Three blocks are connected on the table as shown below. The coefficient of kinetic friction between the block of mass m2 and the table is 0.400. The objects have masses of m1 = 3.00 kg, m2 = 1.45 kg, and m3 = 1.90 kg, and the pulleys are frictionless. Determine the acceleration of each object, including its direction.Determine the tensions in the two cords.

that still doesnt work...this is SOOOOOOOOOOOOOOO frustrating

To determine the acceleration of each object and the tensions in the two cords, we will use Newton's laws of motion.

1. Acceleration of each object:
Let's assume that the direction in which the objects move is to the right.

For block 1 (m1):
The only force acting on m1 is the tension in cord 1 (T1) pulling it to the right. There is no friction or other force acting on it. Therefore, we can write the equation:
m1 * a = T1

For block 2 (m2):
There are two forces acting on block 2: tension in cord 1 (T1) pulling it to the right and the force due to kinetic friction between m2 and the table. The force of kinetic friction can be calculated as:
f_friction = μ * (m2 * g)
where μ is the coefficient of kinetic friction and g is the acceleration due to gravity. The direction of the frictional force is opposite to the motion, so it will be to the left. Therefore, the equation for block 2 becomes:
T1 - f_friction = m2 * a

For block 3 (m3):
The only force acting on m3 is the tension in cord 2 (T2) pulling it to the right. There is no friction or other force acting on it. Therefore, we can write the equation:
m3 * a = T2

2. Tensions in the two cords:
In this system, T1 and T2 are the tensions in the cords. These tensions are the same for both blocks 1 and 2 because they are connected to the same cord.

We can solve these equations simultaneously to find the values of the acceleration of each object (a) and the tensions in the cords (T1 and T2).

Steps to solve the equations:
1. First, calculate the force of kinetic friction (f_friction) using the given coefficient of kinetic friction and the mass of m2.
2. Use the equation T1 - f_friction = m2 * a to find T1.
3. Use the equation m1 * a = T1 to find the acceleration (a).
4. Use the equation m3 * a = T2 to find T2.

Plug in the given mass values (m1 = 3.00 kg, m2 = 1.45 kg, m3 = 1.90 kg), and the coefficient of kinetic friction (μ = 0.400) into the equations to obtain the values of a, T1, and T2.

<< Three blocks are connected on the table as shown below. >>

Where?

Im sorry, m1 is suspended by a pulley and string on the left side, m2 is on the table connected to the pulley by a string in the middle and m3 is suspended on the right side by a pulley and string which is also connected to m2.

I am pretty sure I need to find an equation in terms of m, a, and kinetic friction so I will only have one unknown. From my fbd I figured that the normal force would not equal the weight in the y direction because it is accelerating down. So I don't know how to come up with that equation to solve for a and T.

The next thing I tried was to solve for T from by fbd. I got T=m1g-m1a for the first mass, then T1-T2=-fk*m2g+m1a for the second, and T=m3g+m3a. I don't know if this is right or not. Since I am trying to find the acceleration of each mass can i set these equations equal to each other? That would find the acceleration of the whole system. I just cant figure this out.