a)Find the magnitude of the block\'s velocity just after impact b)What was the i

Question

a)Find the magnitude of the block's velocity just after impact b)What was the initial speed of the bullet? A rifle bullet with mass 8.00g strikes and embeds itself in a block with a mass of 0.992 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 0.600 N is required to compress the spring 0.200 cm Find the magnitude of the block's velocity just after impact What was the initial speed of the bullet?

Explanation / Answer

The spring constant of the spring is given by k = F/x = 0.6N/0.002m = 300 N/m.

As the block moves on a frictionless surface, all of the kinetic energy from the bullet is transfered first to kinetic energy in the block, then to strain energy in the spring.

a.The strain energy is given by E = 0.5*k*x^2 =0.5*300* 0.15*0.15 = 3.375J.
The kinetic energy of the combined block and bullet E = 0.5*m*v^2 = 3.375J

v^2 = 2*3.375/(0.992)

V =v = 2.608 m/s where m = 1kg (0.992+0.008kg)

b. The kinetic energy of the bullet E = 0.5*m*v^2 = 3.375 J

v =2*3.375/0.008

v = 14.52 m/s

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