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 7.8 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 exceedingv0. Ignoring the width of the block, findv0.

Explanation / Answer

energy given to reach the bottle = 1/2 * m * Vo2

Extra energy needed to reach the bottle

= 1/2 * k * (0.0802 – 1/2 * k * 0.052)

w2 = k/m

k = m * w2

m Vo2 = m * 60.84 ( 0.0802 – 0.052 )

Vo = 0.487 m/s

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