Answer:
a) The distance of the object from the center of the Earth is 8.92x10⁶ m.
b) The initial acceleration of the object is 5 m/s².
Explanation:
a) The distance can be found using the equation of gravitational force:
[tex]F = \frac{GMm}{r^{2}}[/tex]
Where:
G: is the gravitational constant = 6.67x10⁻¹¹ Nm²/kg²
M: is the Earth's mass = 5.97x10²⁴ kg
m: is the object's mass = 0.4 kg
F: is the force or the weight = 2.0 N
r: is the distance =?
The distance is:
[tex]r = \sqrt{\frac{GMm}{F}} = \sqrt{\frac{6.67 \cdot 10^{-11} Nm^{2}/kg^{2}*5.97 \cdot 10^{24} kg*0.4 kg}{2.0 N}} = 8.92 \cdot 10^{6} m[/tex]
Hence, the distance of the object from the center of the Earth is 8.92x10⁶ m.
b) The initial acceleration of the object can be calculated knowing the weight:
[tex] W = ma [/tex]
Where:
W: is the weight = 2 N
a: is the initial acceleration =?
[tex] a = \frac{W}{m} = \frac{2 N}{0.4 kg} = 5 m/s^{2} [/tex]
Therefore, the initial acceleration of the object is 5 m/s².
I hope it helps you!
