A rifle bullet with mass 8.00 g strikes and embeds itself in ablock with mass 0.

Question

A rifle bullet with mass 8.00 g strikes and embeds itself in ablock with mass 0.912 kg that rests on africtionless, horizontal surface and is attached to a coil spring.The impact compresses the spring 15.0 cm. Calibration of the springshows that a force of 0.750 N is required to compress the spring0.250 cm. (a) Find the magnitude of the block's velocityjust after impact.
??? m/s

(b) What was the initial speed of the bullet?
??? m/s (a) Find the magnitude of the block's velocityjust after impact.
??? m/s

(b) What was the initial speed of the bullet?
??? m/s

Explanation / Answer

Mass of bullet m = 8 g = 0.008 kg

Mass of block M = 0.912 kg

Compression x = 15 cm =0.15 m

Compression for the force of 0.75 N is x ‘ = 0.25 cm=0.25 * 10 ^ -2 m

Force constant k = F / x ‘

                            = 300 N / m

(a). from law of conservation of energy , kinetic energy of theblock bullet system just after impact = potential energy at maximumcompression

( 1/ 2) ( m+ M ) v ^ 2 = ( 1/ 2) k x ^ 2

From this magnitude of the block’s velocity ust afterimpact v = x [ k / ( m + M ) ]

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