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Questions tagged [displacement]

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What makes displacement a vector?

Displacements are vectors because they add like vectors is the answer. It is also an experimental fact. Though rotations are displacements but not vectors. Is there any more fundamental or intuitive ...
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Conceptual explanation: Finding revolutions over a given time interval

The following question from NJCTL was assigned for me as homework. It is not a heavy computational problem, but rather, a conceptual one. I reviewed the meta guide regarding these types of questions ...
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In the equation for acceleration (with known $v$, $u$ and $s$) why velocity is squared and displacement is multiplied by 2? [closed]

In the following equation $$a = \frac{v^2 − u^2 } {2s} ,$$ where $v$ is the final velocity, $u$ is the initial velocity, and $s$ is displacement. Why is velocity squared and displacement multiplied by ...
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2answers
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Confusion on Horizontal & Vertical Components of a Parabolic Motion

This was a question I found about projectile motion, the question was what's the bike's speed when it took off. Using $S=ut + 0.5at^2$, the time taken to reach the ground is $0.505 s$, they used ...
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Acceleration as the second derivative of displacement function

Let $x$ be displacement as a function of time $t$ and some other physical quantity $k$ such that $ x = f(t,k) $ Now, 1) Will the acceleration $a$ be $\frac{\partial^2 x}{\partial t^2}$ or $\frac{d^...
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What's the relation between acceleration, position and angular velocity?

I just encountered a problem involving lift and oscillations where I found the following differential equation: $$\ddot y = -\frac{ \rho gA}{m}y = -\omega^2 y$$ What's the relation between $\ddot y$, ...
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4answers
154 views

Different expressions for distance & displacement : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r|$

I came across these expressions in my book. And the book says that all these are different from each other. The expressions are : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r|$ ...
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1answer
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Representing a wave

I don't know how relevant is asking this but We know that we represent waves by displacement, velocity etc.What about area vectors? I mean what about representing a wave by area vectors or even volume?...
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Frequency modes of the rectangular shell

The shapes of three natural modes having the frequencies $w_1$, $w_2$, $w_3$ of the rectangular shell are presented in the figure. The exciting pressure $p(t)$ applied uniformly all over the one side ...
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2answers
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Why is work defined with respect to distance rather than time? [duplicate]

The common way of finding the work done on some object is by applying the equation: force*displacement. However, suppose we apply a force of F newtons on an object of mass M for a duration of T ...
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1answer
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How to know what the area under curve represents?

Is there a way to find out what the area under the curve represents? For eg. If i gave you a graph of $v$ with respect to $t$ would you be able to tell me what the area under the curve represents ...
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Hooke's Law: Is the extension of a spring the same as its displacement?

This question might make no sense, but I'd like to ask it anyway. The elastic potential energy of a spring is the area under the force-extension/compression graph. The work done on a spring is ...
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2answers
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How to study the work done by a varying force on a system moving in two dimensions?

My book states that: $$W=\int_{x_i}^{x_f}{F_x dx}$$ We can calculate the area under the curve representing force as a function of position when the displacement and the force are in one direction ...
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2answers
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Does Euler number $e$ have a role in kinematics?

Euler number $e$ is often explained with the example of compound continuous interest. I was wondering if it could also be illustrated with an example about the displacement of a body (although not an ...
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2answers
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Why work definition involves displacement?

$$W=\left\Vert\vec{F}\right\Vert \left\Vert\Delta\vec{r}\right\Vert \cos{\theta}$$ A greater magnitude force will have a greater influence than a smaller magnitude one when they have the same $\theta \...
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1answer
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Relation between strain and velocity

The strain tensor writes $\epsilon_{ij}=\frac{1}{2}\Big(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_i}{\partial x_j}\Big)$ with $u_i$ the displacement in the $i$ direction. Then $\frac{\...
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1answer
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Strain gauge vs linear variable displacement transducer

