Relevant concepts and equations: momentum of a particle/object: P = my (component form: Px = mvx) perfectly inelastic collision: (1) The particles stick together after they collide. (2) Momentum of the system is conserved. kinetic energy of a particle/object: K = _ m v2 conservation of energy statement, relevant when the kinetic energy and internal energy of a system change: AEnt + AK = W The change in internal energy of a system due to work by kinetic friction, a non-conservative force, which acts over path-length d: AEint = fkd Am = 8.00-g bullet is fired into a my = 270.0-g block of wood at rest on a horizontal surface. After impact, the block slides d = 7.14 m before coming to rest. The coefficient of kinetic friction between the block and the surface is p = 0.440. What is the speed of the bullet before impact? step 1: Momentum is conserved in this perfectly inelastic collision. State this concept mathematically in terms of the masses of the bullet and block of wood, along with their "initial" and "final" velocities (right before and right after the collision). Name the velocity of the system immediately following the collision Vw+. What is the relationship between the unknown initial velocity of the bullet v, and Vw+? Enter the answer both symbolically and numerically, in terms of the given values (mb and mw): vb = ( ? _Juwtb my + m 2 1 2 Vb V wtb m 1 X Vwtb step 2: Use conservation of energy considerations to find the speed of block+wood immediately following the collision. Consider this value, Vw+b, now the 'initial speed" of the system, which comes to a stop after d meters due to the work of a non-conservative force. Hint: you will need to draw a free-body diagram to find the magnitude of this non-conservative force. Consider: do any other forces do work on the system? Enter the answer both symbolically and numerically, in terms of the given values (, d, and gravitational constant g): Zum,gd Vwtb = my + m 2 X Vwtb = m/s step 3: Use the mathematical statements from step 1 and step 2 to solve for the initial speed of the bullet, in m/s. Vb = m/s