What's the minimum horizontal force that needs to be applied to the bottom block of mass X so that the top block of mass x slides off? The coefficient of friction between the bottom block and the floor is µ1, the coefficient of friction between the two blocks is µ2.
To find the minimum horizontal force required to make the top block slide off the bottom block, we can consider the forces acting on the system.
First, let's start with the force acting on the bottom block. The applied force will oppose the forces of friction acting on the bottom block. The friction force between the bottom block and the floor can be calculated using the equation:
Friction1 = µ1 * Normal Force
Next, let's consider the force acting on the top block. The force of friction acting between the top and bottom blocks will oppose their relative motion. The friction force between the two blocks can be determined using the equation:
Friction2 = µ2 * Normal Force
However, since the top block must just start sliding, the friction force acting between the two blocks will be at its maximum value. Therefore, Friction2 will be equal to the maximum value of µ2 * Normal Force, which equals µ2 * m2 * g, where m2 is the mass of the top block and g is the acceleration due to gravity.
Now, let's analyze the net force acting on the top block. It is the difference between the applied force, F_applied, and the maximum friction force between the two blocks, Friction2.
Net Force = F_applied - Friction2
For the top block to slide off the bottom block, the net force needs to be greater than zero. Otherwise, the friction force would prevent the top block from moving.
Therefore, to find the minimum horizontal force required, we set the net force equal to zero and solve for F_applied.
0 = F_applied - Friction2
F_applied = Friction2
F_applied = µ2 * m2 * g
So, the minimum horizontal force required to make the top block slide off the bottom block is µ2 * m2 * g, where µ2 is the coefficient of friction between the two blocks, m2 is the mass of the top block, and g is the acceleration due to gravity.