A block with mass of 4.90 kg is attached to a horizontal spring with spring cons

Question

A block with mass of 4.90 kg is attached to a horizontal spring with spring constant k = 4.16 A block with mass of 4.90 kg is attached to a hori 10^2 N/m, as shown in the figure. The surface the block rests upon is frictionless. The block is pulled out to xi = 0.0450 m and released. (a) Find the speed of the block at the equilibrium point. m/s (b) Find the speed when x = 0.033 m. m/s (c) Repeat part (a) if friction acts on the block, with coefficient ?k = 0.130. m/s Suppose the spring system in the last example starts at x = 0 and the attached object is given a kick to the right, so it has an initial speed of 0.62 m/s. (a) What distance from the origin does the object travel before coming to rest, assuming the surface is frictionless? m (b) How does the answer change if the answer if the coefficient of kinetic friction is ?k = 0.130? (Use the qu

Explanation / Answer

a)1/2 kx2 = 1/2 mv2

v=x(k/m) = 0.045 * (416/4.9) = 0.415 m/s

b)1/2 mv'2 = 1/2 kx2 - 1/2 kx'2 = 1/2 * 416 *(0.0452-0.0332) = 0.194688

v'2 = 2*0.194688 / 4.9 = 0.0795

v' = 0.282 m/s

c)1/2 mv2 = 1/2 kx2 - mgx = 1/2 * 416 * 0.0452 - 0.130 * 4.9 * 9.8* 0.045 = 0.140283

v2 = 2*0.140283/4.9 = 0.0573

v = 0.239 m/s

Second Part

1/2 kx2 = 1/2 mv2

x= v(m/k) = 0.62 * (4.9/416) = 0.0673 m

b)1/2 mv2 = 1/2 kx2 + mgx

1/2 * 416x2 + 0.13*4.9*9.8x - 1/2*4.9*0.622 = 0

208x2 + 6.2426x -0.94178 =0

x=0.05394 m

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