3. If the force of gravity between two objects 5m apart is 1.27 x 10-8 N and the mass of one object is 50kg, what is the mass of the other object?
+33616 F = G*m1*m2/r2, where F is force, G is gravitational constant(6.673×10−11 N·(m/kg)2), m's are masses and r is distance between masses.
$${\mathtt{1.27}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{8}}} = {\frac{{\mathtt{6.673}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{11}}\right)}{\mathtt{\,\times\,}}{\mathtt{50}}{\mathtt{\,\times\,}}{\mathtt{m}}}{{{\mathtt{5}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{m}} = {\frac{{\mathtt{105\,151\,356\,211\,599}}}{{\mathtt{1\,105\,000\,000\,000}}}} \Rightarrow {\mathtt{m}} = {\mathtt{95.159\: \!598\: \!381\: \!537\: \!556\: \!6}}$$
The other mass is approximately 95 kg
.
+33616 F = G*m1*m2/r2, where F is force, G is gravitational constant(6.673×10−11 N·(m/kg)2), m's are masses and r is distance between masses.
$${\mathtt{1.27}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{8}}} = {\frac{{\mathtt{6.673}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{11}}\right)}{\mathtt{\,\times\,}}{\mathtt{50}}{\mathtt{\,\times\,}}{\mathtt{m}}}{{{\mathtt{5}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{m}} = {\frac{{\mathtt{105\,151\,356\,211\,599}}}{{\mathtt{1\,105\,000\,000\,000}}}} \Rightarrow {\mathtt{m}} = {\mathtt{95.159\: \!598\: \!381\: \!537\: \!556\: \!6}}$$
The other mass is approximately 95 kg
.
