In the drawing, the weight of the block on the table is 428. N and that of the hanging block is 195. N. Ignore friction, the mass of the rope, and the mass of the pulley. Find the acceleration of the two block system in m/s2.

m1 = 428/9.81

m2 =195/9.81

195 - T = m2 a

T = m1 a

so 195 - m1 a = m2 a

a = 195 /(m1+m2)
which we should have said without doing all that

To find the acceleration of the two-block system, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).

In this case, we have two blocks - one on the table and one hanging. The force acting on the table block is its weight (428 N), and the force acting on the hanging block is its weight (195 N), which is also the tension in the rope.

Let's assume that the acceleration of the two-block system is "a." Since the table block is stationary, its net force is zero (as there is no horizontal motion). Therefore, the force acting on the table block due to the hanging block is equal to the force of friction between the table and the block.

The force of friction can be calculated using the formula: Frictional Force = coefficient of friction * normal force. However, in this case, we are told to ignore friction. So, the force acting on the table block due to the hanging block is zero.

Now, let's find the net force acting on the hanging block. The weight of the hanging block is 195 N, but it is being pulled upwards by the tension in the rope. Therefore, the net force can be calculated by subtracting the force due to tension from the weight of the hanging block.

Net force on the hanging block = Weight - Tension
= 195 N - Tension

According to Newton's second law, the net force on the hanging block is equal to its mass multiplied by its acceleration.

Net force on the hanging block = mass of hanging block * acceleration
= m * a (assuming the mass of both blocks is the same)

Setting up the equation, we get:
195 N - Tension = m * a

Now, let's consider the system as a whole. Since the rope is inextensible and the blocks are connected to each other, they will have the same acceleration (a) and the same tension (T).

We know that the tension in the rope is also equal to the weight of the table block (428 N).

So we can now write another equation for the system:
Tension = Weight of the table block
= 428 N

Substituting this value back into our earlier equation, we get:
195 N - 428 N = m * a

Simplifying further:
-233 N = m * a

Finally, we can solve for the acceleration (a) using the given mass values (m):
acceleration (a) = -233 N / m

Note: The negative sign indicates that the acceleration is in the opposite direction of the force due to tension (as it is acting upwards).

Without knowing the value of the mass (m), we cannot compute the exact acceleration. To find the acceleration in m/s², we need to know the mass of the blocks in kilograms (kg).