The gravitational force Fg between two objects is given by the equation:
Fg=(G*m₁*m₂)/r₂, where G=6.67*10^-11 m³ kg⁻¹ s⁻² is the gravitational constant, m₁ and m₂ are the masses of the two bodies and r is the distance between those bodies.
Due to the gravitational attraction the pencil and the eraser will attract if we there is no friction on the surface.
m₁=10 g=0.01 kg is the mass of the pencil
m₂=20 g=0.02 kg is the mass of the eraser
r=2.5 cm = 0.025 m
First we calculate the Fg:
Fg={(6.67*10^-11)*0.01*0.02}/(0.025²)=2.1344*10^-11 N
To get the velocity v of the pencil:
v²=2as, where a is the acceleration of the pencil and s is the path. In our case s=r so we can write:
v²=2ar
a=Fg/m₁= 2.133*10^-9 m/s²
v²=2*(2.133*10^-9)*0.025=1.0665*10^-10
v=√(1.0665*10^-10)=1.0327*10^-5 m/s
We have the velocity and the acceleration, so we can calculate the time t with the equation:
t=v/a=(1.0327*10^-5)/(2.133*10^-9)=4841.6 s
1 hour has 3600 s so when we divide time t in seconds by 3600 we get time T in hours:
T=t/3600=4841.6/3600=1.3449 h.
So the time for the pencil and eraser to touch is T=1.3449 hours.
Also time T can be expressed like T= 1h and 20 mins and 41.64 s
