A block rests on a frictionless horizontal surface and is attached to a spring.

Question

A block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block oscillates back and forth with an angular frequency of 9.5 rad/s. The drawing shows the position of the block when the spring is unstrained. This position is labeled ''x = 0 m.'' The drawing also shows a small bottle located 0.080 m to the right of this position. The block is pulled to the right, stretching the spring by 0.050 m, and is then thrown to the left. In order for the block to knock over the bottle,it must be thrown with a speed exceeding v0. Ignoring the width of the block, find v0

.

Explanation / Answer

The total energy of block in the intial position should convert to potential energy of spring to hit bottle.

sqrt(k/m)=9.5

k=90.25m

0.5*k*0.052+0.5m*v02=0.5*k*0.082

substituting k=90.25m and solving for v0

v0=0.59m/s

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