Posted by **Timothy Tran** on Tuesday, September 22, 2009 at 11:28am.

Two boxes sit side-by-side on a smooth horizontal surface. The lighter box has a mass of 5.91 kg, the heavier box has a mass of 7.67 kg. Calculate the contact force between these boxes when a horizontal force of 5.09 N is applied to the light box.

and Calculate the contact force if the 5.09 N force is applied to the heavy box instead.

- Physic -
**MathMate**, Tuesday, September 22, 2009 at 3:23pm
They would accelerate initially at the same acceleration, a m/s/s.

Total mass, M = m1+m2 = 5.91 + 7.67 kg

Force, F = 5.09 N.

Acceleration, a = F/M

The contact force is the force required to set the farther block in motion at the calculated acceleration a.

The force is in turn equal to ma, where m is the mass of the farther block.

- Physic -
**Timothy Tran**, Tuesday, September 22, 2009 at 5:53pm
Thanks for your help but I'm still a bit confuse. By using F=ma, we are solving for acceleration, but how would I conduct that into finding the horizontal force? Thank you very much for you help

- Physic -
**MathMate**, Tuesday, September 22, 2009 at 6:03pm
If the two blocks move together, their acceration will be the same. The force is mass of the block * acceleration, hence

F=ma.

Schematically, it is:

External force, F -> block1 -> block2

The external force F is applied on block1. Block1 in turn applies a force F2 to block2. Both of them move in tandem with an acceleration of a.

Thus F2=m2*a

and net force on block1 is F-F2=m1*a

This also means that the acceleration can be determined from

F=(m1+m2)*a

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