Find the force corresponding to the potential energy U(x) = (Use the following as necessary: a, b, and x. Express your answer in vector form.) F(x) =

Q: A mass m = 2kg is placed at the end of a horizontal spring that has a spring constant k = 500N/m and…

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Q: A particle of mass m moves in the horizontal xy plane in the right triangle OAB under the effect of…

A: Given that Force vector is F→ =( 4i^ - 2j^) N Displacement OA = 3 m OA→ = 3i^ m Displacement AB = 4…

Q: Find the force corresponding to the potential energy U(x) = (Use the following as necessary: a, b,…

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Q: Below is a side-view picture, where a box is brought up to a height at point A and moves a distance…

A: The gravity’s work done on the box can be given by the work-energy theorem as, Here, U represents…

Q: Suppose the potential energy function for a particle moving in 1D is given by U(x) below. Find all…

A: To find the equilibrium points

Q: Find the force corresponding to the potential energy U(x) = -a/x + b/x?. 2b A F= b a B F = .2 3 F =…

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Q: A small particle of mass m is pulled to the top of a frictionless half-cylinder (of radius R) by a…

A: Free body diagram

Q: A particle of mass moves in 1 dimensional space with the following potential energy: (in figure)…

A: The potential energy of a particle moving in 1-D is given by the function,  U(x)=Uo[2(xa)2-(xa)4]…

Q: A mysterious force acts on all particles along a particular line and always points towards a…

A: *The given force is F = br3 The expression for the force in terms of potential energy is given as,…

Q: Use the definition of scalar product, a→⋅b→ = ab cos θ, and the fact that a→⋅b→ = axbx + ayby + azbz…

A: From the definition of the scalar product, it is given as,

Q: A potential energy function for a two-dimensional problem is of the form U=4xy2-3x2y3. Find the…

A: force is the negative gradient of potential energy.

Q: • A force given by F(x) = 5x³ i N acts on a 2 kg mass moving on a frictionless surface. The 3 m to x…

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Q: Find the force corresponding to the potential energy U(x) (Use the following as necessary: a, b, and…

A: Given : potential energy is U(x) =  - a/x2 + b/x3

Q: The work done by the applied force on a system is positive when the projection of force onto delta r…

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Q: An object starts from rest at Position 1 on a track and slides to Position 3, At Position 2, the…

A: Here given the diagram with a object starts from position 1 and ends at position 3. Also given that…

Q: What is the total work WE done on the box by the appled force in this case? Express your answer in…

A: The force due to friction is given by Ff = μN, where μ =  coefficient of friction, N = normal force.…

Q: Calculate the work done by the force F(x, y) = y2 i + xy j in moving a particle along the line which…

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Q: A mass m has a velocity v at a position x what will be the work done if the distance traveled is…

A: Given, Mass, m Velocity, v Distance, x New distance, 4x

Q: (I) (a) If the kinetic energy of a particle is tripled, by whatfactor has its speed increased? (b)…

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Q: A particle of mass m moves in one-dimensional motion through a field for which the potential energy…

A: Given: The relation between potential energy and position of particle is given as,

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A: The force can be written as the negative gradient of potential and it is F=-∇UU=-∫F·dx…

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A: Given data: Force is given as, F→ = 2yi^ + x2j^ Formula used: Total Work done during the journey is,…

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Q: passes through the point x 0, y 4.4 m. (a) What is the kinetic energy of the particle as it passes…

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A: Given data: The potential energy of a pair of hydrogen atoms separated by a large distance x is…

Q: Consider Theorem 7.3, given below. If a constant force F is applied to an object, and the resulting…

A: Given values: Magnitude of force, F=35 lb Displacement, d=70 ft Angle with horizontal, θ=25 °

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Q: (Use the following as necessary: a, b, and x. Express your answer in vector form.) Find the force…

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Q: Find the force corresponding to the potential energy U(x) = −a/x + b/x2.

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A: Given, Mass of the block = 20 slug Angle of the incline = 20° Initial velocity of the block = 72.168…

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A: Given : F0 = (A × 2) N Displacement, d = 5.0

Q: Find the work done in moving a particle in a force field given by F = (3xy)i - (5z)j + (10x)k. Along…

A: Given data :                     F → = (3xy)i-(5z)j+(10x)kx=t2+1y = 2t2z = t3t : 1 to 2 Formula :…

Q: The spring is now compressed so that the unconstrained er x = L. Using the work integral

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Q: Due date: wed, Oci T6 2019 **34. Initially, a 10-kg block is sliding along a level floor at a speed…

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A: Dear student It is clear that the given path equation is of circle. So the particle is moving in a…

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest.