We are asked to determine the tension in the system. To do that we will add the vertical forces on the 50g mass using the following free-body diagram:
Where:
Adding the vertical forces we get (taking downward forces to be positive and upward negative):
Where "a" is the acceleration of the system.
If we divide by mass "m" we get:
Now, we add the horizontal forces for the 250g mass using the following free-body diagram:
Where:
Now, we add the horizontal forces we get:
The friction force is given by:
Since the object is not accelerating in the vertical direction this means that the normal force is equivalent to the weight of the 250g mass, therefore, we have:
Substituting in the sum of forces we get:
Now, we divide both sides by the mass "M":
Since the acceleration is the same for both masses we can set them equal together and we get:
Now, we solve for the tension "T". First, we distribute both denominators:
Now, we add T/m:
Now, we add the coefficient of friction and the gravity to both sides:
Now, we take "T" as a common factor:
Now, we divide both sides by the factor:
Now, we substitute the values:
Solving the operations:
Therefore, the force of tension is 0.45 N.
Now, we determine the acceleration by substituting the value of the force of tension in any of the two formulas for acceleration:
Substituting the values:
Solving the operations:
Therefore, the acceleration is 0.8 m/s/s.
The net force on the system is given by Newton's second law:
Where "M + m" is the total mass of the system and "a" is the acceleration of the system. Substituting the values we get:
Solving the operations:
Therefore, the net force is 0.24 N.