Physics 10 Lecture 6A "And in knowing that you know nothing, that makes you the smartest of all. --Socrates
Momentum Which is harder to stop a small ball moving at 1 m/s or a car moving at 1 m/s? Obviously it is the car, but how do we quantify how hard it is to stop moving things? We define momentum (usually denoted with the letter p) which measures how hard it is to stop moving things. Specifically, we say that momentum is the product of the mass of a moving object and that object s velocity (momentum is a vector). Mathematically: Momentum = mass velocity = mv
Impulse If you are going to change the momentum of an object, it is most likely that you change the velocity of that object. In order to change the velocity of an object you must accelerate the object. This means that you applied a force to the object. This applied force that changes momentum is known an impulse. Impulse involves a force acting over a time interval. Impulse = change in momentum = (force) (time) Impulse = Ft = Δmv
Impulse What can you do if you want to minimize the impulse you deliver to an object? You can apply a force over a short time period. Or you can apply a small force over a time period. Why would you want to minimize force? If you were in a car accident you would want to have as small as a force acting on you as possible. Thanks to air bags, which extend the time period over which your body comes to a stop, and thus leads to a smaller force acting on you.
Impulse
Conservation of Momentum When a quantity remains unchanged during a process, the quantity is said to be conserved. If there is no external net force on a system, then momentum is conserved. This known as the law of conservation of momentum. Or in other words: In the absence of an external force, the momentum of a system remains unchanged. We particularly like to apply the conservation of momentum to collisions or explosions.
Collisions If I throw a ball up into the air, I can fully describe the motion until it hits the ground. There is a collision, it adds a force; how much we are not sure. Conservation of linear momentum can help us to describe the resulting motion. There are two types of collisions: elastic and inelastic.
Collisions For a collision, the net momentum before the collision will equal the net momentum after the collision. When two objects collide without deforming or generating heat, it is called an elastic collision. When two objects collide and either deform or generate heat it is called an inelastic collision. Usually when they stick together after the collision we call it a perfectly inelastic collision. Momentum is conserved for both elastic and inelastic collisions.
Explosions Just like collisions, explosions will also conserve momentum (as long as we define our system properly). Let s say that we have a bomb sitting on a table and then it explodes into two pieces. What is the final momentum of the system? The final momentum of the system should be zero since there are no external net forces affecting the bomb. 0.5kg 2.0kg
Label each object in the diagram. Include the direction of velocity. Collisions When confronted with a collision problem it makes sense to draw before and after diagrams. Keep track of your subscripts. For perfectly inelastic collisions, remember that they will have the same final velocity and have a combined mass.
Collisions The harder cases are collisions (or explosions) in two dimensions (or three). Just know that perpendicular directions (x and y) are independent. If for external forces, ΣF x = 0 and ΣF y = 0, then p x and p y are conserved. Apply conservation of momentum separately to each direction.
Clicker Question 6A-1 Whenever an interaction occurs in a system. Forces occur in equal and opposite pairs. Which of the following do NOT always occur in equal and opposite pairs? A) Impulses. B) Accelerations. C) Momentum Changes. D) All of these occur in equal and opposite pairs. E) None of these occur in equal and opposite pairs.
Clicker Question 6A-2 Which would be more damaging? A) Driving into a massive concrete wall. B) Driving at the same speed into a head-on collision with an identical car traveling toward you at the same speed. C) Both choices A and B would produce equivalent damage.
For Next Time (FNT) Study for Friday s Quiz 1 on Chapters 1, 2, 3, 4, 5, and 6. After the quiz, read Chapters 7 and 8.