1) The gravitational force on Earth is 2.65 N
2) The acceleration of the Earth is [tex]4.4\cdot 10^{-25} m/s^2[/tex]
Explanation:
1)
First of all, we start by finding the gravitational force exerted by the Earth on the rock. This is equal to the weight of the rock, which is:
[tex]F=mg[/tex]
where:
m = 0.27 kg is the mass of the rock
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
Substituting,
[tex]F=(0.27)(9.8)=2.65 N[/tex]
Now we can apply Newton's third law, which states that:
"When an object A exerts a force on an object B, then object B exerts an equal and opposite force on object A".
This means that the force exerted by the Earth on the rock (the weight of the rock) is equal in magnitude to the force exerted by the rock on the Earth: therefore, the gravitational force on Earth is also 2.65 N.
2)
To find the acceleration of the Earth, we use Newton's second law:
[tex]F=Ma[/tex]
where:
F is the net force on the Earth
M is the Earth's mass
a is its acceleration
Here we have:
[tex]F=2.65 N[/tex]
[tex]M=6.0\cdot 10^{24} kg[/tex] is the Earth's mass
And solving for a:
[tex]a=\frac{F}{M}=\frac{2.65}{6.0\cdot 10^{24}}=4.4\cdot 10^{-25} m/s^2[/tex]
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