A rifle bullet with mass 8.00 g strikes and embeds itself in a block with a mass

Question

A rifle bullet with mass 8.00g  strikes and embeds itself in a block with a mass of 0.992kg  that rests on a frictionless, horizontal surface and is attached to a coil spring. (See the figure below (Figure 1) .) The impact compresses the spring 15.0cm . Calibration of the spring shows that a force of 0.650N  is required to compress the spring 0.300cm .

Find the magnitude of the block's velocity just after impact.

A rifle bullet with mass 8.00g strikes and embeds itself in a block with a mass of 0.992kg that rests on a frictionless, horizontal surface and is attached to a coil spring. (See the figure below (Figure 1) .) The impact compresses the spring 15.0cm . Calibration of the spring shows that a force of 0.650N is required to compress the spring 0.300cm. Find the magnitude of the block's velocity just after impact. What was the initial speed of the bullet?

Explanation / Answer

k=0.650/0.3 =2.167

let V= initial vel

V1 =vel of block after impact

conserving energy we get

0.5 (0.0080*V^2=0.5*(0.992+0.008)*V1^2+0.5*2.167*(0.15)^2

F=Kx=ma

V1^2-V^2=2ax=2kx^2/m

by two equation solving we get V and V1

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