Answered: Show that when potential energy can be… | bartleby

Related questions

Question

Show that when potential energy can be written as V = V (x¡) and V = V (qi)
then the total energy of a closed conservative system of particles remains
constant. Also in this case which quantity is equal to the total energy of the
system?

Expert Solution

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

A ball of unknown mass m is tossed straight up with initial speed v. At the moment it is released, the ball is a height h above a spring-mounted platform, as shown in the figure. The ball rises, peaks, and falls back toward the platform, ultimately compressing the spring a maximum distance d from its relaxed position. Assume that the spring is perfectly ideal, with spring constant k, and that the mass of the spring and platform is negligible. What is the mass of the ball, m, assuming that there is no friction or air resistance? Using g to represent the acceleration due to gravity, enter an expression for m in terms of g, h, d, k, and v. kg m = m h www d
Say we have a mass, m, situated at a height, h, above an ideal spring with force constant k. The mass is dropped vertically onto the spring. Derive an expression for the compression of the spring from equilibrium (x) as a function of m, k, and h. By what factor is the compression changed if the mass is dropped from a height of 3h? What is the speed of the mass just as it contacts the spring?
A particle, of mass m, is moving in one dimension under the influence of a conservative force with potential V (x). (a) If the potential is given by V (x) = x² – x*, (2) - find any equilibrium points and determine their stability. (b) The particle is started from the origin x = 0 with speed v, and moves under the influence of the potential V (x) defined in equation (2). How large does v need to be for the motion to be unbounded?
Two objects of masses m and M interact with a central force that varies as 1/r4 with proportionality constant k as follows: F = k/r4 Derive an expression for the potential energy function, with the location of the reference for your formula being U(∞) = 0.
Why is the work done by a conservative force the negative of the change in potential energy? The equation for the work done is W = q∆V = -∆PE.
A box of mass 'm' is pushed into a spring with spring constant 'k'. The spring is displaced a total length of Δx, and then we let go of the box. From the work-energy theorem, what is the final velocity of the box after we let go?
Suppose there is a conservative force with potential energy function U(x, y) =−ax − bx2 + 3cy3, where a, b, and c are positive constants, throughout the entire x-yplane. Find the associated force F~ (x, y). Consider a bead of mass m that is free tomove along a frictionless wire that is fixed to the x axis. If the bead is released fromrest at the origin, in which direction will it start to move? How fast will it be travelingafter it moves a distance L?
Assume that a common flea can jump straight up to a maximum height of 20 cm. If the flea has mass m = 0.5 milligrams, calculate the potential energy of the flea (in Joules, J) once it reaches its maximum height. If the flea in jumps to its maximum height but misses jumping onto a 4-legged friend, then obviously, the flea will fall to the ground. Calculate the force of gravity acting on the flea, during its free-fall to the ground? Assume that the flea falls straight down from its maximum jump height. Express the answer in Newtons.
An object of mass m = 3 kg moves in the x direction with the potential energy U (x) shown. There are no other forces acting. On the axes provided below the graph of U (x), sketch the force F(x) that the mass experiences. If the object is released from rest at x = -2 where U = 16J, what is its velocity at x = O where U = -8J? %3D U(x) (J) |16 х (m) F(x) (N) х (m)
answer vii) onwards and dont use chatgpt thank you!
A particle of mass m is constrained to lie along a frictionless, horizontal plane subject to a force given by the expression F(x) = -kx. It is projected from x = 0 to the right along the positive x direction with initial kinetic energy To 1/2 kA". k and A are positive con- stants. Find (a) the potential energy function V(x) for this force; (b) the kinetic energy, and (c) the total energy of the particle as a function of its position. (d) Find the turning points of the motion. (e) Sketch the potential, kinetic, and total energy functions. (Optional: Use Mathcad or Mathematica to plot these functions. Set k and A each equal to 1.) 2.4
The figure shows a plot of potential energy U versus position x of a 0.260 kg particle that can travel only along an x axis under the influence of a conservative force. The graph has these values: UA = 9.00 J, UC = 20.0 J and UD = 24.0 J. The particle is released at the point where U forms a “potential hill” of “height” UB = 12.0 J, with kinetic energy 7.50 J. What is the speed of the particle at (a)x = 3.50 m and (b)x = 6.50 m? What is the position of the turning point on (c) the right side and (d) the left side?

SEE MORE QUESTIONS