The magnitude of the Earth's acceleration is [tex]6.39\cdot 10^{-25} m/s^2[/tex].
Explanation:
We have to use different concepts to answer this question.
First of all, we have to find the gravitational force exerted by the Earth on the apple: this is known as weight, and it is calculated as
[tex]F=mg[/tex]
where
m = 0.39 kg is the mass of the apple
[tex]g=9.8 m/s^2[/tex] is hte acceleration of gravity
Substituting, we find the force exerted on the apple by the Earth:
[tex]F=(0.39)(9.8)=3.82 N[/tex]
For the second part, we have to use Newton's third law of motion, which states that:
"When an object A exerts a force on an object B, object B exerts an equal and opposite force on object A"
Therefore in this situation, if we identify object A with the apple and object B as the Earth, we can say that the force exerted by the Earth on the apple is equal (and opposite) to the force exerted by the apple on the Earth. Therefore, also the Earth experiences a force of
F = 3.82 N
Now we can finally calculate the Earth's acceleration by using Newton's second law of motion:
[tex]F=Ma[/tex]
where
F = 3.82 N is the net force on the Earth
[tex]M=5.98\cdot 10^{24} kg[/tex] is the mass of the Earth
a is the Earth's acceleration
And solving for a, we find
[tex]a=\frac{F}{M}=\frac{3.82}{5.98\cdot 10^{24}}=6.39\cdot 10^{-25} m/s^2[/tex]
Learn more about Newton's second law here:
brainly.com/question/3820012
About forces and weight:
brainly.com/question/8459017
brainly.com/question/11292757
brainly.com/question/12978926
About Newton's third law:
https://brainly.com/question/11411375
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