Potential energy Definition and 1000 Threads

Homework Statement Using the equations, show the bulk modulus is about r^-4. Homework Equations The Attempt at a Solution Tried to plug Uij but it is not same as U. To be honest, I don't know where to start.

Homework Statement A point charge +Q is placed at the centre of an isolated conducting shell of radius R. Find the electrostatic potential energy stored outside the spherical shell if the shell also contains a charge +Q distributed uniformly over it. Homework Equations [/B] E=kQ/r2...

I have just read chapter 7.4 FORCE AND POTENTIAL ENERGY in Sears and Zemansky's university physics 14th edition. There they show that a conservative force always acts to push the system toward lower potential energy in a one-dimensional motion with the equation Fx(x) = - dU(x)/dx. As I...

Homework Statement A 4.0 kg block starts at rest and slides a distance d down a frictionless 35.0 incline, where it runs into a spring. The block slides an additional 16.0 cm before it is brought to rest momentarily by compressing the spring, whose spring constant is 429...

It is commonly said that if you lift an object above the Earth it gains potential energy equal to mgh (m=mass, g=gravitational acceleration, h=height), suggesting that the potential energy is in the lifted mass. This cannot be. Consider the case of two perfectly rigid spheres, isolated in...

Homework Statement Charge q1= 8.5 nC is located at the coordinate system origin (0,0), while charge q2= -4.46 nC is located at (a,0), where a= 1.5 m. The point P has coordinates (a,b), where b=0.95 m. A third charge q3= 16.5 nC will b added later. It is a 3 part question, first asking for the...

Homework Statement A particle has the potential energy shown in the figure. (Figure 1) What is the x-component of the force on the particle at x =5, 15, 25, and 35 cm? I'm stuck on finding the Fx at 25 & 35 cm.Homework Equations F = -du/dx 100 N = 1J/cm The Attempt at a Solution Slope...

Chapter 24, Question 61 Given two configurations, ##C_1##, ##C_2## of ##N## point charges each, determine the smallest value of ##N## s.t. ##V_1>V_2##. ##C_1##: ##N## point charges are uniformly distributed on a ring s.t. the distance between adjacent electrons is constant ##C_2##: ##N-1##...

Homework Statement A uniform electric field of magnitude 4.1 ✕ 10^5 N/C points in the positive x-direction. Find the change in electric potential energy of a +5.3 µC charge as it moves from the origin to each of the points given below. (a) (0, 6.9 m) __ J (b) (6.9 m, 0) __J (c) (6.9 m...

Homework Statement For my extended essay as part of the IB, I am investigating the effect of changing the distance and the number of stationary ball bearings in a Gaussian gun. I was hoping to look at the energy transfer during each stage of magnets and therefore calculate the efficiency...

Homework Statement The potential energy V(R) of a two particle system exhibiting oscillatory behavior near a local minimum at the equilibrium separation Ro. V(R)= -(A/R)+(B/R^2) , where R is the interparticle separation. A) Sketch V(R), what happens to V(R) as R→0 B) At what value of R is...

Homework Statement A body of mass "m" is let go from on top of a surface A, where it slides down to B(without friction). From that point on, it displaces itself on an horizontal surface 5 meters away from B, where it stops at C. Being "m" a mass in kg "h" in meters and g = 10 m/s^2 The value...

Homework Statement A ball with radius ##r## is inside a hollow cylinder with radius ##r+R##. In the first part of the assignment, one has to calculate the minimum kinetic energy the ball has to have at the bottom in order to complete a full loop in the cylinder. It turns out to be...

Homework Statement A spring of negligible mass exerts a restoring force on a point mass M given by F(x)= (-k1x)+(k2x^2) where k1 and k2 >0. Calculate the potential energy U(x) stored in the spring for a displacement x. Take U=0 at x=0. Homework Equations ΔU=∫F(x)dx U=½kx^2 The Attempt at a...

Assuming the resistance of a wire in a series circuit, consisting only of 1 component (e.g. filament lamp) and a battery, is negligible; does each Coulomb of charge commit all of its electrical potential energy, supplied by the battery's potential difference, as work done across the component...

