A block of mass 0.500 kg is pushed against a horizontal spring of negligible mas

Question

A block of mass 0.500 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance Delta x (Fig. P7.51). 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 vB = 13.0 m/s, and the block experiences an average frictional force of 7.00 N while sliding up the track. Figure P7.51. What is Delta 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? The block reaches the top of the track. The block falls off before reaching the top.

Explanation / Answer

a)Conserving energy,

0.5kx2=0.5mv2

x=sqrt(m/k)*v=0.433m

b)Conserving energy,

0.5mvB2=mg*2R+f*2r+0.5mv2

0.5*0.5*132=0.5*9.8*2+7*2+0.25*v2

0.25*v2=-11.53

Since v2 cannot be negative, the block does not reach the top of the track.

The block falls of before reaching the top.

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