Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Puck $A$ (mass $m_{A} )$ is moving on a frictionless, horizontal air table in the $+x$ -directionwith velocity $\vec{v}_{A 1}$ and makes an elastic, headon collision with puck $B\left(\text { mass } m_{B}\right),$ which is initially at rest. After the collision, both pucks are moving along the $x$ -axis. (a) Calculate the velocity of the center of mass of the two-puck system before the collision. (b) Consider a coordinate system whose origin is at the center of mass and moves with it. Is this an inertial reference frame? (c) What are the initial velocities $\vec{u}_{\Delta 1}$ and $\vec{u}_{B 1}$ of the two pucks in this center-of-mass reference frame? What is the total momentum in this frame? (d) Use conservation of momentum and energy, applied in the center-of-mass reference frame, to relate the final momentum of each puck to its initial momentum and thus the final velocity of each puck to its initial velocity. Your results should show that a one-dimensional, elastic collision has a very simple description in center-of-mass coordinates. (e) Let $m_{A}=0.400 \mathrm{kg}$ ,$m_{B}=0.200 \mathrm{kg},$ and $v_{A 1}=6.00 \mathrm{m} / \mathrm{s}$ . Find the center-of-mass velocities $\vec{u}_{A 1}$ and $\vec{u}_{B 1},$ apply the simple result found in part (d),and transform back to velocities in a stationary frame to find the final velocities of the pucks. Does your result agree with Eqs. $(8.24)$ and $(8.25) ?$

Get the answer to your homework problem.

Try Numerade free for 7 days

Input your name and email to request the answer

Like

Report

a. $v_{\mathrm{sm} x}=\frac{m_{A} v_{A \mathrm{I}}}{m_{A}+m_{B}}$b. The center of mass moves with constant speed so this coordinate system is an inertial frame.c. 0d. $p_{B 2 x}=-p_{B 1 x}$e. $8.00 \mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Moment, Impulse, and Collisions

Cornell University

Rutgers, The State University of New Jersey

University of Winnipeg

Lectures

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

03:30

In physics, impulse is the integral of a force, F, over the time interval, t, for which it acts. Given a force, F, applied for a time, t, the resulting change in momentum, p, is equal to the impulse, I. Impulse applied to a mass, m, is also equal to the change in the object's kinetic energy, T, as a result of the force acting on it.

10:07

Two hockey pucks approach …

03:32

The two balls depicted in …

02:26

Two balls of equal mass ap…

04:40

The drawing shows a collis…

06:19

On a frictionless, horizon…

13:22

A $0.300-\mathrm{kg}$ puck…

03:21

Two skaters are studying c…

04:23

A 0.300 -kg puck, initiall…

On a frictionless. horizun…

No transcript available

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:06

a frog and duck lay eggs . ls there any difference in their life cycle expla…

01:29

Rewrite the following in standard form: 845 x 10-5 kg

02:08

At what height above the earth’s surface would the value of acceleration due…

02:18

The last limit of temperature 237 0C was named as absolute zero. true or fal…

02:03

A boy climbs on a pole of height 5 m. In doing so, he does 5000 J of work. F…

01:50

The image shows the path of incident rays to a concave mirror where would th…

02:02

A particle's velocity is 4 m/s in the +ve x-direction at t = 4s and is …

02:31

Rajesh is a student of class X and Ram is studying in class VII. Rajesh told…

02:05

A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. When…