Two masses are in contact on a horizontal frictionless surface. A horizontal force is applied to $M_1$ and a second horizontal force is applied to $M_2$ in the opposite direction. What is the magnitude of the contact force between the masses?

Question

A 3 kg mass, $M_1$ , and a 10 kg mass, $M_2$ , are in contact on a horizontal frictionless surface. A constant horizontal force 14.3 N in the positive x direction is applied to $M_1$ and a constant horizontal force 12.2 N in the negative x direction is applied to $M_2$ . The masses stay in contact while they move. Calculate the magnitude of the contact force between the two masses.

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Answer 1 · 2018-01-17T14:19:37

$13.8 N$

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See the free body diagrams made,
from it we can write,
$14.3 - R = 3a.......1$ (where, R is the contact force and a is acceleration of the system)

and, $R-12.2 = 10.a....2$

solving we get, $R$ =contact force= $13.8 N$