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At the maximum height, the kinetic energy and the speed are zero, so if the object were initially traveling upward, its velocity would go through zero there, and y max would be a turning point in the motion. At ground level, y 0 = 0, the potential energy is zero, and the kinetic energy and the speed are maximum: \[U_{0} = 0 = E - K_{0},\]
Interpreting a one-dimensional potential energy diagram allows you to obtain qualitative, and some quantitative, information about the motion of a particle. At a turning point, the potential energy equals the mechanical energy and the kinetic energy is zero, indicating that the direction of the velocity reverses there.
Let's continue our discussion of potential energy graphs by introducing some new terms - turning points and equilibrium points. We already saw turning points in the last section - these were the point in the motion at which the object stopped moving and turned around to go the other direction.
Interpreting a one-dimensional potential energy diagram allows you to obtain qualitative, and some quantitative, information about the motion of a particle. At a turning point, the potential energy equals the mechanical energy and the kinetic energy is zero, indicating that the direction of the velocity reverses there.
Given the graph of a one-dimensional potential energy function and the total energy of a particle, give a qualitative description of the motion of this particle and locate its turning points, if any, and regions of acceleration and deceleration. S2.
Turning Points. Turning points are simply places in space where a particle has no more kinetic energy and must either stop or turn back. To find turning points, you can just draw a horizontal line on the energy graph at the value of the total energy.
1. State the relationship between the line integral of a conservative force between speci ̀„ed limits and the potential energy di®erence between those limits (MISN-0-21). 2. Given the graph of a simple function, such as f = x exp(- a x), demonstrate the relationship between slope and derivative at any given point (MISN-0-1).
Create and interpret graphs of potential energy; Explain the connection between stability and potential energy
Moving beyond equilibrium, we can also use conservation of energy and turning points to say useful things about the motion, without having to assume a small angle. Suppose the pendulum starts at \( \phi = 0 \), and we give it a push so that it starts moving with initial speed \( v_0 \).
At a turning point, the potential energy equals the mechanical energy and the kinetic energy is zero, indicating that the direction of the velocity reverses there. The negative of the slope of the potential energy curve, for a particle, equals the one-dimensional component of the conservative force on the particle.