For measuring deformation experiments, it seems that strain gauges and linear variable displacement transducers (LVDT) are commonly used. If the material exhibits geometric linearity, then couldn't we ...
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1answer
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I need to find the drag coefficient of a pendulum bob [closed]

Is it possible to find the drag coefficient of a pendulum bob from the damping caused on it during swinging. I will be able to measure its displacement from the point of origin and plot it against ...
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1answer
76 views

Displacement current quantum mechanical interpretation?

while there are quite many classical explanations of displacement current to make Maxwell's equations work, see e.g. here: Displacement current - how to think of it , it sounds just a little bit like ...
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2answers
58 views

Is the direction of average velocity the same as that of average acceleration and that of displacement?

Average velocity is defined as: $\vec{\Delta v} = \frac{\vec{\Delta r}}{\Delta t}$, and average acceleration as $\vec{\Delta a} = \frac{\vec{\Delta v}}{\Delta t}$. It is apparant from these ...
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2answers
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Are distance and displacement always frame independent?

I'm aware that distance and displacement, both are independent of reference frames, when the two frames are stationary wrt each other. Because the actual distance (or the shortest distance) between ...
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Displacement using work energy principle

How do you use the work energy principle to find the displacement of an object. With of course the mass, speed and friction forces given?
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Boundary condition: displacement

I have a controversial case. I have a rod, which is fixed from one end (constraint). From another end, I apply a compressive force, by pressing the rod down. So in a way I have a constraint, but at ...
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2answers
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What is the displacement between $t=1$ and $t=8$? [closed]

Given the graph above, what is the displacement between $t=1$ and $t=8$?I thought this was a straight forward questions: It's supposed to be the area under the curve. Moving the time axis up to where ...
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0answers
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Why are all the other sub-displacements included into to the total displacement? [closed]

Problem: During a jaunt on your sailboat, you sail $5\,\mathrm{km}$ east, then $5\,\mathrm{km}$ southeast, and then an additional distance in an unknown direction. Your final position is $20\,\...
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Travelled displacement - how do we take care of the possibility that it might be negative?

so this is a very basic question but I can't really find a full answer. So let's assume we have a point of mass $m$ travelling along the x-axis with a acceleration a. The travelled displacement is: $...
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3answers
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What does the 'displacement' refer to in the definition of work?

The definition of work given in books is The work is said to be done by a force on a body, when the body is moved by the force through some 'displacement'. Now let a body of mass $m$ at rest. When a ...
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1answer
2k views

Why is work scalar and the dot product of force and displacement?

I asked many people why work is scalar. But the questions and the answers just cycles. My question : Why is work a scalar quantity? Their answer : Because it is the dot product of Force and ...
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2answers
390 views

Displacement vector vs position vector

Below are my attempted definitions of the two terms. Are these correct and do they clearly distinguish between the two terms? My understanding is that the displacement vector comes first and that is ...
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1answer
200 views

Spring Displacement

I am having trouble understanding the sign/direction of displacement for the equation F=-kx. I am not going to elaborate on what the specific problem is that goes along with this visual since that's ...
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1answer
339 views

Sign of work done by friction

In Goldstein's classical mechanics (3rd ed.) we read: "The independence of W12 on the particular path implies that the work done around such a closed circuit is zero,i.e. $$\oint \textbf{F}.d\...
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1answer
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Orthonormality of displacement operators

I'm trying to prove that displacement operators are orthonormal in quantum mechanics, e.g.: $$\text{Tr}\{D^{\dagger}(\alpha)D(\beta)\} =\pi \delta^2(\alpha - \beta)$$ I used the completeness property ...
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3answers
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What is the “displacement” of the object in the definition of work?

Work in physics is mathematically defined as force $F$ applied on an object multiplied by the displacement $d$ it covers in the direction of the force. In a system where, a restrictive force exists ...
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Calculating Intitial Position given the ratio between the last two seconds of free fall for 1D motion

I've tried this problem in multiple different ways and can't seem to come up with an acceptable answer. The question is, A rock is dropped from the top of a tall building. The rock's displacement ...
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1answer
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What exactly is “displacement” and “velocity”? [duplicate]

I'm finding two different definitions for what the displacement of an object is: 1) How far the object is from a starting point in a specified direction (direction represented through a straight line ...
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2answers
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Is my total work infinite?

