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Object Ais stationary while objects BandCare in motion. Forces from object Ado10Jof work on object Band5Jof work on object C. Forces from the environment do 4Jof work on object Band8Jof work on object C. Objects BandCdo not interact. What are KtotandUintif

(a) objects A,B,andCare defined as separate systems and

(b) one system is defined to include objects A,B,andCand their interactions?

Short Answer

Expert verified

(a) Total change in kinetic energyktotal=17JandUinternal=0.

(b) The change in total kinetic energy and internal energy is Ktotal=12Jand

Uintemal=5Jrespectively.

Step by step solution

01

Introduction

A system is a collection of related items that act together as pieces of an integrated network or process.

02

Explanation (a)

SinceA,B, and Care defined as distinct systems, add Kfor each system to get the total. If Ais stationary then its Kdoes not change. Therefore,

KA=0

According to the work energy theorem, the force of A on B increases KBby 10Jand the forces due to environment increase it by 4J. Therefore,

KB=10J+4J

=14J

The force of A on C decreases its kinetic energy by 5Jand the forces due to the environment increase it by 8J. Therefore,

KC=8J-5J

=3J

The sum of all these change in energy is calculated as follows,

Kweal=KA+KB+Kc

=0J+14J+3J

=17J

All of the effort is done to change the kinetic energy of the individual systems because all of the forces are external to the system.

As a result, A, B, and C have the same internal energy.

Therefore,

All of the effort is done to change the kinetic energy of the individual systems because all of the forces are external to the system.

As a result, A, B, and C have the same internal energy.

Therefore,

Uinternal=0

Therefore, total change in kinetic energy is Kwotal=17Jand Uintemal=0.

03

Explanation (b)

When all three items are considered as one system, the interaction energy increases owing to object interaction. AonBandC. Therefore, change in total internal energy is calculated as follows,

Uintemal=10J-5J

=5J

In this case, the kinetic energy is increased by the work done by external forces (environment).

Therefore,

Klotal=8J+4J

=12J

Hence, the change in total kinetic energy and internal energy is Ktotal=12Jand

Uintemal=5Jrespectively.

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