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mi CM = r1 R r2 m2 = Figure 3.3 The CM of two particles lies at the position (m₁r₁+m2r2)/M. You can prove that this lies on the line joining m₁ to m2, as shown, and that the distances of the CM from m₁ and m₂ are in the ratio m₂/m₁. 3.18** (a) Prove that the CM of any two particles always lies on the line joining them, as illustrated in Figure 3.3. [Write down the vector that points from m₁ to the CM and show that it has the same direction as the vector from m₁ to m2.] (b) Prove that the distances from the CM to m₁ and m₂ are in the ratio m2/m1. Explain why if m₁ is much greater than m2, the CM lies very close to the position of m1. 1

mi CM = r1 R r2 m2 = Figure 3.3 The CM of two particles lies at the position (m₁r₁+m2r2)/M. You can prove that this lies on the line joining m₁ to m2, as shown, and that the distances of the CM from m₁ and m₂ are in the ratio m₂/m₁. 3.18** (a) Prove that the CM of any two particles always lies on the line joining them, as illustrated in Figure 3.3. [Write down the vector that points from m₁ to the CM and show that it has the same direction as the vector from m₁ to m2.] (b) Prove that the distances from the CM to m₁ and m₂ are in the ratio m2/m1. Explain why if m₁ is much greater than m2, the CM lies very close to the position of m1. 1

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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mi CM = r1 R r2 m2 = Figure 3.3 The CM of two particles lies at the position (m₁r₁+m2r2)/M. You can prove that this lies on the line joining m₁ to m2, as shown, and that the distances of the CM from m₁ and m₂ are in the ratio m₂/m₁.
Transcribed Image Text:mi CM = r1 R r2 m2 = Figure 3.3 The CM of two particles lies at the position (m₁r₁+m2r2)/M. You can prove that this lies on the line joining m₁ to m2, as shown, and that the distances of the CM from m₁ and m₂ are in the ratio m₂/m₁.
3.18** (a) Prove that the CM of any two particles always lies on the line joining them, as illustrated in Figure 3.3. [Write down the vector that points from m₁ to the CM and show that it has the same direction as the vector from m₁ to m2.] (b) Prove that the distances from the CM to m₁ and m₂ are in the ratio m2/m1. Explain why if m₁ is much greater than m2, the CM lies very close to the position of m1. 1
Transcribed Image Text:3.18** (a) Prove that the CM of any two particles always lies on the line joining them, as illustrated in Figure 3.3. [Write down the vector that points from m₁ to the CM and show that it has the same direction as the vector from m₁ to m2.] (b) Prove that the distances from the CM to m₁ and m₂ are in the ratio m2/m1. Explain why if m₁ is much greater than m2, the CM lies very close to the position of m1. 1
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