![A particle of mass 5 kg is subject to a conservative force whose potential energy (in joules) as a function of position (in meters) is given by the equation U(x) =-100x5e-1x [where x > 0] (a) Determine the position xo where the particle experiences stable equilibrium (b) Find the potential energy Uo of the particle at the position x 2106 The particle is displaced slightly from position x = xo and released (c) Determine the effective value of the spring constant for this potential energy function about the point x = x0. X N/m (d) Determine the period of the small-amplitude oscillations that the particle undergoes](http://img.homeworklib.com/questions/42559ea0-1efb-11eb-a036-416296da2ff7.png?x-oss-process=image/resize,w_560)
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A particle of mass 5 kg is subject to a conservative force whose potential energy (in...
3. A particle of mass is constrained to move without friction along the x-axis, subject to...
3. A particle of mass is constrained to move without friction along the x-axis, subject to a potential energy siven by Ue) Uo/ constants. Show that for small oscillations about x 0, the particle undergoes simple harmonic motion. What condition on x is required for the oscillations to be "small" (i.e. simple harmonic)? Find the period Tof the oscillations. - 1) where Uo and b are positive
Particle of mass m moves along x-axis under a conservative force given by F=A(e^(-2(x-xo)/xo)-e^(-x/xo)) where A...
Particle of mass m moves along x-axis under a conservative force given by F=A(e^(-2(x-xo)/xo)-e^(-x/xo)) where A and xo are constants. Assume potential energy at infinity (Uo) =0. Calculate the potential energy of the particle in term of A,x,and xo.
Problem 1: A particle of mass 5 10-8 kg is attached to a massless spring whose...
Problem 1: A particle of mass 5 10-8 kg is attached to a massless spring whose spring constant is 2 10-3N/m. Maximum displacement of the particle from the equilibrium position is 3 - 10-9m. The world is one- dimensional. (a) Find the (classical) amplitude of these oscillations. Yes, funny question, but I had to ask (b) Calculate the quantum of energy ho of this harmonic oscillator. he oea rthe prtic estimale the cormesponding uanitum umher. (d) If this harmonic oscillator...
3. A particle subject only to conservative forces has the potential energy vs. position curve shown...
3. A particle subject only to conservative forces has the potential energy vs. position curve shown to the right. The function for the potential is: U(x)-k where γ 1.00 J.m2 and k-7.00 Jr. The particle has a mass of 3.00 kg. (a) Calculate the force on the particle as a function of position, F(x). (b) At which points, (A, B, C, D), must the particle be placed at rest such that it will stay at rest? Why must the particle...
A particle with mass 1.39 kg oscillates horizontally at the end of a horizontal spring. A...
A particle with mass 1.39 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.959 m and a duration of 127 s for 79 cycles of oscillation. Find the frequency, f the speed at the equilibrium position, Vmax, the spring constant, k, the potential energy at an endpoint, Umax, the potential energy when the particle is located 54.1% of the amplitude away from the equilibrium position, U, and the kinetic energy, K, and...
A particle with mass 2.73 kg oscillates horizontally at the end of a horizontal spring. A...
A particle with mass 2.73 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.869 m and a duration of 131 s for 69 cycles of oscillation. Find the frequency, f, the speed at the equilibrium position, Vmax, the spring constant, k, the potential energy at an endpoint, Umax, the potential energy when the particle is located 37.3% of the amplitude away from the equilibrium position, U, and the kinetic energy, K, and...
A particle with mass 2.47 kg oscillates horizontally at the end of a horizontal spring. A...
A particle with mass 2.47 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.913 m and a duration of 121 s for 71 cycles of oscillation. Find the frequency, the speed at the equilibrium position, vimax the spring constant, k, the potential energy at an endpoint, U the potential energy when the particle is located 41.7% of the amplitude away from the equilibrium position, U, and the kinetic energy, K, and the...
A particle with mass 1.09 kg oscillates horizontally at the end of a horizontal spring. A...
A particle with mass 1.09 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.891 m and a duration of 131 s for 68 cycles of oscillation. Find the frequency, f, the speed at the equilibrium position, vmax, the spring constant, k, the potential energy at an endpoint, Umax, the potential energy when the particle is located 50.3% of the amplitude away from the equiliibrium position, U, and the kinetic energy, K, and...
A particle with mass 1.59 kg oscillates horizontally at the end of a horizontal spring. A...
A particle with mass 1.59 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.901 m and a duration of 125 s for 68 cycles of oscillation. Find the frequency, f, the speed at the equilibrium position, vmax, the spring constant, k, the potential energy at an endpoint, Umax, the potential energy when the particle is located 50.3% of the amplitude away from the equiliibrium position, U, and the kinetic energy, K, and...
A particle with mass 2.15 kg oscillates horizontally at the end of a horizontal spring. A...
A particle with mass 2.15 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.909 m and a duration of 121 s for 76 cycles of oscillation. Find the frequency, f, the speed at the equilibrium position, Vmax, the spring constant, k, the potential energy at an endpoint, Umax, the potential energy when the particle is located 51.9% of the amplitude away from the equiliibrium position, U, and the kinetic energy, K, and...
3. A particle of mass is constrained to move without friction along the x-axis, subject to a potential energy siven by Ue) Uo/ constants. Show that for small oscillations about x 0, the particle undergoes simple harmonic motion. What condition on x is required for the oscillations to be "small" (i.e. simple harmonic)? Find the period Tof the oscillations. - 1) where Uo and b are positive
Problem 1: A particle of mass 5 10-8 kg is attached to a massless spring whose spring constant is 2 10-3N/m. Maximum displacement of the particle from the equilibrium position is 3 - 10-9m. The world is one- dimensional. (a) Find the (classical) amplitude of these oscillations. Yes, funny question, but I had to ask (b) Calculate the quantum of energy ho of this harmonic oscillator. he oea rthe prtic estimale the cormesponding uanitum umher. (d) If this harmonic oscillator...
3. A particle subject only to conservative forces has the potential energy vs. position curve shown to the right. The function for the potential is: U(x)-k where γ 1.00 J.m2 and k-7.00 Jr. The particle has a mass of 3.00 kg. (a) Calculate the force on the particle as a function of position, F(x). (b) At which points, (A, B, C, D), must the particle be placed at rest such that it will stay at rest? Why must the particle...
A particle with mass 1.39 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.959 m and a duration of 127 s for 79 cycles of oscillation. Find the frequency, f the speed at the equilibrium position, Vmax, the spring constant, k, the potential energy at an endpoint, Umax, the potential energy when the particle is located 54.1% of the amplitude away from the equilibrium position, U, and the kinetic energy, K, and...
A particle with mass 2.73 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.869 m and a duration of 131 s for 69 cycles of oscillation. Find the frequency, f, the speed at the equilibrium position, Vmax, the spring constant, k, the potential energy at an endpoint, Umax, the potential energy when the particle is located 37.3% of the amplitude away from the equilibrium position, U, and the kinetic energy, K, and...
A particle with mass 2.47 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.913 m and a duration of 121 s for 71 cycles of oscillation. Find the frequency, the speed at the equilibrium position, vimax the spring constant, k, the potential energy at an endpoint, U the potential energy when the particle is located 41.7% of the amplitude away from the equilibrium position, U, and the kinetic energy, K, and the...
A particle with mass 2.15 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.909 m and a duration of 121 s for 76 cycles of oscillation. Find the frequency, f, the speed at the equilibrium position, Vmax, the spring constant, k, the potential energy at an endpoint, Umax, the potential energy when the particle is located 51.9% of the amplitude away from the equiliibrium position, U, and the kinetic energy, K, and...
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