Chapter 9 Centre of Mass and Linear Momentum
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1 Chater 9 Centre o Mass and Linear Moentu Centre o ass o a syste o articles / objects Linear oentu Linear oentu o a syste o articles Newton s nd law or a syste o articles Conseration o oentu Elastic and Inelastic Collisions
2 Conseration o Moentu I F ext F ext That is, oentu is consered when the net external orce acting on an object is zero. This alies also to an isolated syste o two or ore objects (no external orces) that ay be in contact - the total oentu is consered. Coare Newton s irst law: t 0 then 0 elocity is constant when the net orce is zero.
3 Conseration o Moentu Two isolated asses collide. The initial total oentu is: With 0 0 While the asses are in contact, they exert equal and oosite orces on each other (Newton s third law). F F So the iulse acting on is equal in agnitude and oosite in direction to the iulse acting on
4 Thereore, (change in oentu = iulse) Ater the collision: So, the total oentu ater the collision is: That is, total oentu is consered:
5 Exale: An ice boat slides without riction horizontally across the ice. Soeone jus ertically down ro a bridge onto the boat. Does the oentu o the boat change? As the oentu o the erson is downward, not sideways, the horizontal oentu o the boat is unchanged. M o M As the ass o the boat is increased by the ass o the erson, the boat oes ore slowly, so that the oentu is unchanged. 0M M
6 Exale: A 55-kg swier is standing on a stationary 0-kg loating rat. The swier then jus o the rat horizontally with a elocity o +4.6 /s relatie to the shore. Find the recoil elocity that the rat would hae i there were no riction and resistance due to the water.
7 How ast was the bullet? Mass o bullet: = 0.0 kg Mass o block: =.50 kg The Ballistic Pendulu
8 Elastic and Inelastic Collisions Elastic collision: The total kinetic energy ater collision is equal to the total kinetic energy beore collision. Inelastic collision: The total kinetic energy is not the sae beore and ater the collision. I objects stick together ater collision, the collision is erectly inelastic no bouncing o one object ro the other. Reeber that oentu is always consered i no net orce is acting on the syste!
9 Elastic Collision Exale: A ball o ass = 0.5 kg akes a erectly elastic collision with a ball o ass = 0.8 kg. Elastic Collisions Initial oentu : Moentu ater collision: Moentu is consered : i 0 0
10 Elastic Collision Exale: A ball o ass = 0.5 kg akes a erectly elastic collision with a ball o ass = 0.8 kg. Moentu is consered : 0 Elastic Collisions 0
11 Elastic Collision Exale: A ball o ass = 0.5 kg akes a erectly elastic collision with a ball o ass = 0.8 kg. Moentu is consered : 0 Cobine with conseration o kinetic energy: 0 Elastic Collisions
12 Elastic Collision Exale: A ball o ass = 0.5 kg akes a erectly elastic collision with a ball o ass = 0.8 kg. Elastic Collisions Do soe algebra:
13 Elastic Collision Exale: A ball o ass = 0.5 kg akes a erectly elastic collision with a ball o ass = 0.8 kg. Elastic Collisions Do soe algebra: Two solutions: 0 0
14 Elastic Collision Exale: A ball o ass = 0.5 kg akes a erectly elastic collision with a ball o ass = 0.8 kg. Elastic Collisions Do soe algebra: Cobine and 0 0 0
15 Finally: Elastic Collision Exale: A ball o ass = 0.5 kg akes a erectly elastic collision with a ball o ass = 0.8 kg i, then, i Elastic Collisions
16 Elastic Collision Exale: A ball o ass = 0.5 kg akes a erectly elastic collision with a ball o ass = 0.8 kg. Elastic Collisions Finally: kg, 5 /s. 6 /s, 0. 8 kg,. 38 /s
17 Elastic Collisions Elastic Collision: In general: For any two objects with asses and colliding elastically and initially at rest!
18 Exale: An electron collides elastically with a stationary hydrogen ato. The ass o the hydrogen ato is 837 ties that o the electron. Assue that all otion, beore and ater the collision, occurs along the sae straight line. What is the ratio o the kinetic energy o the hydrogen ato ater the collision to that o the electron beore the collision?
19 The reight car on the let catches u with the one on the right and connects u with it. They trael on with the sae seed. Conseration o oentu:
20 Exale: 0 65, 000 kg, 0. 8 /s, 0 9, 000 kg. 3 /s Kinetic Energy: /s KE KE What haened to the issing energy? i J 9366 J 0 0 Missing 574 J This was an inelastic collision soe o the kinetic energy was conerted to heat and sound.
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