How Do Newton's Laws Apply in Calculating Contact Force Between Boxes?

[pulau_tiga]

Hi.

I have a physics question. I cannot get the right naswer.

The question:
Three boxes rest side-by-side on a smooth horizontal floor. Their masses are 1.10 kg, 3.45 kg, and 5.55 kg, with the 3.45 kg one in the center. A horizontal force of 20.0 N pushes on the 1.10 kg mass which pushes against the other two masses. What is thte contact force between the 3.45 kg and 5.55 kg boxes?

My solution:
I know that the force applied (20.0 N) is not constant throughout. However, acceleration of the full system is. Therefore I thought I could use Newton's 2nd Law. Fnet = ma.

Fnet of mass 1.10 kg = ma
rearranging gives a = 18.18 m/s^2.

Fnet of mass 3.45 = ma = 62.7 N

I thought this would be my contact force as this is the force that the 3.45 kg block pushes against the 5.55 kg box?/ Isn't this the answer? Can someone point me in the right direction or help me out.?? Thanks.

 

[Leong]

Have you drawn the free body diagram of the boxes individually ?
Have you applied Newton's third law as well ?For example, two forces acts on the 1.10 kg block which are the 20.0 N force and the contact force exerted on it by the middle block.
The 20.0 N force applied is constant of course or the question will get quite complicated.

 

[niehls]

i assume friction is negligible.
i would like to use Newton's second law like this
first, the 20N force accelerates the whole system:
20N = (1.10 + 3.45 + 5.55)(kg)*a; => a_total = 1.99m/^s^2
so, the acceleration of the whole system of boxes is 1.99m/s^2.
Next, for the last box of weight 5.55kg to get an acceleration of 1.99m/s^2 you will need the contact force
F = m*a = (5.55)(kg)*(1.99)(m/s^2) = 10.95N.
This should be the force excerted on the last box of 5.55kg. Haven't had my morning coffee yet though, so i might be wrong :)

/edit
although the easiest way to solve this problem would be to examine the quota F/m. since the acceleration is the same for all parts of the system you could solve it like
F_tot/m_tot = F_3/m_3 and thus get the force on the third box (F_3)