Velocity of a mass m that moves along the x-axis

Thread starter lily
Start date Oct 17, 2021
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Calc 1 Mass Velocity

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The discussion centers on the relationship between velocity and displacement for a mass m moving along the x-axis, using the equation dv/dt(mv^2 - mv0^2) = dv/dt(kx0^2 - kx^2). Participants explore the implications of differentiating both sides with respect to time, emphasizing the connection between kinetic and potential energy. The relevant equation 1/2m(v^2 - v0^2) = 1/2k(x0^2 - x^2) is highlighted to illustrate energy conservation. The conversation delves into the mathematical derivation and physical interpretation of these relationships. Overall, the discussion aims to clarify the dynamics of motion under the influence of spring forces.

Oct 17, 2021

lily

Homework Statement: A particle of constant mass m moves along the x-axis. Its velocity v and position x satisfy the equation: 1/2m(v^2 - v0^2) = 1/2k(x0^2-x^2), where k, v0 and x0 are constants. Show that whenever v does not equal 0, mdv/dt=-kx.

Relevant Equations: 1/2m(v^2 - v0^2) = 1/2k(x0^2-x^2)

mdv/dt=-kx.

dv/dt(mv^2-mv0^2) = dv/dt(kx0^2-kx^2)

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Oct 17, 2021

anuttarasammyak

Gold Member

lily said:

Relevant Equations:: 1/2m(v^2 - v0^2) = 1/2k(x0^2-x^2)

Differentiate the both hand sides by time i.e. d/dt

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