A 2kg mass, m1 and a 10 kg mass, m2 are in contact on a horizontal frictionless surface. a constant horizontal force 13.7 N in the positive X direction is applied to m1 and a constant horizontal force 10.7 N in the negative X direction is applied to m2. the masses stay in contact whole they move. find the magnitude of the contact force between the two masses.
answers can be: 27.4, 13.2, 14.2, 11.42, 0.5 (all are N)
help pls
To find the magnitude of the contact force between the two masses, we need to consider the net force acting on the system.
Let's denote the contact force between the two masses as Fc. Since the surface is frictionless, there is no frictional force to consider in this case.
The net force acting on the system can be calculated by considering the individual forces applied to each mass.
For mass m1, the applied force is 13.7 N in the positive X direction. Since there is no other force acting on m1, the net force is simply the applied force: F_net1 = 13.7 N.
For mass m2, the applied force is 10.7 N in the negative X direction. Again, since there is no other force acting on m2, the net force is the negative of the applied force: F_net2 = -10.7 N.
Now, since m1 and m2 are in contact and move together, the magnitude of the contact force Fc between them must be the same. This is according to Newton's third law, which states that the force exerted by one object on another is equal in magnitude but opposite in direction.
Therefore, we can equate the net forces acting on m1 and m2 to find the magnitude of the contact force:
F_net1 = F_net2 + Fc
13.7 N = -10.7 N + Fc
Rearranging the equation, we have:
Fc = 13.7 N - (-10.7 N)
= 13.7 N + 10.7 N
= 24.4 N
Therefore, the magnitude of the contact force between the two masses is 24.4 N.