a. The free body diagram for the two masses can be drawn as follows:
For the mass m1:
- There is a downward force due to its weight, mg1.
- There is an upward normal force from the table, N1.
- There is a frictional force opposing the motion, f1.
For the mass m2:
- There is a downward force due to its weight, mg2.
- There is an upward tension force from the cable, T.
b. To calculate the frictional force on the block, we can use the equation: friction = coefficient of friction * normal force.
In this case, the normal force is equal to the weight of the block, which is mg1. Therefore, the frictional force is given by: f1 = coefficient of friction * mg1.
c. To calculate the acceleration of the system, we can use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration. In this case, the net force is the difference between the tension force and the frictional force.
The net force can be calculated as: net force = T - f1.
The mass of the system is given by: m = m1 + m2.
Using these equations, we can find the acceleration of the system: a = (T - f1) / m.
d. To find the tension in the string, we can use Newton's second law again. For mass m2, the net force is equal to its weight minus the tension force. So, we have: mg2 - T = m2 * a.
By rearranging the equation, we can solve for the tension force: T = mg2 - m2 * a.
