At one instant, the center of mass of a system of two particles is located on th

Question

At one instant, the center of mass of a system of two particles is located on the x -axis at x = 2.0 m and has a velocity of (5.0 m/s ) i^ . One of the particles is at the origin. The other particle has a mass of 0.10 kg and is at rest on the x -axis at x = 8.0 m .

Part A

What is the mass of the particle at the origin?

Express your answer using two significant figures.

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Part B

Calculate the total momentum of this system.

Express your answer using two significant figures.

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Part C

What is the velocity of the particle at the origin?

Express your answer using two significant figures.

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At one instant, the center of mass of a system of two particles is located on the x -axis at x = 2.0 m and has a velocity of (5.0 m/s ) i^ . One of the particles is at the origin. The other particle has a mass of 0.10 kg and is at rest on the x -axis at x = 8.0 m .

Part A

What is the mass of the particle at the origin?

Express your answer using two significant figures.

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Part B

Calculate the total momentum of this system.

Express your answer using two significant figures.

m1 = kg

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Part C

What is the velocity of the particle at the origin?

Express your answer using two significant figures.

P^ = kgm/si^

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v1 = m/si^

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Explanation / Answer

Given position of centre of mass x = 2 m and Vcm = 5m/s

M2 = 0.1 kg , x2 = 8m and x1 = 0

Part A) Now, taking moment about the center of mass
M*2 = 0.1*[ 8-2]
M = 0.3 kg
the mass of the particle at the origin is 0.3 kg

Part B) now using ,

Sum of the momentum of the particles = the momentum of the center of mass.
So,

Total momentum = [0.3 + 0.1]*5

= 2 kg m/s

Part C) now finding the velocity ,

0.3 u + 0.1*0 = 2
u = 2/0.3 = 6.67m/s.

Therefore , velocity = 6.67 m/s

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