A block of mass 30 m can’t move without friction on a horizontal table. Block is attached to another block of mass by 8 m by a cord that passes over a frictionless pulley as shown. If the masses of the cord and the pulley our neglect a bowl what is the magnitude of the acceleration of the descending block hole?If the masses of the cord in the pulley are negligible what is the magnitude of the acceleration of the descending block?
To find the magnitude of the acceleration of the descending block in both cases, 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 = m * a).
Case 1: Neglecting the masses of the cord and the pulley:
In this case, we can assume that the mass of the cord and the pulley is negligible, meaning that their masses can be ignored when calculating the net force.
The downward force acting on the descending block is due to the force of gravity (m * g), where m is the mass of the descending block and g is the acceleration due to gravity.
The tension in the cord is equal to the weight of the descending block, since the cord is inextensible and experiencing no friction. Therefore, the net force acting on the descending block is (Tension - m * g).
Since the net force is equal to the mass of the descending block (m) multiplied by its acceleration (a), we can write the equation as follows:
m * a = Tension - m * g
Now, we need to consider the other block that is attached to the cord. It is being pulled upwards by the tension in the cord, so the net force on that block is (m * g - Tension).
As the blocks are connected by the cord, the acceleration of one block is equal in magnitude but opposite in direction to the acceleration of the other block. Hence, we can write the equation for the other block as follows:
m * a = m * g - Tension
Now we can solve these two equations simultaneously to find the magnitude of acceleration (a).
Case 2: Neglecting the masses of the cord and the pulley, assuming a frictionless pulley:
In this case, we can assume that the pulley is frictionless, so the tension in the cord is the same on both sides.
Using the same approach as in Case 1, we can write the equation for the downward force acting on the descending block (m * g), and the upward force acting on the ascending block (m * g).
Since the net force acting on each block is equal to the mass of the block (m) multiplied by its acceleration (a), we can write the equations as follows:
m * a = m * g (for the descending block)
m * a = m * g (for the ascending block)
In this case, since both blocks have the same mass (m) and experience the same gravitational force, the magnitude of acceleration for both blocks will be equal and can be calculated by dividing the gravitational force (m * g) by the mass (m):
a = g
Note: In real-life situations, the masses of the cord and the pulley may not be negligible, and the pulley may have friction. Hence, these assumptions affect the calculations.