A rifle bullet with mass 8.00 g strikes and embeds itself in a block with mass 0

Question

A rifle bullet with mass 8.00 g strikes and embeds itself in a block with mass 0.970 kg that rests on a frictionless, horizontal surface and is attached to a coil spring. The impact compresses the spring 15.0 cm. Calibration of the spring shows that a force of 0.750 N is required to compress the spring 0.240 cm.

A rifle bullet with mass 8.00 g strikes and embeds itself in a block with mass 0.970 kg that rests on a frictionless, horizontal surface and is attached to a coil spring. The impact compresses the spring 15.0 cm. Calibration of the spring shows that a force of 0.750 N is required to compress the spring 0.240 cm. Find the magnitude of the block's velocity just after impact. m/s What was the initial speed of the bullet? m/s

Explanation / Answer

K for spring = 0.75/0.0024 = 312.5 N/m

Energy stored in spring = energy of block just after embedding = .5*K*(.15)^2 = 3.52 J

Let v = velocity of block just after impact

3.52 = .5*.978*v^2

We get v = velocity of block just after impact = 2.68 m/s

Initial speed of bullet = u = (.978*2.68)/.008 = 327.79 m/s

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