Answered: Find the force corresponding to the…

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.)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: Consider the vector field F(x,y)=(4x^3y^2−2xy^3)i+(2x^4y−3x^2y^2+4y^3) a. Find the potential…

Q: An object moves in the xy-plane under the influence of a single force given by F(x)= - αx^2i+βyj,…

A: Given force is F(x)= - αx^2i+βyj, where α and β are known constants. For conservative force we have…

Q: The potential energy function associated with a force acting on a system is U = 3x7y - 2x. What is…

Q: Given the force field F=(2x- y+z)î+(x+y-zrj+(3x-2y +4z)k . 2.1 Is the force field a conservative…

Q: A particle of mass 6 kg is constrained to move along the trajectory y(x) = -8 x2 + 49 (m). If the…

Q: 15. Using your derivations in the previous two questions, calculate the coefficient of kinetic…

A: This equation can be solved using Newton's 2nd law by resolving force components along both x-axis…

Q: A 7 kg particle is in a potential given by U(x) = 3 x^4 - 1 x^2 - 4 x + 8 (J). Calculate the…

A: Given: The mass of the particle m = 7 kg. The function of potential energy U(x) = (3x4-x2-4x+8) J.

Q: An astronaut working on the Moon tries to determine the gravitational constant G by throwing a Moon…

Q: Given the potential energy function U(x) =−x^2 + 4x+ 2 calculate the force F(x) associated with…

Q: A particle of mass 6 kg is constrained to move along the trajectory y(x) = -5 x2 + 10 (m). If the…

A: Given trajectory: y(x)=-5x2+10 (m)∴dy=-10x _______(1) Force: F=7 N (constant) Displacement…

Q: Consider the vector field F= Find the work done by F in moving a particle from (1,e,0) to (e,1,1),…

A: To determine: The work done by F in moving a particle from 1,e,0 to e,1,1 The field is…

Q: Problem #2: Find the work done by the following force field F(x, y) = 4(y + 6) i + 28x (v + 6)6 j in…

Q: Consider the Lennard-Jones potential between atoms of mass m in a solid material.c) Consider two…

A: Given,Mass of the atoms=mF=Focosωt Let us denote the natural frequency of oscillation to be ωo

Q: 3.1 Taking into consideration the information given above, show that the Lagrangian for a pendulum…

A: Say we have a pendulum of mass m, length l which makes an angular displacement θ with the vertical.…

Q: A constant force of 40 lb in the positive z-direction is applied to a particle whose velocity versus…

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,

Q: Problem 1 Show that the force F = y*+xŷ √√1-x²y² is conservative, and find a scalar potential for…

A: The force of the system is F⇀=yx^+xy^1-x2y2.

Q: Asmall block of mass 137 g starts at rest at A at a height of y7.2 m. slides to where its speed is…

Q: Confirm that the force field F(x, y) = ye"Y i+xe"Yjis conservative in some open connected region…

A: In this question we have to find the work done by the force field. Please give positive feedback if…

Q: Evaluate the work done by the force, F = 3xi+4yj, moving along the path y = x^2 from (0,0) to (3,9).

Q: This question is about analytical mechanics. Show that the forces below(a,b) are conservative…

Q: Section 5.3: Work and Line Integrals 20. Compute the work done by the force F=zyi-uj along the path…

Q: A 40 m long chain hangs freely from a ledge. Suppose the chain has a total mass of 800 kg. How much…

Q: Find the work done by the force field F = (2x + 4y, 4x + 8y) in moving a particle from (-1,1) to…

A: (a) by direct evaluation of the line integral :…

Q: onsider a force in R³ defined by F(x, y, z) = (4xy2,4x²y + 2 y,0). Find the potential energy U(x, y,…

Q: 3.1 Taking into consideration the information given above, show that the Lagrangian for a pendulum…

Q: F(r)=nrn-²r where, as usual, r = = x + y + z2 and r = x² + y² + z² and n is an integer.

