# hw20 - Overton Mays – Homework 20 – Due 4:00 am –...

This preview shows pages 1–3. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Overton, Mays – Homework 20 – Due: Mar 22 2005, 4:00 am – Inst: Turner 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 3) 10 points Consider the general case of collisions of two masses m 1 = m with m 2 = 2 m along a fric- tionless horizontal surface. Denote the initial and the final center of mass momenta to be p i cm = p 1 + p 2 , and p f cm = p 1 + p 2 . And the initial and final kinetic energies to be K i = K 1 + K 2 , and K f = K 1 + K 2 . m 1 m 2 v 1 v 2 For an elastic collision which pair of state- ments is correct? 1. p i cm = p f cm , K i < K f 2. p i cm > p f cm , K i = K f 3. p i cm < p f cm , K i = K f 4. p i cm < p f cm , K i > K f 5. p i cm > p f cm , K i > K f 6. p i cm = p f cm , K i = K f correct 7. p i cm > p f cm , K i < K f 8. p i cm = p f cm , K i > K f 9. p i cm < p f cm , K i < K f Explanation: Momentum and energy are always con- served in elastic collision. 002 (part 2 of 3) 10 points Consider a perfectly inelastic head-on colli- sion, with initial velocity of m 1 to be v 1 and that of m 2 to be v 2 = 0. Note: Perfectly inelastic means that the two particles stick together after the collision. Find the final speed v cm of the ( m 1 + m 2 ) system. 1. v cm = 3 5 v 1 2. v cm = 1 4 v 1 3. v cm = 1 2 v 1 4. v cm = 1 3 v 1 correct 5. v cm = 3 4 v 1 6. v cm = 2 3 v 1 7. v cm = 2 v 1 8. v cm = 1 5 v 1 9. v cm = v 1 10. v cm = 2 7 v 1 Explanation: In a collision the linear momentum is always conserved. From conservation of linear momentum we get m 1 v 1 + m 2 0 = ( m 1 + m 2 ) v f v cm = v f = m 1 ( m 1 + m 2 ) v 1 = m 3 m v 1 = v 1 3 003 (part 3 of 3) 10 points Now consider an elastic head-on collision again with initial velocity of m 1 to be v 1 and of m 2 to be v 2 = 0. Find the final speed v f 2 of m 2 . 1. v f 2 = 2 7 v 1 Overton, Mays – Homework 20 – Due: Mar 22 2005, 4:00 am – Inst: Turner 2 2. v f 2 = 1 4 v 1 3. v f 2 = 1 2 v 1 4. v f 2 = 2 3 v 1 correct 5. v f 2 = 1 5 v 1 6. v f 2 = 3 4 v 1 7. v f 2 = 2 v 1 8. v f 2 = 3 5 v 1 9. v f 2 = 1 3 v 1 10. v f 2 = v 1 Explanation: The CM velocity is given by V CM = ∑ i m i v i ∑ i m i = m 1 v 1 m 1 + m 2 as v 2 = 0. Thus, in the CM frame, m 2 has a velocity v ( CM ) 2 = v 2- V CM =- V CM =- m 1 v 1 m 1 + m 2 . After a one dimensional elastic collision, each body changes the direction of its momentum with the magnitude of the momentum con- served. Note: In the CM frame the total momen- tum is still zero if each velocity changes sign. Hence, the final velocity of m 2 in the CM frame is v ( CM ) 2 ,f = V CM = m 1 v 1 m 1 + m 2 The velocity v lab 2 ,f ( v f 2 ) in the lab frame is v lab 2 ,f = v ( CM ) 2 ,f + V CM = 2 V CM = 2 m 1 v 1 m 1 + m 2 = 2 3 v 1 ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 7

hw20 - Overton Mays – Homework 20 – Due 4:00 am –...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online