Question
Mass A (3 kg) and mass B (6 kg) sit on the ground, 3 m apart.
a.) What is size of the the gravitational force:
on A from B? (Ans in Newtons)
on B from A? (Ans in Newtons)
b.) What is the size of the gravitational force:
on A from the Earth? (Ans in Newtons)
on B from the Earth? (Ans in Newtons)
c.) Explain why we normally only worry about the gravitational force on such objects from the Earth, and don't worry about including the gravitational force on objects from each other.
d.) Do A and B exert forces back on the Earth itself? If so, are those forces of smaller, equal, or larger size than your answers for part b?: same-size smaller larger
Explanation / Answer
Data: Mass of A, M1 = 3 kg Mass of B, M2 = 6 kg Distance between A and B, r = 3 m Universal gravitational constant, G = 6.67 x 10^-11 N.m^2/kg^2 Acceleration due to gravity, g = 9.8 m/s^2 Solution: a) Gravitational force on A from B: F1 = G M1 M2 / r^2 = 6.67 x 10^-11 * 3 * 6 / 3^2 = 1.334 x 10^-10 N Ans: F1 = 1.334 x 10^-10 N Gravitational force on B from A: F2 = G M2 M1 / r^2 = 6.67 x 10^-11 * 6 * 3 / 3^2 = 1.334 x 10^-10 N Ans: F2 = 1.334 x 10^-10 N b) Gravitational force on A from earth: The gravitational force due to earth is equal to the weight of the given body F1 = Weight of the object = M1 g = 3 * 9.8 = 29.4 N Ans: F1 = 29.4 N Gravitational force on B from earth: The gravitational force due to earth is equal to the weight of the given body F2 = Weight of the object = M2 g = 6 * 9.8 = 29.4 N Ans: F1 = 58.8 N c) The gravitational force on an object due to other objects is very small compared to the gravitational force due to earth. So, we need not worry about the gravitational forces due to other objects. d) yes, A and B exert forces back on the Earth. They are exactly same as that of part - b ( according to Newton's gravitational law ) Gravitational force on B from A: F2 = G M2 M1 / r^2 = 6.67 x 10^-11 * 6 * 3 / 3^2 = 1.334 x 10^-10 N Ans: F2 = 1.334 x 10^-10 N b) Gravitational force on A from earth: The gravitational force due to earth is equal to the weight of the given body F1 = Weight of the object = M1 g = 3 * 9.8 = 29.4 N Ans: F1 = 29.4 N Gravitational force on B from earth: The gravitational force due to earth is equal to the weight of the given body F2 = Weight of the object = M2 g = 6 * 9.8 = 29.4 N Ans: F1 = 58.8 N c) The gravitational force on an object due to other objects is very small compared to the gravitational force due to earth. So, we need not worry about the gravitational forces due to other objects. d) yes, A and B exert forces back on the Earth. They are exactly same as that of part - b ( according to Newton's gravitational law ) Gravitational force on B from earth: The gravitational force due to earth is equal to the weight of the given body F2 = Weight of the object = M2 g = 6 * 9.8 = 29.4 N Ans: F1 = 58.8 N c) The gravitational force on an object due to other objects is very small compared to the gravitational force due to earth. So, we need not worry about the gravitational forces due to other objects. d) yes, A and B exert forces back on the Earth. They are exactly same as that of part - b ( according to Newton's gravitational law )