7.3 Conservation of Momentum Internal and external forces can act on a system. System Environment Internal forces = rider pushes on handlebars; handlebars push back on rider External forces = tire exerts force on road; road exerts force against tire Only external forces can change a system's momentum. Internal forces have no effect on a system's momentum. Internal forces, like all forces, always occur in action-reaction pairs. Because the forces in action-reaction pairs are equal and opposite - as required by Newton's Third Law - internal forces always sum to zero: Because internal forces always cancel, the total force acting on a system is equal to the sum of the external forces acting on it: We don't have to consider internal forces when calculating the total force on a system.

Momentum remains equal to zero until a nonzero total external force causes it to change. If the total force is zero, Ftotal = 0, then the initial and final momenta must be the same, pf = pi. This is momentum conservation. I = F t = pf - pi

Momentum conservation applies to all systems. Momentum conservation results in recoil. http://www.intelsec.com/product_detail_heartbeat.html https://youtu.be/EL13quhcUMw

p. 247 37.) No, because conservation of momentum would be violated. 34.) the total momentum cannot change. 35.) They do not. 36.) Momentum is conserved for the system of the two skaters. Internal forces are those the two skaters exert on each other. External forces are weights and normal forces. 37.) No, because conservation of momentum would be violated. 38.) The momentum of the keys is not conserved because the external force of gravity continually increases their momentum. However, the momentum of the universe remains the same because both the Earth and the keys experience equal and opposite gravitational forces that change their momenta by the same amount but in opposite directions.

7.4 Collisions Collisions Collision = a situation where two objects free from external forces strike one another. Collisions Elastic collision Inelastic collision Momentum is conserved Momentum is conserved KE is conserved KE is not conserved Some of the initial KE is converted to sound, heat, and deformation Objects rebound off each other Completely inelastic collision Most of the initial KE is converted to sound, heat, and deformation Colliding objects stick together

ptotal = ptotal mv = 2mvf 1/2 v = vf KEinitial = 1/2 m v2 Completely Inelastic Collisions: Same mass Momentum: Car 1 Car 2 p1 = mv p2 = 0 ptotal = mv + 0 = mv p1 = mvf p2 = mvf ptotal = mvf + mvf = 2mvf ptotal = ptotal mv = 2mvf 1/2 v = vf Kinetic Energy: KEinitial = 1/2 m v2 KEfinal = 1/2 (2m) (1/2 v)2 = 1/4 m v2 = 1/2 KEinitial

Completely Inelastic Collisions: Different masses pi = pf Completely Inelastic Collisions: Two Dimensions p. 253 (Both the x and the y components of momentum are conserved separately. Here x is chosen arbitrarily.)

pf = pi KEf = KEi Elastic Collisions p. 256 Elastic collisions conserve energy and momentum. pf = pi KEf = KEi Remember that since we are using velocities, not speeds, the objects can reverse directions, so their velocities can be positive or negative. p. 256 49.) If no external forces act on the system, then the total momentum cannot change. 50.) they are equal 51.) It is converted to other forms of energy. 52.) a completely inelastic collision 53.) The total external force (such as friction, gravity, normal forces, etc.) must be zero. 54.) No; the collision could be partially inelastic