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Chapter 6 Momentum and Collisions Section 6-1 Momentum Momentum Momentum describes an object’s motion. Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, then it has momentum . The amount of momentum an object has depends on two things : How much stuff is moving How fast the stuff is moving Momentum Momentum is a vector quantity (magnitude and direction). It is represented by the symbol p Formula : Comes from the word progress P=mv Momentum equals mass times velocity SI Units : kg∙m/s kilogram-meters per second Examples of Momentum Bowling ball vs. Playground ball at same speed. Which will have more momentum? Example of Momentum A small object moving with a very high velocity has a large momentum. Hailstones By the time they reach Earth, they have enough momentum to hurt you or cause serious damage to cars and buildings. Let’s Practice Together. Determine the momentum of a ... 60-kg halfback moving eastward at 9 m/s. 1000-kg car moving northward at 20 m/s. 40-kg freshman moving southward at 2 m/s. Impulse A change in momentum takes force and time. Momentum is closely related to force. For a CONSTANT force, impulse is the product of the force and time acted on an object. Impulse – Momentum Theorem The impulse experienced by an object is always equal to the change in its momentum. Formula FΔt =Δp force x time interval = change in momentum From this formula we can say : A small force acting for a long time can produce the same change in momentum as a large force acting for a short time. Example : Change in Momentum Preview of Collisions In a collision, an object experiences a force for a given amount of time which results in its mass undergoing a change in velocity. What happens to the momentum of the object? Newton’s 3rd Law The Law of Action-Reaction Newton's 3rd Law is naturally applied to collisions between two objects. In a collision between two objects, both objects experience forces which are equal in magnitude and opposite in direction. Such forces cause one object to speed up (gain momentum) and the other object to slow down (lose momentum). Section 2 : Conservation of Momentum Principle The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects. Momentum is conserved in collisions. Momentum is conserved for objects pushing away from each other. Conservation of Momentum m1v1,i + m2v2,i = m1v1,f + m2v2, f Total Initial Momentum = Total Final Momentum (Same Formula for Elastic Collisions) Section 3 :Collisions The total momentum remains constant in any type of collision. Total kinetic energy is not always conserved. KE is converted to internal energy when the objects deform. Elastic Collisions In elastic collisions, two objects collide and return to their original shapes with no change in total kinetic energy Both momentum and kinetic energy are conserved in an elastic collision. Elastic Collisions Elastic Collisions Elastic Collisions m1v1,i + m2v2,i = m1v1,f + m2v2, f (same formula as conservation of momentum) Perfectly Inelastic Collision When two objects collide and move together as one mass, the collision is called perfectly inelastic. The two objects become one object after the collision. Objects in this type of collision are deformed during the collision and lose some kinetic energy. KE changes to different forms of energy. Perfectly Inelastic Collision When an arrow pierces a target and remains stuck in the target, the arrow and target have undergone a perfectly inelastic collision (assuming no debris is thrown out) Perfectly Inelastic Collision m1v1,i + m2v2,i = (m1+m2)vf After colliding, the objects stick together and move with the same final velocity (Vf).