2 P6 (C) Calculate the mechanical energy of, power generated within, impulse applied to, and momentum of a physical system.Two identical cars collide head on. Each car is traveling at 100 km/h. The impact force on each car is the same as hitting a solid wall at: (a) 100 km/h (b) 200 km/h (c) 150 km/h (d) 50 km/h
3 Since the collision is head on and each car is identical and traveling at the same speed, the force of impact experienced by each car is equal and opposite. This means that the impact is the same as hitting a solid wall at 100 km/h
4 Impulse = Momentum Momentum is defined as “Inertia in Motion” Ns Consider Newton’s 2nd Law and the definition of acceleration Units of Impulse: Units of Momentum:NsKg x m/sMomentum is defined as “Inertia in Motion”
5 Impulse – Momentum Theorem CHANGE IN MOMENTUMThis theorem reveals some interesting relationships such as the INVERSE relationship between FORCE and TIME
7 Impulse – Momentum Relationships ConstantSince TIME is directly related to the VELOCITY when the force and mass are constant, the LONGER the cannonball is in the barrel the greater the velocity.Also, you could say that the force acts over a larger displacement, thus there is more WORK. The work done on the cannonball turns into kinetic energy.
8 How about a collision?Consider 2 objects speeding toward each other. When they collide Due to Newton’s 3rd Law the FORCE they exert on each other are EQUAL and OPPOSITE. The TIMES of impact are also equal. Therefore, the IMPULSES of the 2 objects colliding are also EQUAL
9 How about a collision?If the Impulses are equal then the MOMENTUMS are also equal!
10 Momentum is conserved!The Law of Conservation of Momentum: “In the absence of an external force (gravity, friction), the total momentum before the collision is equal to the total momentum after the collision.”
11 Types of CollisionsA situation where the objects DO NOT STICK is one type of collisionNotice that in EACH case, you have TWO objects BEFORE and AFTER the collision.
12 A “no stick” type collision Spbefore =Spafter-10 m/s
13 Types of CollisionsAnother type of collision is one where the objects “STICK” together. Notice you have TWO objects before the collision and ONE object after the collision.
14 A “stick” type of collision Spbefore =Spafter5 m/s
15 The “explosion” typeThis type is often referred to as “backwards inelastic”. Notice you have ONE object ( we treat this as a SYSTEM) before the explosion and TWO objects after the explosion.
16 Backwards Inelastic - Explosions Suppose we have a 4-kg rifle loaded with a kg bullet. When the rifle is fired the bullet exits the barrel with a velocity of 300 m/s. How fast does the gun RECOIL backwards?Spbefore =Spafter-0.75 m/s
17 Collision Summary Elastic Collision = Kinetic Energy is Conserved Sometimes objects stick together or blow apart. In this case, momentum is ALWAYS conserved.When 2 objects collide and DON’T stickWhen 2 objects collide and stick togetherWhen 1 object breaks into 2 objectsElastic Collision = Kinetic Energy is ConservedInelastic Collision = Kinetic Energy is NOT Conserved
18 Elastic CollisionSince KINETIC ENERGY is conserved during the collision we call this an ELASTIC COLLISION.
19 Inelastic CollisionSince KINETIC ENERGY was NOT conserved during the collision we call this an INELASTIC COLLISION.
20 ExampleGranny (m=80 kg) whizzes around the rink with a velocity of 6 m/s. She suddenly collides with Ambrose (m=40 kg) who is at rest directly in her path. Rather than knock him over, she picks him up and continues in motion without "braking." Determine the velocity of Granny and Ambrose.How many objects do I have before the collision?How many objects do I have after the collision?214 m/s
21 Type 1 - Two objects push apart from each other. (Variations: Something is thrown, launched, or shot; a person starts moving on a boat (or rollingobject); a rocket or a balloon.)Note: In all of these examples there are two objects at rest before that push off of each other (Newton’s3rd law). After the push they are both moving in opposite directions.Equation: 0 = p1a + p2aEx1 -. Two people on ice skates push against each other. The person on the left is 50 kg, the person on the rightis 60 kg. If the person on the right ends up going 3 m/s, how fast is the other person going?
24 Type 2 - Two objects collide and do not stick together. (Variations: Only one of the objects is moving before or after; head on collisions; rear end collisions; aprojectile shot through an object.)Note: The direction of the object doesn’t matter before or after or if one of them is at rest, just be sureto put in a negative velocity for those moving left and a zero velocity for those at rest.Equation: p1b + p2b = p1a + p2aEx2 - A 6 kg object going 3 m/s to the right hits a 4 kg object going 4 m/s to the left. If afterward the6 kg object ends up going 4 m/s to the left, find out what happens to the 4 kg object.
27 Type 3 - Two objects collide and stick together. (Variations: Only one of the objects is moving before or after; head on collisions; rear end collisions; aprojectile shot into an object.)Note: Perfectly inelastic collisions. Only difference between this and Case 2 is that in this case there isonly one moving object afterwards, so combine the masses. The velocity will be the same for both.)Equation: p1b + p2b = pa1+2Ex3 - A 0.25 kg arrow going 35 m/s is shot into a 6 kg target. The target is on wheels, so find how fast it willroll backwards.
28 Type 4 - An object splits apart. (Variations: explosions; two objects together and moving push off from each other.)Note: Simply the opposite of Case 3, if the split occurs only in one direction. If it happens twodimensionally (as in an explosion), you have to do Conservation of Momentum in each directionindependently. In the second dimension, the original momentum was zero, so it is actually just Case 1.Equations: x-dir: pb1+2 = p1a + p2a; y-dir: 0 = p1a + p2aEx4 - A 200 kg car is rolling at 10 m/s when its fuel tank explodes into 4 pieces. If 40 kg of it goes forward at 25m/s, 80 kg goes backwards, 30 kg goes to the left at 10 m/s, and a piece goes to the right. Find how much massis going to the right and how fast it is moving. Also find out how fast the 80 kg piece is moving backwards.
29 Collisions in 2 Dimensions The figure to the left shows a collision between two pucks on an air hockey table. Puck A has a mass of kg and is moving along the x-axis with a velocity of +5.5 m/s. It makes a collision with puck B, which has a mass of kg and is initially at rest. The collision is NOT head on. After the collision, the two pucks fly apart with angles shown in the drawing. Calculate the speeds of the pucks after the collision.vAvAsinqvAcosqvBcosqvBsinqvB
30 Collisions in 2 dimensions vAvAsinqvAcosqvBcosqvBsinqvB