Two objects attract each other with a gravitational force of magnitude 1.01 10^-8 N when separated by 19.9 cm. ?
Two objects attract each other with a gravitational force of magnitude 1.01 10^-8 N when separated by 19.9 cm. If the total mass of the two objects is 5.02 kg, what is the mass of each?
I know that the heavier mass is 3 but I got 1.8 for the lighter mass and that was incorrect. Can someone please help?
- billrussell42Lv 71 month agoFavourite answer
1.01 10^-8 N ?? is that 1.01x10^-8 N
F = G m₁m₂/r² = 1.01e-8
(6.674e-11) m₁m₂/(0.199)² = 1.01e-8
m₁ + m₂ = 5.02
two eq is two unknowns
m₁ = 5.02 – m₂
(6.674e-11) m₂(5.02 – m₂)/(0.199)² = 1.01e-8
–(6.674e-11) m₂²/0.0396 + m₂(6.674e-11)(5.02)/0.0396 – 1.01e-8 = 0
1.685e-9m₂² – 8.46e-9m₂ + 1.01e-8 = 0
1.685m₂² – 8.46m₂ + 10.1 = 0
m₂² – 5.02m₂ + 5.99 = 0
m₂ = 3.07, 1.95
1.95 is the answer...
Gravitational attraction in newtons
F = G m₁m₂/r²
G = 6.674e-11 m³/kgs²
m₁ and m₂ are the masses of the two objects in kg
r is the distance in meters between their centers
- Demiurge42Lv 71 month ago
"I know that the heavier mass is 3...". 3 what? You need units for this to make any sense.
The total mass is 5.02 kg. If you know the mass of one of the objects, just subtract that amount from 5.02 kg to get the mass of the other object.