You and your colleague at the local engineering firm are sitting around on a slo

Question

You and your colleague at the local engineering firm are sitting around on a slow afternoon thinking about ballistics. Specifically, you are thinking of ways that you could accurately measure the speed of a 10-g bullet fired from a rifle. Your friend suggests using a mass-spring system. A spring would be attached securely to a wall on one end and to a 1-kg wooden block on the other end. The block would rest on a smooth horizontal table. The bullet would be fired horizontally into the side of the block opposite the spring, causing it to oscillate back and forth across the table. You happen to have a spring in the shop and you know from a previous project that the spring stretches 5-cm beyond its equilibrium length when you hang a 1-kg block vertically from it. You and your friend also observe that the spring can only be compressed a total of 10-cm from its equilibrium length because of the design of the coils. With this information, your friend claims that she can determine the fastest bullet speed that could be measured with this set-up. What is that speed? LOTS OF DETAILS PLEASE

Explanation / Answer

Mass of bullet, mb = 10 g
Mass of wooden block, mw = 1 Kg

Force constant of spring, F = k*x
m*g = k*x
1*9.8 = k * 5.0 * 10^-2
k = 196 N/m

With Max Compression, Potential Energy Stored in spring mass system = 1/2*k*x^2
U = 1/2 * 196 * 0.1^2 J
U = 0.98 J

Using Energy Conservation,
1/2 * (mb + mw)* v^2 = 0.98
1/2 *(10/1000 + 1)* v^2 = 0.98
v = 1.39 m/s

Using Momentum Conservation,
Let the speed of bullet be , Vmax
mb*Vmax = (mb + mw) * v
10/1000 * Vmax = (10/1000 + 1) * 1.39
Vmax = 140.4 m/s

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