Calculating Net Force on Boxes of Different Masses in Contact

[harrycc]

Homework Statement

Two boxes full of books are in contact with each other on a smooth table. Box H has twice the mass of Box G. If you push on box G with a horizontal force F, then box H will expereince a net force of?

Homework Equations

F =ma

The Attempt at a Solution

answer from answer key is 2/3F


I though since the mass of H is twice of G, the F needed will be 2F... but I am wrong.. Please help with the question! Thank You

 

[DrDan]

First you need to find the acceleration of both blocks combined. If you call box H = 2G then you can write an equation F= (G + 2G) a.

Spoiler

Solve this for a = F/3G. Now consider the net force on box H to make it accelerate with an acceleration of F/3G. FH = 2G * F/3G

 

[harrycc]

Thank You so much! You are very helpful!