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#