Aload of bricks with mass  m1  = 14.0  kg  hangs from one end of a rope that passes over a small, frictionless pulley. a counterweight of mass  m2= 28.4  kg  is suspended from the other end of the rope, as shown in the figure.  the system is released from rest. use  g  = 9.80  m/s2  for the magnitude of the acceleration due to gravity.

For the bricks hangs from one end of a rope the value of acceleration due to counterweight is 3.33 m/s².

Tension is the pulling force carried by the flexible mediums like ropes, cables and string. Tension in a body due to the weight of the hanging body is the net force acting on the body.

The tension in the string when body can be given as,

Here, (m) is the mass of the body, (a) is the acceleration and (g) is the acceleration due to gravity.

The mass of the bricks is 14 kg.

The mass of the counterweight is 28.4 kg and the system is released from the rest.

The tension due to the bricks with mass 14 kg is,

The tension due to the bricks with mass 28.4 kg is,

Equate both the equation as,

Thus for the bricks hangs from one end of a rope the value of acceleration due to counterweight is 3.33 m/s².

Learn more about the tension in the string here;

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Mass m1 and m2 are connected together and the rope is passing over the pulley

here we can see that the two masses are connected so the acceleration will be same but opposite in direction

So here we can use the force equations to solve for the acceleration of two blocks

now for block of mass m1

for block of mass m2

Now add above two equations to find its acceleration

now we will plug in all the values

So the acceleration of two blocks will be 3.33 m/s^2

this is poiselle's equation from fluid mechanic in physics. mech eng