A: For a force is conservative, its curl must be zero. That is, ∇×F→=0 where the operator ∇ is defined…

Q: Consider a particle subject to the potential: V (x) : 1 + x² In other words: x' X' = y' dV dx x² -1…

A: The given potential of the particle is and Initially, Therefore initial total energy considering…

Q: A particle, of mass m, is moving in one dimension under the influence of a conservative force with…

A: Given data, Potential V(x) = x2 - x4

Q: ASSIGNMENT: (0,1.1) Problem 1 Given the force fleld F= 2yi + 2x + 2ak, (-1,0,0) find a scalar…

A: The force is given by, F→=2yı^+2xȷ^+2zk^ The potential ϕ is given by, F=∇·ϕ . Therefore, ϕ=-∫F.dr…

Q: A force field is given by F = Fo (x°i + ryj+ z°k), find the work perform by this force on a circle…

Q: Confirm that the force field F(x, y) = 2xy'i + 3x?y?j is conservative in some open connected region…

Q: In Lagrangian mechanics, the Lagrangian technique tells us that when dealing with particles or rigid…

Q: Prove that the vector A = 3y*z?i+ 4x³z²j – 3x²y²k at (1,1,-6) is solenoidal. |

Q: Consider the one-dimensional potential' U(x) = - Wd²(x² + d²) x + 8d4 Sketch the potential and…

Q: Prove the cosine theorem using the properties of the scalar product.

Q: prove this force are conserved F(x,y)=2a(x-y)i-a(2x-y)j Where a is constant

A: Given that:- Force F(x,y)=2a(x-y)i^ - a(2x-y)j^

Question

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.)
4b
+
,5
-3a
F(x) =

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A 8 kg particle is in a potential given by U(x) = 1 x^4 - 7 x^2 - 3 x + 8 (J). Calculate the acceleration of the particle when it is at x = 1 m, in m/s2. (Please answer to the fourth decimal place - i.e 14.3225)
Answer q1a Q=6
The scalar triple product of three vectors is a • (b x c). Prove that the scalar triple product will not change when you cyclically permute the three vectors. (i.e., prove that a • (b x c) = b • (c x a) = c • (a x b) )
Calculate the following questions if the force F = 290N. Z (0,0,3) Q(1,1,0) F (4,0,0)
Consider a force in R3 defined by f(x,y,z)=(6*x*y^3, 9*x^2*y^2+2*y,0). Find the potential energy U(x,y,z) such that U(0,0,0)=0.
Show that the work done by the force field F=(y' – 2xyz")î+(3+2.xy – x*z')}+(6z° – 3x°yz*)& is path independent and calculate the work done by this force field in moving a particle from (1, -1, 2) to (2,3,1).
Please explain An electrically charged particle is held fixed at the origin. Let V = 1/r be the potential energy of a second particle with unit electric charge located at (x, y, z), where r = sqrt(x^2 + y^2 + z^2). The force on this second particle is given by −∇V . Calculate the force on the particle when it is at (1, 2, −2). Show working
A box with weight of magnitude FG=2.00N is lowered by a rope down a smooth plane that is inclined at an angle ϕ = 30.0 ∘ above the horizontal, as shown in (Figure 1) at left. The normal force acting on the box has a magnitude n=1.73N the tension force is 1.00 N, and the displacement Δr of the box is 1.80 m down the inclined plane. The work done on the box by gravity is 1.8 J What is the work Wn done on the box by the normal force? What is the work WT done by the tension force?
Energy and potential Prove that F = (y, -x, 0) is not conservative.
a.) A particle with mass m is dropped with zero initial velocity a height h above the ground, under the action of the gravitational field (acceration constant g), such that it reaches the ground (z=0) with zero potential energy and velocity v>0. Determine h, in terms of the other quantities given. b.) Another particle moves with Simple Harmonic Motion with centre O.The particle has velocity 13ms–1 when it is 3m from O and 5ms–1 when it is 5m from O.(i) Find the period and amplitude of the motion
is the vector foeld conservative? prove it.
I need the answer as soon as possible