Question

A 3.0kg and 5.0kg box rest side by side on a smooth, level floor. Ahorizontal force of 32N is applied to the 3.0 kg box pushing itagainst the 5.0 kg box and as a result both boxes slide along thefloor. How large is the contact force between the two boxes?

a) 12N
b) 20N
c) 32N
d) 0N

Answer 1

a) 12N

Step-by-step explanation:

The boxes move together, so we can use Newton's second law to find its acceleration

`F=ma`

in this case

`m=m_(1)+m_(2)`

where

`m_(1)=3kg`

and

`m_(2)=5kg`

thus the acceleration, given a force of 32N, is:

`a=(F)/(m)=(F)/(m_(1)+m_(2))=(32N)/(3kg+5kg) =(32N)/(8kg) =4m/s^2`

and now we use this acceleration to find the force between the boxes, using the mass of the first box:

`F=m_(1)a=(3kg)(4m/s^2)=12N`

this is the force between the two boxes (box one on box two, and for the box two on box one is the same magnitude but in the opposite direction).