A block of mass 0.630 kg is pushed against a horizontal spring of negligible mas

Question

A block of mass 0.630 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x (Fig. P8.61). The force constant of the spring is 450 N/m. When it is released, the block travels along a frictionless, horizontal surface to point B, the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track. The speed of the block at the bottom of the track is v_B = 13.7 m/s, and the block experiences an average frictional force of 7.00 N while sliding up the track. What is x? m What speed do you predict for the block at the top of the track? m/s(c) Does the block actually reach the top of the track, or does it fall off before reaching the top? block falls off before reaching the top block reaches top of the track

Explanation / Answer

from energy conservation

1/2kx^2 = 1/2mv^2

x = v*sqrt(m/k)

x = 13.7*sqrt(0.63/450) = 0.513 m

b) work energy theorem

w other = total enrrgy

-f*pi*r = 1/2mvt^2+mg*2r-1/2mvb^2

-7*3.14*1 = 0.5*0.63*vt^2+0.63*9.8*2-0.5*0.63*13.7^2

vt = 8.87 m/s

c) critical velocity = sqrt(rg) = 3.13 m/s at top

block stays on the track

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