What is the maximum speed (in m/s) of a 4.3 g particle that oscillates between x = 2.0 mm and x = 8.0 mm in the diagram? ### Graph of Potential Energy vs. DisplacementThis graph represents the potential energy \( U \) (in joules) as a function of displacement \( x \) (in millimeters). The curve depicted is a parabola, opening upwards, which is typical of systems exhibiting simple harmonic motion, such as springs.#### Graph Features:- **Vertical Axis (Y-axis):** Represents the potential energy \( U \) in joules, ranging from 0 to 5 J.- **Horizontal Axis (X-axis):** Represents the displacement \( x \) in millimeters, ranging from 0 to 8 mm.- **Curve:** The curve shows that the potential energy decreases as the displacement moves towards the center (around 4 mm), reaching its minimum at the vertex of the parabola. Then, it increases symmetrically as the displacement moves away from the center.This graph illustrates how potential energy varies with displacement in a typical spring-mass system, where the minimum potential energy corresponds to the equilibrium position.

Name: What is the maximum speed (in m/s) of a 4.3 g particle that oscillates
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: What is the maximum speed (in m/s) of a 4.3 g particle that oscillates between x = 2.0 mm and x = 8.0 mm in the diagram? ### Graph of Potential Energy vs. DisplacementThis graph represents the potential energy \( U \) (in joules) as a function of dis

From the given graph, the potential energy of the particle at x=2 mm and x=8 mm is 5 J. At the lowest point of the curve, that is, the potential energy is 1 J, the speed will be maximum. The difference in the potential energy, that is converted into the kinetic energy of the particle. Thus, KE=∆U=5 J-1 J=4 JFrom the expression for the kinetic energy, the maximum speed of the particle can be determined as follows. KE=12mv2v=2KEm=24 J4.3 g=24 J4.3×10-3 kg=43.133 m/s