Two blocks ( m1 = 6.8kg, m2 = 5.2kg) are in contact with each other while sitting on a friction less surface. M2 is not resting on the frictionless surface, rather to the side of m1. The coefficient of static friction between the blocks is 0.60, and the coefficient of kinetic friction is 0.40. A horizontal force is applied to m1.
What is the maximum force that m1 must exert of m2 so that they move together?
To find the maximum force that m1 must exert on m2 so that they move together, we need to consider the forces acting on the two blocks and the conditions for equilibrium.
First, let's analyze the forces acting on m1:
1. The force applied to m1 (F_applied): This is the force that we are trying to determine, and it acts in the horizontal direction.
2. The force of friction between m1 and the surface (F_friction): This force opposes the motion and acts in the opposite direction of F_applied.
Since the surface is frictionless, F_friction is zero. Therefore, the only force acting on m1 is F_applied.
Next, let's analyze the forces acting on m2:
1. The force of static friction between m1 and m2 (F_static_friction): This force opposes the relative motion between the two blocks and acts in the opposite direction of F_applied.
2. The force of gravity acting on m2 (F_gravity): This force acts vertically downward and is equal to the weight of m2, which can be calculated as F_gravity = m2 * g, where g is the acceleration due to gravity.
For the blocks to move together, the force of static friction, F_static_friction, must equal or exceed the maximum static friction force, which can be calculated as the coefficient of static friction (μ_static) multiplied by the normal force between the two blocks.
The normal force between the two blocks, N, is equal to the weight of m1 since m1 is resting on the surface, so N = m1 * g.
Therefore, the maximum static friction force, F_max_static_friction, is given by F_max_static_friction = μ_static * N.
To find the maximum force that m1 must exert on m2, we set F_static_friction equal to F_max_static_friction:
F_static_friction = F_max_static_friction
Now we can substitute the values:
μ_static * N = F_max_static_friction
μ_static * (m1 * g) = F_max_static_friction
0.60 * (6.8kg * 9.8m/s^2) = F_max_static_friction
F_max_static_friction = 39.81N
Therefore, the maximum force that m1 must exert on m2 so that they move together is 39.81 Newtons.