Question

A box of mass m1 rests on a smooth, horizontal floor next to a box of mass m2. Suppose the force of 20.0 N pushes on two boxes of unknown mass. We know, however, that the acceleration of the boxes is 1.20 m/s2 and the contact force has a magnitude of 4.45 N. Find the mass of box 1 and box 2.

Answer 1

Mass of box 1 is 12.95 kg

Mass of box 2 is 3.7083 kg

Step-by-step explanation:

We have given the pushing force F = 20 N

Force on the box 2 that is contact force
`F_(m2)=F_(c)=4.45N`

So net force that is force on box 1
`F_(m1)=F-F_c=40-4.45=15.55N`

It is given that acceleration for both the box is same as
`a=1.20m/sec^2`

From newton's law we know that F = ma

So mass of box 1
`m_1=(F_(m1))/(a)=(15.55)/(1.2)=12.9583kg`

Mass of box 2
`m_2=(F_(m2))/(a)=(4.45)/(1.2)=3.7083kg`

Answer 2

Step-by-step explanation:

Given

acceleration of system a =1.2 m/s^2

Normal Force N=4.45 N

Force exerted F=20 N

Thus

`F=(m_1+m_2)a`

`(20)/(1.2)=m_1+m_2`

`16.67=m_1+m_2`-------1

Normal reaction
`N=m_2a`

`4.45=m_2* 1.2`

`m_2=3.70 kg`

therefore
`m_1=16.67-3.70`

`m_1=12.96 kg`