hw27_s - homework 27 YOO, HEE Due: Apr 3 2008, 4:00 am 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: homework 27 YOO, HEE Due: Apr 3 2008, 4:00 am 1 Question 1, chap 10, sect 99. part 1 of 2 10 points Two particles of masses m 1 = 4 . 1 kg and m 2 = 20 . 1 kg are moving toward each other along the x axis with equal speeds 5 . 59 m / s. Specifically, v 1 x = +5 . 59 m / s (particle 1 moves to the right) and v 2 x =- 5 . 59 m / s (particle 2 moves to the left). The particles collide elastically. After the collision, the first particle moves at 1 = 90 to its original direction while the second par- ticle is deflected through a smaller angle 2 < 90 . x y vectorv 1 vectorv 2 vectorv 1 vectorv 2 1 = 90 2 Find the final speed | v 1 | of the first particle. Correct answer: 8 . 51868 m / s (tolerance 1 %). Explanation: In elastic collision, the net momentum vector P and the net kinetic energy K are both con- served. In components, P x = m 1 v 1- m 2 v 2 = 0- m 2 v 2 cos 2 , (1) P y = 0 = m 1 v 1- m 2 v 2 sin 2 , (2) K = m 1 v 2 1 2 + m 2 v 2 2 2 = m 1 v 2 1 2 + m 2 v 2 2 2 . (3) Given v 1 = v , v 2 =- v , eq. (1) gives v 2 cos 2 = parenleftbigg 1- m 1 m 2 parenrightbigg v (4) while eq. (2) implies v 2 sin 2 = m 1 m 2 v 1 ; (5) therefore v 2 2 = ( v 2 cos 2 ) 2 + ( v 2 sin 2 ) 2 = parenleftbigg 1- m 1 m 2 parenrightbigg 2 v 2 + m 2 1 m 2 2 v 2 1 . (6) Substituting this formula into the energy con- servation eq. (3), we arrive at m 1 + m 2 2 v 2 = m 1 2 v 2 1 + m 2 2 bracketleftBigg parenleftbigg 1- m 1 m 2 parenrightbigg 2 v 2 + m 2 1 m 2 2 v 2 1 bracketrightBigg = m 1 ( m 2 + m 1 ) 2 m 2 v 2 1 + ( m 2- m 1 ) 2 2 m 2 v 2 (7) and hence (after a bit of algebra) v 2 1 v 2 = 3 m 2- m 1 m 2 + m 1 . (8) Consequently, v 1 = v radicalbigg 3 m 2- m 1 m 2 + m 1 = 8 . 51868 m / s . (9) Question 2, chap 10, sect 99....
View Full Document

Page1 / 5

hw27_s - homework 27 YOO, HEE Due: Apr 3 2008, 4:00 am 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online