Momentum, p = m v. Collisions and Work(L8) Crash! Momentum and Collisions. Conservation of Momentum. elastic collisions

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1 Collisions and Work(L8) Crash! collisions can be ery coplicated two objects bang into each other and exert strong forces oer short tie interals fortunately, een though we usually do not know the details of the forces, we know fro the 3 rd law that the forces are equal and opposite A I doing any WORK? Moentu and Collisions The concept of oentu is ery useful when discussing how 2 objects interact. Suppose two objects are on a collision course. A B We know their asses and speeds before they hit The oentu concept helps us to see what can happen after they hit. Conseration of Moentu One consequence of Newton s 3 rd law is that if we add the oentu of both objects before the collision it MUST be the sae as the oentu of the two objects after the collision. This is what we ean by conseration: when soething happens (like a collision) soething doesn t change that is ery useful to know because collisions can be ery coplicated! Moentu, p = a 1 kg object oing at 1000 /s has the sae oentu as a 1000 kg object oing at 1 /s (p = 1000 kg /s) Ipulse = p (delta p eans the change in oentu, p) Ipulse = F t = p, so if 2 objects collide, the forces are the sae (Newton s 3 rd law), and t is the sae, so p is the sae for both. the oentu lost by one object is gained by the other object conseration before after elastic collisions oentu before = oentu after =

2 inelastic collisions objects stick together before after oentu before = oentu after = 2 /2 = 2 How uch oentu did the stationary object get in the collision? In the elastic collision the object that was initially at rest got a oentu = in the inelastic collision the object that was at rest got only /2 half as uch! This is another exaple of the fact that ore force is inoled between bouncy objects (elastic) copared to non-bouncy objects (inelastic) Football proides any collision exaples to think about! Colliding players exert equal forces and equal ipulses on each other in opposite directions Before the collision After the collision Moentu of the two players before and after the collision is the sae (200 kg /s) Moentu of running back is 100 kg x 5 /s = 500 kg /s Moentu of linebacker is 75 kg x (-4 /s) = -300 kg /s Total oentu is = kg /s (to the right) oentu ust be 200 kg /s = total ass x final elocity 200 = 175 x final elocity final elocity = 200/175 = 1.14 /s to the right

3 non-iolent collisions Recoil That kick you experience when you fire a gun is due to conseration of oentu. Two stationary ice skaters push off both skaters exert equal forces on each other howeer, the saller skater acquires a larger speed than the larger skater. oentu is consered! recoil Before firing: oentu = 0 after the cannon is fired After firing oentu = 0 Since the cannon ball goes to the right, the cannon ust go to the left. The speed of the cannon ball is uch larger than the recoil speed of the cannon because cannonball cannonball = cannon cannon or sall ass x big speed = big ass x sall speed Recoil in action Rockets hot gas ejected at ery high speed Work and Energy These ters hae a coon eaning in eeryday language which are not the sae as the physics definitions If we hae energy we can do things Energy is the capacity to do work But what is energy?

4 What is work? According to the physics definition, you are NOT doing work if you are just holding the weight aboe your head you are doing work only while you are lifting the weight aboe your head Work requires two things 1) force 2) otion in the direction of the force Force, F distance, d work Who s doin the work around here? to do work on an object you hae to push the object a certain distance in the direction that you are pushing Work = force x distance = F x d If I carry a box across the roo I do not do work on it because the force is not in the direction of the otion NO WORK WORK A rap can reduce the force Raps are useful achines! A achine is any deice that allows us to accoplish a task ore easily. it does not need to hae any oing parts. work = force x distance WORK DONE = big force little distance or little force big distance

5 Kinetic energy If soething oes in any way, it has kinetic energy kinetic energy (KE) is energy of otion If I drie y car into a tree, the kinetic energy of the car can do work on the tree it can knock it oer KE = ½ 2 KE does not depend on Which direction object goes Potential energy If I raise an object to soe height (h) it also has energy potential energy If I let the object fall it can do work We call this Graitational Potential Energy GPE= x g x h = g h in kg, g= 10/s 2, h in, GPE in Joules (J) the higher I lift the object the ore potential energy it gas exaple: pile drier conseration of energy if soething has energy it doesn t loose it It ay change fro one for to another (potential to kinetic and back) KE + PE = constant exaple roller coaster when we do work in lifting the object, the work is stored as potential energy. Auseent park physics the roller coaster is an excellent exaple of the conersion of energy fro one for into another work ust first be done in lifting the cars to the top of the first hill. the work is stored as graitational potential energy you are then on your way! Up and down the track Loop-the-loop h R PE Total energy PE KE Kinetic Energy PE If friction is not too big the ball will get up to the sae height on the right side. Here friction works to our adantage. Without it the ball slides rather than rolls. A ball won t roll without friction! The ball ust start at a height h, at least 2 ½ ties R to ake it through the loop