4. A rifle bullet with a mass of 7.00 g strikes and embeds itself in a block wit

Question

4. A rifle bullet with a mass of 7.00 g strikes and embeds itself in a block with mass 0.884 kg that rests on a frictionless horizontal surface and is attached to a coil spring. The impact compresses the spring 12.0 cm. Calibration of the spring shows that a force of 0.820 N is required to compress the spring 0.170 cm. Hint: Break the problem up into a part for which you can use energy conservation and a part for which you can use momentum conservation Vo a. Find the magnitude of the block's velocity just after impact b. What was the initial speed of the bullet?

Explanation / Answer

a)

Spring Constant

K=F/X =0.82/(0.17*10-2) =482.35 N/m

By Conservation of energy

(1/2)(m+M)Vfinal2 =(1/2)Kx2

(1/2)*(0.007+0.884)*Vfinal2=(1/2)*482.35*0.122

Vfinal=2.792 m/s

b)

By Conservation of momentum

mVinitial =(m+M)Vfinal

(7*10-3)Vinitial=(0.007+0.884)*2.792

Vinitial=355.4 m/s

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