6. The kinetic energy of N particles is K = ∑i=1^N(1)/(2) mi vi^2. Derive an expression for K in

Name: 6. The kinetic energy of N particles is K = ∑i=1^N(1)/(2) mi vi^2. Derive an expression for K in terms of vcm, M (the total mass), mi, and vri (the velocities relative the CM velocity) only.
Uploaded: 2021-03-05T17:02:39-08:00
Duration: 3 min 26 s
Channel: Vishal Sharma
Description: 6. The kinetic energy of N particles is K = ∑i=1^N(1)/(2) mi vi^2. Derive an expression for K in terms of vcm, M (the total mass), mi, and vri (the velocities relative the CM velocity) only.

Step 1: First, we need to express the velocity of each particle in terms of the center of mass v

Question

6. The kinetic energy of N particles is $K = \sum_{i=1}^{N} \frac{1}{2} m_i v_i^2$. Derive an expression for K in terms of $v_{cm}$, M (the total mass), $m_i$, and $v_{ri}$ (the velocities relative the CM velocity) only.

          6. The kinetic energy of N particles is $K = \sum_{i=1}^{N} \frac{1}{2} m_i v_i^2$. Derive an expression for K in terms of $v_{cm}$, M (the total mass), $m_i$, and $v_{ri}$ (the velocities relative the CM velocity) only.

6. The kinetic energy of N particles is K = ∑i=1^N(1)/(2) mi vi^2. Derive an expression for K in terms of vcm, M (the total mass), mi, and vri (the velocities relative the CM velocity) only.

Added by Ashley M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Vishal Sharma

03/05/2021

Step 1

The velocity of each particle can be written as vi = vcm + vir. Show more…

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The kinetic energy of N particles is K=sum (1)/(2)m_(i)v_(i)^(2). Derive an expression for K in terms of v_(cm),M (the total mass), m_(i), and v_(ir) (the velocities relative the CM velocity) only. mi , and vir (the velocities relative the CM velocity) only.