Displacement Definition and 999 Threads

Homework Statement Prove the following relations (for ##\zeta:=r e^{i\theta}##): \begin{align} D(\alpha)^\dagger a D(\alpha)&=a+\alpha\\ S(\zeta)^\dagger a S(\zeta)&= a \cosh r- a^ \dagger e^{i\theta} \sinh r \end{align} Homework Equations ##|\alpha\rangle## is the coherent state. ##a## and...

Homework Statement A long, straight wire has a line charge, λ, that varies in time according to: λ = λ0 exp(-βt). A square wire loop of dimension a is located adjacent to the wire at a distance of a from the wire. Calculate expressions for the displacement current at the center of the wire loop...

1. The problem statement, all variables and given/known Two objects move with initial velocity -8.00 m/s xfinal velocity 16.0 m/s xand constant accelerations. (a) The first object has displacement 20.0 m. Find its accelera- tion. (b) The second object travels a total distance of 22.0 m. Find...

Homework Statement Find the displacement from the equilibrium position of the particle that is in the distance x=£/12 from the wave source, for the moment t=T/4. The amplitude of the wave is A=0.2 m Homework Equations x=A*cos(wt)=A*cos2*pi/T* t The Attempt at a Solution x=£/12...

Homework Statement The displacement vector of a particle of mass 50 gm. is given as a function in time (t) by the relation ##\vec S##=(5t-t2) ##\hat c## where ##\hat c## is a constant unit vector , s is measured in centimetre and t in second .Knowing that the particle started its motion at t=0...

Homework Statement (see attached diagram) Homework Equations (see attached diagram) The Attempt at a Solution I drew a diagram.What I know. Left part of rope is fixed to ceiling so extra rope comes 'from the right' i.e. 'falls down' as pulley is pulled. I also know that rope is conserved.

Homework Statement hi,i am using pipe289 to simulate a marine riser in ansys, the length of marine riser:1000m the outside diameter of marine riser:0.5334m the thickness of marine riser:0.0254 the velocity of current:1m/s the wave peroid:8s the wave height:6.5m boudary conditions: ux/uy on node...

I have a quantity defined as ## r = \left|\vec{r} - \vec{r'} \right| ## and am trying to take the gradient of this quantity. Now the gradient is with respect to the ordinary vector, ## \vec{r}##, and not ## \vec{r'} ##. But after looking at a solution, it says the direction of the gradient is...

If I am attempting to prevent a suspended motor-rotating imbalanced drum of high mass from colliding with its enclosure, how can I attempt to predict the maximum displacement from a balanced center of rotation if I have only a single sensor that can accurately measure(1000 samples/sec)...

I was wondering something, I dropped a box onto my glass desk but it didn't bounce back, I also hit a hammer against a rigid wall, the matter smacked into the wall, it has KE. It never bounced back, I didn't see any deformation or rebound in either situation, I wasn't hitting too hard nor...

Hi everyone. I have trouble finding the velocity of a traveling wave give some information about it's displacement. I am given D (x,t)= 1 cm if |x - 4t| <\= 1 &&&D (x,t) = 0 cm if |x - 4t| > 1. I don't know how to interpret these mathematical statements. I've been trying for 3 hours now :(. I...

Hello, I'm trying to figure out a general physics problem here and I'm trying to relate energy held in a rotating shaft to be dissipated by a torsional spring. Let's say I have energy E (Joules), shaft outer diameter D, and torsional spring capacity T. T is what I'm designing for with all...

Homework Statement If the following Force v. Displacement graph is for a 9.9kg object and it's initial velocity is 28.6 m/s the what is its velocity at 30 m? Homework Equations I am not certain that i am even using the right equations with this but: W = fd KE = 1/2mv(final)^2 -...

Homework Statement a car with an initial velocity of 10.0 m/s (W) decelerates at -2.00 m/s (s to the power of 2) (W) reaching a final velocity of 5.00 m/s (W). What is the displacement of the car? Homework Equations Δdisplacement = (final velocity to the power of 2 - initial velocity to the...

Homework Statement If you blow across the top of an empty soft-drink bottle, a pulse of sound travels down through the air in the bottle. At the moment the pulse reaches the bottom of the bottle, what is the correct description of the displacement of the elements of air from their equilibrium...