Homework Statement A classical particle with total energy E moves under the influence of a potential V(x,y) = 3x3+2x2y+2xy2+y3. What is the average potential energy, calculated over a long time? Homework EquationsThe Attempt at a Solution I think that this can be solved using Virial Theorem...

Hello Physics Gurus, Please critique the following logic... When a runner hikes/runs to the top of a mountain, the chemical potential energy inside the muscles transferred into the potential energy of the runner's body mass at the higher elevation (Pe = mass*gravity*height = mgh). Energy is...

Homework Statement : A ball a, moving with kinetic energy E, makes a head on elastic collision with a stationary ball with mass n times that of A. The maximum potential energy stored in the system during the collision is a)nE/(n+1) b)(n+1)E/n c)(n-1)E/n d)E/n[/B]Homework Equations :Principle of...

In my physics textbook chapter of work 3 statements are made which I am having trouble sorting through. 1. When W>0 the system's energy increases, when W<0 the system's energy decreases. 2. ΔE = ΔK+ΔU+ΔTherm = W 3. ΔU = -W Here is where my confusion begins. If I move a 1kg brick from 0m to 1m...

The principle of minimum total potential energy is frequently used in solid mechanics as an elegant way of deriving the equilibrium equations for an elastic body under conservative forces. This method states that out of all the possible displacement fields that fulfill the boundary conditions...

Hello. I'm new to this forum and to Physics and Chemistry in general and I have a question that's making me go crazy: why does the potential energy decrease as two atoms (say, hydrogen atoms) get closer to form a molecule? I'm talking about this graphic: I've read that it's related to the...

A planar object comprises of two masses joined by a linear spring with relaxed length p. The horizontal and the vertical displacements of the two masses are measured relative to a fixed point of reference as shown in the figure. What would be the potential energy of the spring? My initial guess...

Homework Statement Let's say we have a mass of 5kg at a height of 3 m so it's potential energy is mgh = 147J/1.6e-19 = 9.19 e20 eV. Now we know that E = mc^2... so when finding the mass of this potential energy we get 10.2e3 kg. What the hell is that supposed to mean? Homework Equations None...

Homework Statement You are in a spaceship far from any other objects, and you want to build a clock. You decide to build your clock out of a spring with a mass attached to it. You use a spring with spring constant k = 138 N/m, and you initially displace the mass a distance x=25.0 cm from...

Homework Statement In an experiment, a student wishes to use a spring to accelerate a cart along a horizontal level track. The spring is attached to the left end of the track and produces a non-linear force of magnitude Fs = Ass + Bs, where s is the distance the spring is compressed in meters...

Homework Statement 2 masses are connected by a spring. They are on a frictionless plane inclined relative to the horizontal by ##\alpha##. The masses are free to slide, rotate about their center of mass, and oscillate. 1. Find the Lagrangian as a sum of the Lagrangian for the COM motion and a...

Homework Statement The potential energy of a system of two particles separated by a distance X is given by the equation below, where A,B,U0 are constant. U(X)=U0exp{[-(x/A)-1)((x/B)-]} (a). Find the force F(x) that each particle exerts on the other. (b). show that the is a X where the system...

Why is the rate of change of potential energy always same the rate of change of kinetic energy in a mass spring system? Additiinally, How do we determine the rate of change of potential energy in such case?

Going through several definitions, it appears that escape velocity is equal to the potential energy. That is:$$\frac{1}{2}m v^2=-\frac{G M m}{r}$$but if I solve for velocity, $v$, I get:$$v=\sqrt{-2\frac{G M}{r}}$$So how do I get an escape velocity that isn't imaginary?

I'm trying to understand potential energy, especially with regard to gravity. There's a double negative that's difficult to grasp: The direction of the force is negative because the vector points radially outward and the force of gravity is directed inward, and the work done to bring an object...

Homework Statement [/B] In a movie stunt, a 65 kg skier starts from a rest position at the top of a hill 30 m high. She slides down the hill to the bottom, where she collides with a 45 kg stationary skier. The collision is completely inelastic. Find the final velocity of the skiers. Homework...

...(after infinite distance) falls into earth, would exist infinite potential energy if E=mgh and h is infinite?

In my physics class I was told that potential energy can be negative because it relative, but i thought as long as something has room to fall it has a positive amount of potential energy. So how can potential energy be negative?

