A rifle bullet with mass 8.00 g strikes and embeds itself in a block with mass 0.992 kg that rests on a frictionless, horizontal surface and is attached to a coil spring (?Fig. P8.79?). 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 0.250 cm. (a) Find the magnitude of the block’s velocity just after impact. (b) What was the initial speed of the bullet?

Solution 83P Introduction We have first calculate the spring constant from the given calibration data. Then we can calculate the total potential energy for the given compression. The potential energy of will be equal to the initial kinetic energy of the block plus bullet after collision which will be equal to the kinetic energy of the bullet before collision. Step 1 The spring was compressed by 0.250 cm with 0.750 N force, hence the spring constant is Hence the potential energy of the spring, after fully compressed, is Step 2 Now let us consider blockis the velocity of the block just after collision. The mass of the block just after collision is Hence the kinetic energy is Now equating this two energy we have