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U(U) x(m) 5 10 15 A particle moves under the influence of a conservative force. The...
A 4-kg particle moves along the x-axis under the influence of a conservative force. The potential energy is given by U(x) = bx^3 , where b = 8.0 J/m^3 . What is the magnitude of the acceleration of the particle (in m/s2 ) when it is at the point x = 2 m?
A particle of mass m moves in the vertical plane (xOz) under the influence of two forces: gravity: G-m g (g oriented in the -z direction), and the frictional force: F--k V, where V is the instantaneous velocity. The initial conditions are: a) Find x(t) and zit) b) Find the equation z(x) of the trajectory. Under what conditions is this trajectory a parabola? c) Assuming that Xo > 0, and ї0, find the coordinates (xA,-A) of the highest point on...
5. Consider a particle moving in the region x>0 under the influence of the potential U(x) = C (a/x + x/a), where C=1J, and a=2m. (a) Find the equilibrium positions and determine whether they are stable or unstable. (b) Find U at those equilibrium positions. (c) Sketch U(x) without using a computer (explain how you get the sketch) and discuss the motion of the particle in details in all the different regions if its total energy E1 = 2 J,...
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...
1) A particle with mass m moves under the influence of a potential field . The particle wave function is stated by: for where and are constants. (a) Show that is not time dependent. (b) Determine as the normalization constant. (c) Calculate the energy and momentum of the particle. (d) Show that V (x /km/2h+it/k/m Aar exp (ar, t) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable...
A particle of mass 3.4 kg moves under the influence of the force F(x) = (−5x2 + 7x) N. If its speed at x = −4.0 m is v = 22.0 m/s, what is its speed (in m/s) at x = 4.0 m?
The force on a particle of mass m is given by F⃗ =24iˆ−16t2jˆ where F is in N and t in s. Problem 9.4 1 of 9 eriodic Table ▼ Part A The force on a particle of mass m is given by F 241-16 t2J where F is in N and t in s. What will be the change in the particle's momentum between t 1.0s and t 3.0s? Enter the x and y components of the Δp separated...
A particle of mass 3.2 kg moves under the influence of the force F(x) = (−5x^2 + 7x) N. If its speed at x = −2.8 m is v = 29.0 m/s, what is its speed (in m/s) at x = 2.8 m? ____m/s
A conservative force F(x) acts on a 1.7 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 atx-2.0 m, its velocity is -1.7 m/s. (a) What is F(x) at this position, including sign? Between what positions on the (b) left and (c) right does the particle move? (d) what is its particle's speed at x = 7.0 m? x (m) 0 10 15 0 -5...
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 -1.4 m/s. (a) What is F(x) at this position, including sign? Between what positions on the (b) left and (c) right does the particle move? (d) what is its particle's speed at x = 7.0 m? x (m) 10 15 (a) Number...