Question

A particle of mass m moves under a force F = −cx^3 where c is a...

A particle of mass m moves under a force F = −cx^3 where c is a positive constant. Find the potential energy function. If the particle starts from rest at x = −a, what is its velocity when it reaches x = 0? Where in the subsequent motion does it instantaneously come to rest?

Homework Answers

Answer #1

1. Potential energy function [as force is negative gradient of potential energy i.e.  F(x) = - dU /dx ]

  

2. From law of conservation of energy, total mechanical energy = sum of kinetic and potential energy remains constant

total energy at x = -a is equal to total energy at x = 0

is the velocity at x = 0

3. Let at x' particle instantaneously comes to rest.

when particle comes to rest, its kinetic energy will be zero. so

all its enrgy becomes equal to maximum potential energy at x = a

  is the position where particle comes to instanteous rest

pls upvote

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
particle of mass m moves under a conservative force where the potential energy function is given...
particle of mass m moves under a conservative force where the potential energy function is given by V = (cx) / (x2 + a2 ), and where c and a are positive constants. Find the position of stable equilibrium and the period of small oscillations about it.
A particle of mass m, is under the influence of a force F given by F...
A particle of mass m, is under the influence of a force F given by F = Fo [(sin ωt)ˆi + (cos ωt) ˆj] where F0, ω are positive constants. If at t = 0 the particle is at rest at the origin, find (a) the equations of motion x (t) and y (t) of the particle, and (b) the work done by the force F from t = 0 to t = 2π/ω.
a particle of mass m moves in three dimension under the action of central conservative force...
a particle of mass m moves in three dimension under the action of central conservative force with potential energy v(r).find the Hamiltonian function in term of spherical polar cordinates ,and show φ,but not θ ,is ignorable .Express the quantity J2=((dθ/dt)2 +sin2 θ(dφ /dt)2) in terms of generalized momenta ,and show that it is a second constant of of the motion
mass of 2kg moves horizontally along x axis under the action of a force in terms...
mass of 2kg moves horizontally along x axis under the action of a force in terms of time, given as following: F(t) = b sin wt , where t time in seconds , b and w are constants 1) find the impulse during t1=0 to t2=2 if the mass starts motion from rest at x=0 (Show in integration IN DETAIL) 2) find its velocity as function of time (IN DETAIL) 3) find its position as function of time (IN DETAIL)
A particle of mass 0.0269 kg moves along the x-axis under the influence of a conservative...
A particle of mass 0.0269 kg moves along the x-axis under the influence of a conservative force. The potential energy of the particle is given by the following formula U=-A/x where A = 1,200 Jm. A) Find the work done on the particle by the conservative force in moving it from x = 10.0 m to x = 60.0 m. B) If the speed of the particle was 5.00 m/s at x = 10.0 m, what is its speed at...
A conservative force F(x) acts on a 2.0 kg particle that moves along an x axis....
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 -1.265 m/s. What is F(2.)? (sign gives direction) Between what positions on the left and right does the particle move? Left side? Right side? What is the particle's speed at x = 7.0 m
A particle of mass m=0.2kg moves in the xy plane subject to a force such as...
A particle of mass m=0.2kg moves in the xy plane subject to a force such as that its position as a function of time is given by the vector r(t)= (3.0m/s2)t*2i+[12.0m-(2.0m/s*3)t*3]j what is the magnitude of the torque on the particle about the origin at the moment when the particle reaches the x axis?
5-7 A particle of mass m moves under the action of gravity on the surface of...
5-7 A particle of mass m moves under the action of gravity on the surface of a horizontal cylinder. a) Obtain the Lagrange motion equations for the particle. b) If the particle slides in a vertical plane having left the top of the cylinder at a very small speed, find the reaction force as a function of the position. c) At what point will the cylinder particle separate?
A particle moves according to a law of motion s = f(t), t ≥ 0, where...
A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = 0.02t4 − 0.08t3 (a) Find the velocity at time t. (b) What is the velocity after 3 s? (c) When is the particle at rest? (Enter your answers as a comma-separated list.) (d) When is the particle moving in a positive direction? (Enter your answer using interval notation.) (e) Find the total distance...
A particle of mass 10kg moves in a straight line such that the force (in Newtons)...
A particle of mass 10kg moves in a straight line such that the force (in Newtons) acting on it at time (in seconds) is given by 90t4+70t3+30, If at time t=0 its velocity,v (in ms-1), is given by v(0)=9 , and its position x (in m) is given by x(0)=6 , what is the position of the particle at time ?