}, \vec{c}, \vec{d}$, whose values ...
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2 votes
2 answers
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Equilibrium and the derivative of potential energy

In his Classical Mechanics popular lectures ( Lecture 3, at the beginning) , Susskind illustrates the idea of a stationary quantity using an example involving the notion of equilibrium. Link : https:/...
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Is there a way to calculate an offset force created by torque?

I am trying to figure out how to calculate the force created by an offset torque. The theoretical scenario is a 2x4 piece of lumber mounted by a hinge on the wall at exactly 90°. The weight of the 2x4 ...
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The mass continuity equation

I wanted to derive the equation, $$\frac{\partial m}{\partial r}=4\pi r^2\rho(r),$$ using a different way than simply writing: $$\rho(r)=\frac{dm}{4\pi r^2dr}.$$ I have decided to give it a try with ...
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Why does rotation happens about hinge point in a vertical bar when net force acting on it are zero? [closed]

As we know that if the net external force on a body is zero its center of mass will be at rest and also rotation will happen about center of mass only but in this hinge and rod case it is clear by ...
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2 votes
2 answers
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How does the shear and bending moment diagram relate to the stress tensor field?

I've read a fair amount of material on the physics of elasticity. That mostly covers the states of stress and strain and their relationship at a point. I don't recall ever encountering the so-called ...
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How is shear stress different from normal stress?

I feel like I have not understood the difference between these two concepts as well as I thought. My prior understanding of shear stress was that it is stress generated after force is applied parallel ...
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