A bullet of mass 20 g travelling horizontally at a speed of 500 m/s passes through a wooden block of mass 10.0 kg initially resting on a level surface. The bullet emerges with a speed of 100 m/s , and the block slides 20 cm along the surface before coming to a stop. Determine the friction coefficient between the block and the surface, as shown in the figure.

Step-by-step solution

Let the mass of the bullet be m = 20 g = 0.02 kg and its initial speed be u = 500 m/s . Let the mass of the block be M = 10.0 kg , which is initially at rest ( U = 0 ). After passing through the block, the bullet's final speed is v = 100 m/s . Let the velocity of the block immediately after the collision be V . Applying the principle of conservation of linear momentum: m u + M U = m v + M V 0.02 500 + 10 0 = 0.02 100 + 10 V 10 = 2 + 10 V 10 V = 8 V = 0.8 m/s The block then slides a distance s = 20 cm = 0.2 m before