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Chapter 9: Q14P (page 377)

Agroup of particles of total mass 35kghas a total kinetic energy of 340J. The kinetic energy relative to the center of mass is 85J. What is the speed of the center of mass?

Short Answer

Expert verified

The speed of the center of mass is4.93m/s

Step by step solution

01

Identification of the given data

  • The total mass is m=35kg
  • Total kinetic energy is KT=340J
  • Kinetic energy relative to the center of mass is K=85J
02

Concept of the center of mass of the system

The center of mass of the system is calculated by considering the placement of the of all the objects acting in the system.

03

Determination of the speed of the center of mass

According to the conservation of energy principle,

KT+K=E

Where,

KT= Total kinetic energy

K = Kinetic energy relative to the center of mass

Potential Energy, localid="1653897038194" role="math" E=12mvc2

Substitute Equation (2) in (1),

KT+K=12mvc2vc2=2路KT+Km=2路340+8535vc2=24.29vc=4.93m/s

Hence,the speed of the center of mass is localid="1653897138661" 4.93m/s

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