# 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?

## 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.

Jan 17, 2018

$13.8 N$

#### Explanation:

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

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

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