Problem Statement:

Block A of mass 2kg is placed over block B of mass 8kg. The combination is placed over a rough horizontal surface. The coefficient of friction between block B and the floor is 0.5, and between block A and block B is 0.4. A horizontal force of 10 Newton is applied on block B. Determine the force of friction between block A and block B.

Solution:

To find the force of friction between block A and block B, we need to consider the forces acting on both blocks individually.

Forces on Block B:

1. Weight (Wb): The weight of block B can be calculated using the formula:
Wb = mass * acceleration due to gravity = 8kg * 9.8m/s^2 = 78.4N

2. Normal force (Nb): The normal force on block B is equal to the weight of block A plus the weight of block B, as they are stacked on top of each other:
Nb = Wa + Wb = 2kg * 9.8m/s^2 + 8kg * 9.8m/s^2 = 19.6N + 78.4N = 98N

3. Friction force between block B and the floor (Ff_bf): The friction force can be calculated using the formula:
Ff_bf = coefficient of friction * Nb = 0.5 * 98N = 49N

4. Applied horizontal force (Fa): The applied force acting on block B is given as 10N.

5. Net force on block B (F_net_b): The net force acting on block B can be calculated using the formula:
F_net_b = Fa - Ff_bf = 10N - 49N = -39N (negative sign indicates opposite direction)

Forces on Block A:

1. Weight (Wa): The weight of block A can be calculated using the formula:
Wa = mass * acceleration due to gravity = 2kg * 9.8m/s^2 = 19.6N

2. Friction force between block A and block B (Ff_ab): The friction force can be calculated using the formula:
Ff_ab = coefficient of friction * Nb = 0.4 * 98N = 39.2N

3. Net force on block A (F_net_a): The net force acting on block A can be calculated using the formula:
F_net_a = Ff_ab - Ff_ba = 39.2N - Ff_ba

4. Acceleration of block A (a_a): The acceleration of block A can be calculated using Newton's second law:
F_net_a = mass * acceleration
F_net_a = 2kg * a_a
a_a = F_net_a / 2kg = (39.2N - Ff_ba) / 2kg

Equations for the System:

1. Net force on block B: F_net_b = Fa - Ff_bf

2. Net force on block A: F_net_a = Ff_ab - Ff_ba

3. Acceleration of block A: a_a = (39.2N - Ff