Momentum and its Conservation

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Chapter 9 Momentum and Its Conservation

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Presentation transcript:

Momentum and its Conservation Chapter 9

Momentum p = m v vector An object’s mass times its velocity Moving inertia Inertia is an object’s ability to oppose a change in its motion (Newton’s 1st Law) Mass is most common way to measure inertia, and velocity is the most common way of measuring motion No motion, no momentum Momentum p = m v p : momentum (kgm/s) m : mass (kg) v : velocity (m/s) vector

Impulse-Momentum Theorem Recall Newton’s Second Law: F = ma = m Dv/Dt Newton actually wrote it as F = Dp/Dt, where Dp = pf – pi Rearranging, Dp = FDt = I (Impulse) Impulse is defined as the change in momentum of an object (same units as momentum)

Clips Golfball : ~http://www.youtube.com/watch?v=2Y57pw_iWlk http://www.youtube.com/watch?v=6dG9hb3_blo Billiards : http://www.youtube.com/watch?v=pZqkaJDaz2A Water balloon : http://www.youtube.com/watch?v=90VyvOhPmA0

Conservation of Momentum Momentum must be conserved in a closed, isolated system (perfect physics world). Closed: nothing gets out (no loss of mass) Isolated: nothing gets in (no external forces) Initial momentum must equal the final momentum. pi = pf

Impact Lab Ball 1 Mass of 1 Ball 2 Mass of 2 Predict Observe Procedures Set one end of the ramp on a book. Place one ball 30 cm from the end of the ramp on the floor. Place another one at the top of the ramp. Predict the outcome. Release the ball and observe the collision. Repeat for other collisions. Record each mass. Impact Lab Materials Ramp Soft, tennis, golf, and/or practice ball Scale Objective Observe collisions between two objects Ball 1 Mass of 1 Ball 2 Mass of 2 Predict Observe

Angular Momentum Conservation of Angular Momentum: Li = Lf Just like linear momentum, angular momentum must also be conserved. p = m v  L = I w Notice: same basic equation L : angular momentum (kgm2/s) I : moment of inertia (kgm2) w : angular velocity (rad/s) Conservation of Angular Momentum: Li = Lf

Ch9 HW Answers 56. 0.013 s 57. 14.5 kgm/s, 31,521 N 58. 74 kgm/s, 10 m/s 61. 60 N 64. 41.7 m/s 67. -5.1 kgm/s; -100 N; -10 N 69. 5.2 x10-23 kgm/s; 7.8 N 70. 1,300 s or 22 min 80. 11.2 m/s 82. 0.22 m/s 84. 2.12 x104 kgm/s; 312 N 87. -5 m/s or 5 m/s west Note: signs may be different!