Homework Statement A particle of charge +14.5http://edugen.wileyplus.com/edugen/courses/crs6407/art/qb/qu/c18/lower_mu.gifC and mass 5.09 × 10-5 kg is released from rest in a region where there is a constant electric field of +328 N/C. What is the displacement of the particle after a time of...

Homework Statement I'm just confused about this. I know that displacement=df-di, but using that formula didn't give me the correct displacement in this case. In a 100m sprint, a runner starts from rest and accellerates to 9.6m/s[W] in 4.2 seconds. The runner runs at a constant velocity for...

Homework Statement A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are 4.00 m to the north, 2.00 m northeast, and 1.00 m at 30.0° west of south (Fig. P3.21). Starting at the same initial point, an expert golfer could make the hole in...

Homework Statement Homework Equations Kinematic equations t = 18s when the velocity is back to 54km/h or 15m/s at t = 2, V = 13.3 m/s at t = 4.5, velocity is 1.5 m/s at t = 1, V = 15m/s The Attempt at a Solution I have solved the first part and I have the time at which it is 54km/h again, but...

Homework Statement A person on a bus walks to the front of the bus at 3.0 km/h relative to the bus, while the bus travels south at 15km/h. What is the passenger's total displacement? Homework Equations displacement= final position-initial position total displacement=displacement1+displacement2...

If you're calculating displacement using delta d=df-di, do you make one position positive and one negative and then add? For example, if your first position was 23m[W] and the final position was 34 m [E], would you just do, 34- (-23), making the position that is west negative and the east...

Homework Statement let there be ##\beta(t+\tau)^{-2}e^{-3}cos(at^{3})## where ##\beta##, ##\tau## and ##a## are constants Homework Equations ##\beta(t+\tau)^{-2}e^{-3}cos(at^{3})## The Attempt at a Solution I know the graph is going up and down exponential but how can I draw it more...

I have seen a couple of posts on this website of physics students who were puzzled by what the electric displacement vector D in electromagnetic theory represents. This quantity also had me rather puzzled when I was a student and I think I can provide some insight into its significance. The...

Homework Statement The force generated by a spring is given by F=kx where k is the spring constant and x is the displacement of the spring. The spring in the below figure has a constant of 8 kN/cm. The pressures are P1=5000 kPa, P2=10,000 kPa, and P3=1000 kPa. The piston diameters are D1=8cm...

Homework Statement A car accelerates uniformly from rest along a straight road and experiences negligible frictional forces. The car travels 15m in the second second of its journey. How far does it travel in the fifth second? (OPTIONS: 15m, 35m, 45m, 75m) Homework Equations 3. The Attempt at...

Homework Statement The a-s graph for a rocket moving along a straight horizontal track has been experimentally determined. If the rocket starts from rest, determine its speed at the instants s = 20m, 50m, and 70m, respectively. On the graph, S1 = 50m, a1 = 10 m/s^2, S2 = 70m, and a2 = 20 m/s^2...

Hello--can anyone please help me estimate the PSI required in an air mattress to minimize or even prevent displacement if a person, say 220 lbs, walked across it? Mattress material and wall thickness variable. Surface area variable. Also, if scenarios where the person is standing still...

An object is within a glass sphere of radius R with a refractive index of 1.5 . I'm trying to calculate the displacement of the virtual object relative to the actual when viewed from the side, such that the refracted ray emanating from the object becomes horizontal. I would like to know S (the...

Homework Statement . A 2.0 kg object falls from rest a distance of 5.0 meters onto a 6.0 kg object that is supported by a vertical massless spring with spring constant k = 72 N/m. The two objects stick together after the collision, which results in the mass/spring system oscillating. What is...

I'm having some trouble with this problem (adapted from K&K 1.23). Homework Statement An elevator is programmed to start from rest and accelerate according to \begin{align*} a(t) &= \frac{a_m}{2}\left[1 - \cos\left(\frac{2\pi t}{T}\right)\right] &\mbox{for }0\leq t\leq T \\ a(t) &=...

Homework Statement 35m^3 of a boat's volume is submerged under water. What does the boat weigh? The boat is 14 metres long. Homework Equations pVg=mg The Attempt at a Solution pVg=mg pV=m m=pV=1000*35 This is what my teacher said, but I don't understand it. The submerged volume of the boat...

