A mass m on a horizontal surface is attached to a massless, ideal spring (spring

Question

A mass m on a horizontal surface is attached to a massless, ideal spring (spring constant k). First, assume a frictionless surface: a. If the mass is given an initial velocity v_o at x = 0, at what rightward displacement x has the mass's speed v decreased to 1/2 v_0? Show your work. Express your final answer..., ONLY in terms of variables m, k, v_0, and mathematical constants in SIMPLEST algebraic form with mathematical constants expressed EITHER as simplified pure rational numbers OR as decimal values with three significant figures Now. suppose that the surface does have some kinetic friction: b. Suppose m = 850 g, k = 25 N/m. and the mass is given an initial velocity v_0 = 3.0 m/s at x = 0. The mass reaches a maximum rightward displacement of 18 cm before (momentarily) stopping and turning around. How much energy is lost to friction during the mass's rightward motion? Show your work.

Explanation / Answer

using energy conservation

initally only kinetic energy there which is equal to total energy of system

mv^2/2 = m(v/2)^2 + kx^2/2

mv^2/2 = mv^2/8 + kx2/2

mv^2/2 - mv^2/8 = kx^2/2

3mv^2/4 = kx^2

x = sqrt(3mv^2/k)

part b )

mv^2 = kx^2 + wf

0.850 kg * 3^2 /2 = 25 * 0.18m^2/2 + wf

wf = 3.42 J

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