A particle of mass m = identical springs on a frictionless, horizontal tabletop. Both springs have spring constant k and are initially unstressed, and the particle is at x = 0. (a) The particle is pulled a distance x along a direction perpendicular to the initial configuration of the springs as shown in Figure P7.50. Show that the force exerted by the springs on the particle is 1.18 kg is attached between two 2(1 -) L F = -2kx| 1 V + I?, (b) Show that the potential energy of the system is U(x) = kx + 2kL(L – V + L) (c) Make a plot of U(x) versus x and identify all equilibrium points. Assume L = 1.20 m and k = 40.0 N/m. (d) If the particle is pulled 0.500 m to the right and then released, what is its speed when it reaches x = 0? Overhead view m x = 0 Figure P7.50

A particle of mass m = identical springs on a frictionless, horizontal tabletop. Both springs have spring constant k and are initially unstressed, and the particle is at x = 0. (a) The particle is pulled a distance x along a direction perpendicular to the initial configuration of the springs as shown in Figure P7.50. Show that the force exerted by the springs on the particle is 1.18 kg is attached between two 2(1 -) L F = -2kx| 1 V + I?, (b) Show that the potential energy of the system is U(x) = kx + 2kL(L – V + L) (c) Make a plot of U(x) versus x and identify all equilibrium points. Assume L = 1.20 m and k = 40.0 N/m. (d) If the particle is pulled 0.500 m to the right and then released, what is its speed when it reaches x = 0? Overhead view m x = 0 Figure P7.50

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)...

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Question

A particle of mass m =
identical springs on a frictionless, horizontal tabletop.
Both springs have spring constant k and are initially
unstressed, and the particle is at x = 0. (a) The particle
is pulled a distance x along a direction perpendicular to
the initial configuration of the springs as shown in Figure
P7.50. Show that the force exerted by the springs on the
particle is
1.18 kg is attached between two
2(1 -)
L
F = -2kx| 1
V + I?,
(b) Show that the potential energy of the system is
U(x) = kx + 2kL(L – V + L)
(c) Make a plot of U(x) versus x and identify all equilibrium
points. Assume L = 1.20 m and k = 40.0 N/m. (d) If
the particle is pulled 0.500 m to the right and then released,
what is its speed when it reaches x = 0?
Overhead view
m
x = 0
Figure P7.50

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