Homework Statement Using the superposition principle, determine the resultant displacement of the particles in the medium, at the instant shown. Homework EquationsThe Attempt at a Solution

Homework Statement A cow runs in a straight line, moving 108 m east in 16.4 seconds. It then turns and runs 93 m north in 7.64 seconds. a) What was the cow's average speed over the whole trip? b) What was the cow's average velocity over the whole trip? Homework Equations average speed =...

Hi, Am I right in saying that if the gradient of displacement is negative then stress is negative as in a simple elastic case, sigma = E*du/dx? thanks.

Hi, is displacement gradient du/dx same as strain? i though it would be until someone made a comment that they are not the same thing and now I am confused.

I am wondering how can I find the infinitesimal displacement in any coordinate system. For example, in spherical coordinates we have the folow relations: x = \, \rho sin\theta cos\phi y = \, \rho sin\theta sin\phi z = \, \rho cos\theta And we have that d\vec l = dr\hat r +rd\theta\hat \theta...

Using the formulas: s = \frac{1}{2} \alpha t^2 v = \frac{d}{t} a = \frac{v}{t} When we divide distance "s" by time we get velocity: v = \frac{\frac{1}{2} \alpha t^2}{t} = \frac{1}{2} \alpha t When we divide velocity "v" by time we get acceleration: a = \frac{\frac{1}{2} \alpha...

Homework Statement In the following question, in the solution, why is it that when they calculate the gravitational potential energy at point 2 (impact with spring), it is negative? I know that if both the force and displacement act in the same direction, then the work done should be positive...

The classical definition of power is the rate of work per unit time, and the usual definition of work requires a mass to be displaced. However, power is alternatively stated as the rate of the transfer of energy. Now, suppose for example that one abstractly considers a light beam (without...

Homework Statement Train goes 20 m/s Brakes cause a = -1 m/s2 Displacement at t = 40s ?Homework Equations v = 20 m/s a = -1 m/s2 t = 40s The Attempt at a Solution image upload no limit It seemed like this formula fit perfectly. It had all of the known variables and the one unknown neatly out...

1. The problem statement, all variables and given/known dat A car travels 20 mi at 60 degrees north of west, then 35 mi at 45 degrees north of east. Express each displacement vector in unit vector notation. Take the +x-axis due east and the +y-axis due north. Use the component method to obtain...

Homework Statement A person takes a trip, driving with a constant speed of 89.5 km/h, except for a 22-min rest stop. If the person's average speed is 77.8 km/h a) How much time is spent on the trip? b) How far does the person travel? Homework Equations v1 = 89.5 km/h -> t v2 = 0 km/h...

Hi, The following question is related to my individual design for an engineering subject. I am trying to calculate the fluid displacement in a packed vessel when air is pulsed through a pulse leg, which is connected to the bottom of the vessel. Using equations from literature, I have...

Hi, I'm looking for the result of displacement controlled tensile test. I want to know about the x-axis component and y-axis component of the result, not the whole data. I read about some articles about these and they said displacement control is most common. I've searched a lot but all I found...

Homework Statement For each expression of displacement (x) below, write down the mathematical functions for velocity (v), acceleration (a), and pressure (Pa). Assume a maximum amplitude (A) of displacement = 1. Units are not required. Hint: Think about the phase relationships of pendular...

1. The problem statement, all variables and given/known force F = (4x i + 3y j) acts on object as it moves in the x direction from the origin to x=5m. What is the angle between the force and the displacement Homework Equations I'm not really sure since I have no idea The Attempt at a Solution...

Homework Statement Show that the maximum of the Planck energy density occurs for a wavelength of the form λmax = b/T, where T is the temperature and b is a constant that needs to be estimated. Homework Equations Planck energy density u (v,T) = 8πv2 / c3 * hv / ehv/kT-1 The Attempt at a...

Homework Statement He decelerates uniformly at a rate of -5.00m/s^2 over from a velocity of 7.5m/s to rest. Find the time and displacement. Homework Equations Vf^2=Vo^2 + 2a(displacement) The Attempt at a Solution 0=56.25+2(-5)x is this the right way to find displacement? Solving for the x...

In most of classical mechanics textbooks,the concept of virtual displacement and virtual work is not represented deeply.They just focus in how the method should be used without explaining from where this principle came and why scientists created it in the first place. So to grasp this concept...

An airplane takes off and flies 245 km on a course of 45.0° south of west and then changes direction and flies 175 km due south, where it lands. Find the displacement from its starting point to its landing point. I have literally no idea how to approach this, I worked with physics only...