A block rests on a frictionless horizontal surface and is attachedto a spring. W

Question

A block rests on a frictionless horizontal surface and is attachedto a spring. When set into simple harmonic motion, the blockoscillates back and forth with an angular frequency of 7.0 rad/s.The drawing shows the position of the block when the spring isunstrained. This position is labeled ''x = 0 m.'' Thedrawing also shows a small bottle located 0.080 m to the right ofthis position. The block is pulled to the right, stretching thespring by 0.050 m, and is then thrown to the left. In order for theblock to knock over the bottle,it must be thrown with a speedexceeding v0. Ignoring the width of the block,find v0.

Explanation / Answer

as it is the block would get pulled to left by thespring by 0.050 m, in addition to which it would get compressed further dueto v0 imparted to block. let final compression be a. so, by conserving energy, 1/2*k*a*a = 1/2*k*0.05*0.05 + 1/2*m*v0*v0 now, after this compression, the block would be pushedto the bottle by the same distance a from mean position. so, a = 0.080 m so, 1/2*k*[0.08*0.08 - 0.05*0.05] = 1/2*m*v0*v0 angular frequency of oscillation = = [k/m] = 7.2 rad/s so, k = m* = 51.84*m so, v0 = [0.0039*51.84*m/m] m/s           =0.45 m/s

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