The Force of Gravity: Understanding Acceleration of 2-Kg Rocks

[Stargate]

The force of gravity is twice as great on a 2-kg rock on a 1-kg rock. Why does the 2-kg rock not fall with twice the acceleration?

 

[dextercioby]

The force of gravity is twice as great on a 2-kg rock on a 1-kg rock. Why does the 2-kg rock not fall with twice the acceleration?

$$F=ma$$
If the force is the product between the mass and the acceleration,figure out yourself...

Daniel.

 

[Stargate]

They both have the same mass and acceleration! Right?

 

[dextercioby]

They both have the same mass and acceleration! Right?

Okay,for the first body write
$$G_{1}=m_{1}a_{1}$$(1)
And for the second
$$G_{2}=m_{2}a_{2}$$(2)

Divide (1) through (2)
$$\frac{G_{1}}{G_{2}}=\frac{G_{1}a_{1}}{G_{2}a_{2}}$$(3)
Use the fact that $G_{1}$ is two times $G_{2}$ and that $m_{1}$ is 2Kg,which is two times the value of $m_{2}$ which is 1Kg.Then
$$2=\frac{2a_{1}}{a_{2}} \Rightarrow a_{1}=a_{2}$$

Daniel.