Block A has a mass of 2.60 kg and rests on a smooth (frictionless) table and is connected to
block B, which has a mass of 2.40 kg, after passing over an ideal pulley, as shown. Block B is
released from rest. What is the acceleration of the masses?
To find the acceleration of the masses, we can use Newton's second law of motion, which states that the net force on an object is equal to the product of its mass and acceleration.
First, let's determine the force acting on each block. Block B is pulled downwards by its weight (mg), and the tension in the connecting string is pulling it upwards. Due to the smooth table, there is no friction acting on the blocks.
For block B:
The weight of block B (mg) = mass (m) * gravitational acceleration (g)
The tension in the string (T) is equal to the weight of block A since they are connected and experience the same tension.
Now, we can set up the equations to find the acceleration. Let's call the acceleration of both blocks "a".
For block A:
T = ma (equation 1)
For block B:
T - mg = ma (equation 2)
Since T is equal to both equations (equation 1 and equation 2), we can set them equal to each other and solve for "a".
ma = ma + mg
ma - ma = mg
a = g
So, the acceleration of the masses in this system is equal to the gravitational acceleration (g).