5. A mass mm on a horizontal surface is attached to a massless, ideal spring (sp

Question

5. A mass mm on a horizontal surface is attached to a massless, ideal spring (spring constant k) First, assume a frictionless surface: a. (2 pts.) If the mass is given an initial velocity vo at 0, at what rightward displacement s has the mass's speed v decreased totv? Show your work. Express your final answer.. ONLY in terms of variables m, k, a, and mathematical constants in SIMPLEST algebraic form with mathemarical constants expressed EFTHER as simplified pure rational nambers OR as decimal values with three significant figures Now, suppose that the surface does have some kinetic frictior b. (4 pts.) Suppose m 770 g.k 19 N/m, and the mass is given an initial velocity Yo 2.5 m's at r -0. The mass reaches a maximum rightward displacement of 23 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

a)

1/2mVo^2 - 1/2m(Vo/3)^2 = 1/2kx^2

mVo^2 - mVo^2/9 = kx^2

m(Vo^2 - Vo^2/9) = kx^2

m(8Vo^2/9) = kx^2

x = Vo*sqrt(8m/9k)

b)

Energy lost = 1/2*mVo^2 - 1/2kx^2

Energy lost = (0.5 x 770 x 2.5^2) - (0.5 x 19 x 0.23^2)

Energy lost = 2406 J

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