Given ∆U=W, show that a spring’s potential energy is given by U(x)= 1/ 2 kx2.

Question

Question

Given ∆U=W, show that a spring’s potential energy is given by U(x)= 1/ 2 kx².

science physics

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

Given ∆U= W, show that potential energy implies a force according to F(x)= - dU(x)/ dx...

Given ∆U= W, show that potential energy implies a force according to F(x)= - dU(x)/ dx .
One solution to the harmonic oscillator, with a potential energy V(x)=1/2 kx2, is ?(?) = ???^...

One solution to the harmonic oscillator, with a potential energy V(x)=1/2 kx2, is ?(?) = ???^ (− ??^ 2) /2 , where N is a normalization constant and ? = √ ??/ ħ^ 2 . Determine the energy of this wave function using the time independent Schrödinger equation
The potential energy of an object constrained to the x-axis is given by U(x) = 3x^2...

The potential energy of an object constrained to the x-axis is given by U(x) = 3x^2 - 2x^3. If x = 2.0 m, determine the force F(x) associated with this potential-energy function. Your Answer: Answer units

A potential energy function is given by U(x) = (x ^−8) *e^ (x ^2) . Let’s...

A potential energy function is given by U(x) = (x ^−8) *e^ (x ^2) . Let’s only focus on the region where x > 0. a) Find the position where the potential energy is a minimum b) For small oscillations around this minimum, what is the angular frequency ω? c) At what distance (either to the left or right) from the equilibrium point is the exact value of the force (derived from the full potential) more than 10% different from...
The potential energy is given by U(X) = 3xe^-x a) Determine the force b) Is the...

The potential energy is given by U(X) = 3xe^-x a) Determine the force b) Is the force conservative? Justify your answer
Given a potential energy function U(x), the corresponding force F is in the positive x direction...

Given a potential energy function U(x), the corresponding force F is in the positive x direction if:a) u is positiveb) u is negativec) u is an increasing function of xd) u is an decreasing function of x

An object's total energy is affected by a potential energy of the form U(x)=-6x^-2 (the potential...

An object's total energy is affected by a potential energy of the form U(x)=-6x^-2 (the potential has units of joules). What is the magnitude of the conservation force (in newtons) responsible for this potential when the object is at x=0.72 m. Give your answer with 2 sig figs.
A particle of mass m moves in one dimension. Its potential energy is given by U(x)...

A particle of mass m moves in one dimension. Its potential energy is given by U(x) = -Voe-22/22 where U, and a are constants. (a) Draw an energy diagram showing the potential energy U(). Choose some value for the total mechanical energy E such that -U, < E < 0. Mark the kinetic energy, the potential energy and the total energy for the particle at some point of your choosing. (b) Find the force on the particle as a function...
A potential-energy function in two dimensions is given by U(x)=a(x2−y2), where x and y measure position...

A potential-energy function in two dimensions is given by U(x)=a(x2−y2), where x and y measure position in m and a is a positive constant with the units of J/m2J/m2. (a) Show that this function has an equilibrium at x=0, y=0. (b) Is the equilibrium stable against small displacements in the x-direction? What about the y-direction?

A particle of mass m and energy E moving along the x axis is subjected to a potential energy function U(x).

\((25\) marks) A particle of mass \(m\) and energy \(E\) moving along the \(x\) axis is subjected to a potential energy function \(U(x) .\) (a) Suppose \(\psi_{1}(x)\) and \(\psi_{2}(\mathrm{x})\) are two wave functions of the system with the same energy \(E .\) Derive an expression to relate \(\psi_{1}(x), \psi_{2}(x)\), and their derivatives. (b) By requiring the wave functions to vanish at infinity, show that \(\psi_{1}(x)\) and \(\psi_{2}(x)\) can at most differ by a multiplicative constant. Hence, what conclusion can you...