PHY183-Lecture18-1 - February 15, 2012 Physics for

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Unformatted text preview: February 15, 2012 Physics for Scientists&Engineers 1 1 Physics for Scientists & Engineers 1 Physics for Scientists & Engineers 1 Spring Semester 2012 Lecture 18 Special Cases for Elastic 1d Collisions, 2D Collisions Elastic Scattering Elastic Scattering Yesterday we introduced the following for the elastic collision of two objects in one dimension Today we will examine several interesting and common special cases February 15, 2012 Physics for Scientists&Engineers 1 2 v f1, x = m 1 m 2 m 1 + m 2 v i1, x + 2 m 2 m 1 + m 2 v i2 , x v f2, x = 2 m 1 m 1 + m 2 v i1, x + m 2 m 1 m 1 + m 2 v i2, x v f1, x = m 1 m 2 m 1 + m 2 v i1, x + 2 m 2 m 1 + m 2 v i2 , x v f2, x = 2 m 1 m 1 + m 2 v i1, x + m 2 m 1 m 1 + m 2 v i2, x February 15, 2012 Physics for Scientists&Engineers 1 3 Special Case 1: Equal Masses, m 1 = m 2 Special Case 1: Equal Masses, m 1 = m 2 In this case, terms proportional to m 2 - m 1 vanish! 2m 2 /(m 1 +m 2 ) = 2 m 1 /(m 1 +m 2 ) = 1 The two objects of equal mass simply exchange their momenta! Same is true for the velocities (obvious, because masses are identical): p f1, x = p i2, x p f2, x = p i1, x v f1, x = v i2, x v f2, x = v i1, x February 15, 2012 Physics for Scientists&Engineers 1 4 Special Case 2: One object initially at rest Special Case 2: One object initially at rest Pick one of the two objects and set its initial momentum to 0 (does not matter which, say object 1) For this special case of p i1, x = we get from the general formulas: momenta velocities Now we can distinguish 3 cases, depending on the ratio of the two masses, m 2 = m 1 , m 2 > m 1 , m 2 < m 1 : In all 3 cases object 1 moves in the same direction that object 2 had initially, but p f1, x = 2 m 1 m 1 + m 2 p i2, x p f2, x = m 2 m 1 m 1 + m 2 p i2, x v f1, x = 2 m 2 m 1 + m 2 v i2, x v f2, x = m 2 m 1 m 1 + m 2 v i2, x Clicker Quiz Clicker Quiz Two carts are on a level air track. The less massive (Cart II) of the two carts is at rest and the more massive (Cart I) of the two moves to the right, as shown in the diagram below. The two carts undergo an elastic collision. After the collision, the direction of their velocities will be: A. both to the right B. both to the left C. Cart I to the left and cart II to the right D. Cart I to the left E. Cart I at rest and Cart II to the right February 15, 2012 Physics for Scientists&Engineers 1 5 Clicker Quiz Clicker Quiz Two carts are on a level air track. The more massive (Cart II) of the two carts is at rest and the less massive (Cart I) of the two moves to the right, as shown in the diagram below. The two carts undergo an elastic collision....
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PHY183-Lecture18-1 - February 15, 2012 Physics for

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