Linear Momentum and Collisions PDF

Linear Momentum and Collisions (Recommended reading: Chapter 7, Giancoli) Linear Momentum The linear momentum of a body is defined as the product of its mass multiplied by its linear velocity: SI units kg m/s Momentum is a vector quantity – its direction is the same as the direction of the veloci...

Linear Momentum and Collisions (Recommended reading: Chapter 7, Giancoli) Linear Momentum The linear momentum of a body is defined as the product of its mass multiplied by its linear velocity: SI units kg m/s Momentum is a vector quantity – its direction is the same as the direction of the velocity vector Linear Momentum Everyday usage of the term momentum is in accord with its definition, a fast-moving car has more momentum than a slow-moving car of the same mass; a heavy truck has more momentum than a small car moving with the same speed. The more momentum an object has, the harder it is to stop it, and the greater effect it will have on another object if it collides with it.  Newton’s Second Law Newton’s statement of the second law of motion is: The rate of change of momentum of an object is equal to the net force applied to the object. Total Linear Momentum of an isolated system of objects The total momentum of a system of objects is the sum of the momentum of each object For a system of n objects What has more momentum? What has more momentum? a) A car of mass 1800 kg travelling east of 3 m/s. b) A bullet of mass 0.05 kg travelling east at 2000 m/s. p=mv Linear Momentum and Collisions Consider a collision between two objects. We assume that the only significant forces that act during the collision are the forces that each object exerts on the other Or possibly……  Total Momentum Although the momentum of each object changes as a result of the collision, the total momentum of the system before the collision is found to be the same as the total momentum of the system after the collision. The total momentum is the sum of the momentum of each object: Law of Conservation of Linear Momentum Law of Conservation of Linear Momentum states that when two or more objects act on each other, the total momentum of the system before the action is equal to the total momentum after the action, provided that no external forces act on the system. The total momentum of an isolated system of objects remains constant. Law of Conservation of Linear Momentum Consider a collision between two objects We know that the total momentum before the collision (initial total momentum) is equal to the total momentum after the collision (final total momentum) i.e.  Types of Collisions The two objects move in the same direction before and after the collision The two objects move in the same direction after the collision. One of the objects is stationary before the collision In this case 2 is stationary before the collision Types of Collisions The two objects stick together and move with a common velocity after the collision Both objects change direction after the collision Types of Collisions Elastic and Inelastic Collisions Linear Momentum is conserved in all collisions Total energy is conserved in all collisions Collisions in which kinetic energy is conserved are elastic collisions, and those in which the kinetic energy is not conserved are inelastic collisions Therefore, a full analysis of a collision requires that we quantify the amount of energy transferred during the collision and so we will return to collisions in the Energy section Collisions Note: Momentum is a vector quantity the direction of which is determined by the direction of the velocity vector. In collision problems it is usual to assign the velocity of the object moving in the +x direction (to the right) as positive. Therefore the momentum of any object moving in the +x direction is positive. Consequently, the velocity of any object moving in the opposite direction (i.e. moving to the left) is negative and the momentum of the object is also negative.  Problem Sheet Conservation of Linear Momentum Question 1. Determine the momentum of an object of mass 510 g moving at a velocity of 21 m/s due east. Question 2. An object of mass 4.0 kg moving in the+ x direction with a velocity of 10.0 m/s collides with an object of mass 1.0 kg moving in the – x direction with a velocity of 4.0 m/s. Assuming that the two masses couple together, determine the common velocity after the collision Problem Sheet Conservation of Linear Momentum Question 3. An object of mass 4.00 kg traveling along the + x direction with a velocity of 2.00 m/s collides with an object of mass 6.00 kg traveling along the – x direction with a velocity of 4.00 m/s. The two objects bounce off one another and after the collision the larger mass has a velocity of 0.80 m/s in the + x direction. Determine the velocity of the smaller mass after the collision