A block of mass 2 kg is connected to a freely hanging block of mass 4 kg by a light and inextensible string which passes over pulley at the edge of a table. The 2 kg mass is on the surface of the table assumed to be smooth. Calculate the acceleration of the system and the tension in the string

6.7ms

To calculate the acceleration of the system, we can use Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration (F = ma).

Let's analyze the forces acting on each block separately:

1. For the 4 kg block:
- The force of gravity (weight) is acting downwards with a magnitude of 4 kg * 9.8 m/s^2 = 39.2 N.
- The tension force in the string is acting upwards.

2. For the 2 kg block:
- The force of gravity (weight) is acting downwards with a magnitude of 2 kg * 9.8 m/s^2 = 19.6 N.
- The tension force in the string is acting to the right.

Since the 2 kg block is on a smooth table, there is no frictional force acting on it. Therefore, the only horizontal force on the 2 kg block is the tension force.

Now, let's apply Newton's second law to each block:

For the 4 kg block:
Tension force - Weight = mass * acceleration
T - 39.2 = 4a (Equation 1)

For the 2 kg block:
Weight = mass * acceleration
19.6 = 2a (Equation 2)

Since the tension force in the string is common to both blocks, we can set the tension force equal in both equations:

T - 39.2 = 4a
T = 4a + 39.2 (Equation 3)

T = 2a (Equation 4)

Now, let's solve the equations:

From Equation 2:
19.6 = 2a
a = 9.8 m/s^2

Substitute the value of acceleration (a) into Equation 4 to find the tension force (T):

T = 2a
T = 2 * 9.8
T = 19.6 N

Therefore, the acceleration of the system is 9.8 m/s^2, and the tension in the string is 19.6 N.