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Matter & Interactions
Found in: Page 128

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Short Answer

Suppose that all the people of the Earth go to the North Pole and, on a signal, all jump straight up. Estimate the recoil speed of the Earth. The mass of the Earth is 6×1024 kg, and there are about 6 billion people (6×109).

The recoil speed of Earth is 5.88×10-12 m.s-1

See the step by step solution

Step by Step Solution

Step 1: Identification of given data

The mass of the earth is mearth=6×1024 kg

The number of people on earth is n=6×109

The number of attacking neutrons before fission is n2=3

Step 2: Concept Introduction

According to Newton’s Second law, we know that the rate of change of linear momentum can be expressed as the total applied force, such that, a change in the momentum of mv in time t, will be expressed as,


Rearranging the above equation, we get


Step 3: Determination of the total mass of all the people on the earth

If we assume that the average mass of each person on earth is 60 kg then the total mass of all the people will be,

mtotal=n×maverage=6×109×60 kg=3.6×1011 kg

Step 4: Calculation of the recoil force

Initially, the Earth is at rest, so when all people jump simultaneously, the impulse will be equal to the total change in the Earth’s momentum, which can be expressed as,

Change in Earth's momentum=Impulsemearthv=Ftotal×t.........1

Where v is the change in Earth’s speed, Ftotal×t is the total impulse in time t

Now, the force due to all people can be estimated as,

Ftotal=mtotal×g=3.6×1011 kg×9.8 m.s-2=3.53×1012 kg.m.s-2

Now, substitute the given values and t=1 s in the equation (1), and we get,

6×1024 kg×v=3.53×1012 kg.m.s-2×1 sv=3.53×1012 kg.m.s-2×1 s6×1024 kgv=5.88×10-12 m.s-1

Thus, the recoil speed of Earth is 5.88×10-12 m.s-1

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