Chapter 6 Momentum and Collisions Chapter Objectives Define linear momentum Compare the momentum of different objects Describe impulse Conservation of momentum Contrast types of collisions Linear Momentum Momentum is a vector quantity defined as the product of an object’s mass and velocity. Up until this point, we have been able to define several characteristics of motion: how far (displacement), how fast (velocity), how quick (acceleration), how long did it take (time), but nothing about how much? That is momentum, it is a measure of the quantity of motion itself. p = mv lowercase p means momentum The units on momentum are just like the formula tells you kg m s Things to Think about Dealing with Momentum Momentum is based on both mass and velocity. That means that an object of larger mass does not always have the greater momentum. If an object is not moving, it has no momentum. Momentum can be positive or negative based on the direction of the velocity. Momentum must also include a angle direction based on the velocity. Impulse According to Newton’s First Law, an object wants to stay in motion unless acted upon by an external force And the longer we apply that net external force, the more we will change the object’s motion. Changing motion is changing momentum! Impulse is the product of the net external force and the time over which it acts on the object. More simply put, impulse is equal to the change in momentum. Impulse = FΔt = Δp = mvf - mvi Things to Think about Dealing with Impulse Impulse has the same units as momentum. Stopping distances depend on our formula for impulse as it relates to change in momentum. That is we must know the force that the brakes can apply and how fast the vehicle is traveling to tell us a time it will take to stop. Then we can find the distance using one of our linear kinematic equations. A change in momentum over a longer time requires less force. Conservation of Momentum Newton’s Third Law, for every action there is an equal and opposite reaction, is responsible for the conservation of momentum. The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the two objects. So momentum is conserved in all collisions. Also, momentum is conserved for objects pushing away from each other; such as people on roller skates, explosions and splitting of atoms. pi = pf m1v1i + m2v2i = m1v1f + m2v2f Types of Collision An inelastic collision is when two objects collide and continue in the same direction after the collision. This would be like a bowling ball striking a bowling pin. A perfectly inelastic collision is when two objects stick together and move with a common velocity after colliding. This is best described as a car accident. You start with two objects that stick together to form one object after colliding. An elastic collision is when two objects collide and change direction of both objects. This is like when two billiard balls collide. Kinetic energy is conserved is elastic collisions. Solving Collision Problems What Happens Elastic Inelastic Perfectly Inelastic Formula Conserved Quantity m1v1i + m2v2i = m1v1f + m2v2f Momentum Kinetic Energy Objects become deformed in some way and move in same direction. m1v1i + m2v2i = m1v1f + m2v2f Momentum Two objects stick together to form one object with constant velocity. m1v1i + m2v2i = (m1 + m2)vf Momentum Two objects bounce and move separate in opposite directions.