Suppose I'm in space. I push a ball with a force. Then it will start to move and continue to move forever. So the distance traversed by the ball is infinite. So we know, $$W=F × S =F × Infinity ...
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Is the formula for work $W= \vec{F}\cdot \vec{s}$ or $W=\int_C \vec{F} \cdot d\vec{s}~$?

I'm pretty much not so much introduced to calculus (I am grade 11 of India and they teach integration part of basic calculus by the end of grade 12) so I would be glad if the answer will be much more ...
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0answers
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Lattice to continuum transformation in one dimension (arbitrary range interaction)

Please help me convert the ionic displacement $u_l$ of the $l^{th}$ ion to a continuous field $u'(y)$ in the following problem. I am trying to derive the Hamiltonian of a 1-D lattice (spacing $=n_0^{-...
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2answers
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How do we know that force is a vector?

With displacement, our axoims and 'laws' of vectors work because that is how we designed vectors to work, as it seems obvious that displacement would follow the 'triangle law of vector addition', but ...
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4answers
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Why don't we use $F=−kx$ while finding a spring constant?

A block of mass $m$ is attached to a vertical spring in equilibrium, and is stretched a distance $d$. As Hook's law is $F=-kd$ If I take $y$-axis to be positive upward, the net force in the $y$ ...
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3answers
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Why can the deformation of a spring at a given point of the spring be considered directly proportional to the relative distance of the point?

Hello i have been studying differential equations and in one example my professor tries to deduce the partial differential equation that describes the longitudinal displacement on a elastic, ...
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2answers
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Distance and Displacement from a velocity vs. time graph

My teacher is saying that the distance covered will be equal to the area of the trapezium in the graph, but the displacement will be equal to the area of the triangle (with purple hypotenuse). I ...
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1answer
155 views

Integrating position/displacement with respect to time

We know that we get displacement if we integrate velocity with respect to time. But from my curiosity I am now wonder, what will I get if I integrate position/displacement with respect to time?
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Why is small work done always taken as $dW=F \cdot dx$ and not $dW=x \cdot dF$?

I was reading the first law of thermodynamics when it struck me. We haven't been taught differentiation but still, we find it in our chemistry books. Why is small work done always taken as $dW=F \cdot ...
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1answer
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Does water get displaced by itself when being filled in a glass or does it “pile up” like a denser substance?

Disclaimer: I do not have a very strong background in physics so if this is too elementary I apologize The Question: When water is being poured into a glass, is the stationary water (i.e. that which ...
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what is $x$ in $f=kx$

hey I keep getting confused with this formula since different places get $\ x $ in different ways and I want to be sure im doing it the right way. so i have a spring with a constant $\ 1300$ N/m, ...
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1answer
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Work, Energy, and Power- Hooke's Law & graphing

The purpose of the work, energy, and power lab is to demonstrate the validity of Hookes Law over a limited range of displacements, measure the spring constant of several springs, and determine the ...
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1answer
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Displacement and mass of water in a column [duplicate]

I attempted to modify a classic experiment to demonstrate Archimedes principle to my 5th graders and I created an error I can’t explain. We started with a graduated cylinder containing 20 mL of ...
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1answer
26 views

Spatially and temporally variable velocity

I have the velocity function of an atom, $v(x,t)$, which changes with time and space. I'm looking for a general relationship for finding the location of the atom at time $t_s$. The atom start to ...
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3answers
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Calculating acceleration from displacement measurements

I have a table of measurements s(t): t[s], s[m] 0, 0 12.48, 26.4 18.06, 52.8 22.32, 79.2 I have calculated all values for $a$ using $$ a=\frac{2s}{t^2} $$ and simply sticking the values into the ...