Two blocks connected by a string are pulled across a rough horizontal surface by a force applied to one of the blocks, as shown. The acceleration of gravity is 9.8 m/s2 . If each block has an acceleration of 5.2 m/s2 to the right, what is the magnitude of the applied force? Answer in units of N

To find the magnitude of the applied force, we can use Newton's second law, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration:

Net force = mass × acceleration

In this case, we have two blocks connected by a string, so the net force acting on both blocks will be the same. Let's call the mass of the first block "m1" and the mass of the second block "m2."

Since both blocks are accelerating to the right, we know that the net force acting on both blocks is in that direction. Let's call this force "F."

The acceleration of the blocks is given as 5.2 m/s^2, and the acceleration due to gravity is not relevant to this problem. Therefore, the net force on both blocks can be written as:

F = (m1 + m2) × acceleration

Next, we need to express the masses of the blocks in terms of the force acting on them. We know that the force acting on the second block (m2) is simply the force F itself, as it is pulling the first block. However, the net force acting on the first block is the force F acting on it, minus the force of tension in the string (T). Therefore, the net force on the first block can be written as:

Net force on first block = F - T

Since the net force on the first block is equal to its mass multiplied by its acceleration, we can write:

F - T = m1 × acceleration

Now we can solve for T, the force of tension:

T = F - m1 × acceleration

Since the blocks are connected by a string, the tension T is the same for both blocks. Therefore, we can write:

T = F - m1 × acceleration = F - m2 × acceleration

Now we have two equations:

F = (m1 + m2) × acceleration
T = F - m1 × acceleration

We can substitute the second equation into the first equation:

(m1 + m2) × acceleration = T + m1 × acceleration

Rearranging the equation, we get:

m2 × acceleration = T

Now we can substitute the value of T from the second equation:

m2 × acceleration = F - m1 × acceleration

Rearranging again, we find:

F = m2 × acceleration + m1 × acceleration

Substituting the given values of m1, m2, and acceleration:

F = m1 × acceleration + m2 × acceleration
F = (m1 + m2) × acceleration

Finally, we can calculate the magnitude of the applied force by substituting the values:

F = (m1 + m2) × acceleration
= (m1 + m2) × 5.2 m/s^2

Make sure to substitute the mass values of the blocks in kilograms and acceleration in meters per second squared to get the answer in Newtons (N).