01quiz_11

01quiz_11 - Physics 9A-C Practice Quiz Week#1 Name ID(last 4

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Unformatted text preview: Physics 9A-C 4/1/2011 Practice Quiz Week #1 Name: ID (last 4): When two vectors a√ and b√ are drawn from a common point as shown, the angle between the  them is  ƒ.  Using vector techniques: a) (7 pts)  Show that the magnitude of their vector sum is   a + b = a 2 + b 2 + 2 ab cos φ To add vectors place them head-to-tail as shown ( 3 pts) Solution 1(law of cosines):  The angle opposite  a√ + b√  is  π - ƒ, so the law of cosines applied to this triangle is:  | a√ + b√ |   =  a  + b  -  2 a b cos(π - ƒ).  (3 pts) 2  2 a√ + b√  2 But,  cos(π - ƒ)  =  - cos ƒ.  õ (1 pt) π-ƒ ƒ a√ a√ ƒ b√  | a√ + b√ |   =  a    +  b   +  2 a b cos ƒ .   2 2  2 Solution 2 (components):    Choose the x axis along vector b√.  Resolve into components and add: 2 ˆ a = a cos φ i + a sin φ ˆ j a + b = ( a cos φ + b) + a 2 sin 2 φ ˆ b= bi +0 ˆ j     (4 pts) .   = ( a 2 cos 2 φ + 2 ab cos φ + b 2 ) + a 2 sin 2 φ      (3 pts). ˆ a + b = ( a cos φ + b)i + a sin φ ˆ j = a 2 + b 2 + 2 ab cos φ b) (3 pts)  When the angle between them is 90°, show that   a + b  is given by the Pythagorean  theorem.   When the angle between them is 90° use the above result  note that cos 90° = 0. a + b = a 2 + b 2 + 2 ab cos 90° = a 2 + b 2   which is the Pythagorean theorem. ...
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This note was uploaded on 09/28/2011 for the course PHY 9A taught by Professor Svoboda during the Spring '08 term at UC Davis.

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