X has a mass of 55 kg and hangs from a rope. As a result of this the rope stretches by 0.6 m. Calculate the energy stored in the rope as a result of stretching. Solution: F = kx and E = 0.5x^2. Using this fetches the answer as 161.5 However, the change in potential energy (calculated using mgh )...

Homework Statement Consider the earth-moon system (whose constituent pats we take to be the Earth and the moon separately). a) Compute this system's gravitational potential energy (in joules) and the mass deficit (in kilograms). The radius of the moon's orbit is 384,000 km, and its period is...

Why doesn't the potential energy of a substance change when the pressure changes? Or in what case will the potential energy of a substance change?

the question is : particles m1 and m2 each of mass m are connected by a massless rod with length l , these particles move on a frictionless horizontal plane as shown in the screen shot , the movement of m1 is fixed on a frictionless circular track of radius R , find the E.O.M ! Homework...

Homework Statement A particle in central force field has the orbit r=cφ^2, c is a constant. Find the potential energy, Find r and phi in terms of t. I get how to find the potential energy and found it to be U=-l^2/mu (2c/r^3+l/2r^2) l is angular momentum and mu is the reduced mass But how do I...

Homework Statement Question :- Two stars, each of a solar mass and radius ##10^7 m## are at a distance of ##10^{12} m## from each other. Find the speed of each star before collision if initial speed is negligible. Homework Equations $$V(r) = {-G Mm \over r}$$ The Attempt at a Solution...

Does spacetime have potential energy, and does an object with more potential energy have more mass? (E=mc^2)

Homework Statement There is a solid cylinder of radius a and then empty space then a shell cylinder of radius b. Show that half of the stored potential energy lies within a cylinder of radius $$\sqrt{ab}$$ Homework Equations In the attempt The Attempt at a Solution I'm not sure what they...

Homework Statement (a) Prove that the time average of the potential energy of a planet in an elliptical orbit about the sun is -k/a. (b) Calculate the time average of the kinetic energy of the planet. Homework Equations F = \frac {-dV} {dr} = - \frac {k} {r} The Attempt at a Solution [/B]...

Homework Statement Two metal spheres of equal radius ##R## are placed at big distance one from the other. Sphere 1 has total charge ##q## and sphere 2 has no charge. The two speheres are moved one towards the other until they touch, then they are moved again far away one from the other. What is...

Hello! I'm Steven, and I'm currently working on the following problem: The Earth can be seen as a conducting sphere with an electric field: E= -(150V/m)r (on its surface) and where r is the unit vector . The Earth has a radius 6371 km. So, I am asked to calculate the electrostatic potential...

Homework Statement A teeter toy is composed of a massless central stick of length L and two massless sticks of length l attached at angles α, each with a mass m at the end (see the figure). We imagine tilting the toy by an angle θ from the upright position. a) Find an expression for the...

Homework Statement The binding potential energy in a diatomic molecule (N2 for example) is often approximated by the Morse potential energy which has the form U(r) = De (1-e^[-a(r-re)])2 where De is a constant that reflects the well depth (dissociation energy), a is a constant that reflects the...

Homework Statement Alrighty, so here's my problem in a nutshell: Some particle of mass m is confined to move along a ring of radius R. Since it's on a ring, it has periodic boundary conditions--i.e.: For the boundary defined as ##-\pi R \leq x \leq \pi R##, ## x = -\pi R ## and ## x = \pi R...

Homework Statement A small bead of mass m is constrained to move on a helix: r (θ) = (R cos(θ), R sin(θ), q θ) where R and q are constants, and θ=θ(t) describes the position of the bead along the helix at time t. The bead is also subjected to a gravitational acceleration g downward (-z...

Homework Statement I am given that an object of mass m has an attractive force F=-A/x^2 acting on it, where A is a constant and x>0. I need to find the potential energy. After i need to suppose initial conditions (x0, v0) such that total energy=0. I need to find the trajectory x(t) with v>0...

Homework Statement A conservative force F(x) acts on a 2.0 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is graphed in the figure. When the particle is at x = 2.0 m, its velocity is –1.2 m/s. (a) What isF(x) at this position, including sign? Between what...