Answer to Question #105123 in Classical Mechanics for Franco Yap

Question

1. In the queue at the bus stop, two students (with masses 80 and 60 kg respectively) are standing a distance 0.7 m apart. What is the magnitude of the gravitational force between them?

Treat both objects as point masses, use G = 6.67×10^−11 Nm^2 kg^−2.

F = ___ micro newtons (to one significant figure, and note the units)

2. Ceres is the largest asteroid. Its mean radius is 476 km and its mass is 9.4×10^20 kg. Using this, and G = 6.67×10^−11 Nm^2 kg^−2, and approximating it as a sphere, compute the speed required to escape the gravity on the surface of Ceres.

Speed = ___ m.s^ (to two significant figures, don't use scientific notation)

Answer 1

1.

Gravitational force is given by $\dfrac{Gm_1m_2}{r^2}$

$\dfrac{6.67\times10^{-11}\times80\times60}{0.7^2}$

$65338.8\times10^{-11}\\6.5\times10^{-7} N$

2.

Escape velocity is given by $\sqrt{\dfrac{2GM}{R}}$ $=\sqrt{\dfrac{2 \times 6.67\times10^{-11}\times9.4×10^{20}}{476\times10^3}}=\sqrt{0.26\times10^6}m/s$

$=0.5\times10^3 m/s$