To solve for the acceleration of the 6 kg block, you can use Newton's second law, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
In this case, the tension in the rope is the force acting on the 6 kg block. So, you can set up the equation:
Tension = 18 N
Mass of the 6 kg block = 6 kg
Acceleration = ?
Using the equation F = ma, you can solve for acceleration:
18 N = 6 kg * acceleration
Dividing both sides of the equation by the mass (6 kg), you get:
acceleration = 18 N / 6 kg = 3 m/s^2
So, the acceleration of the 6 kg block is 3 m/s^2.
To find the mass (m) of the hanging block, you need to consider the forces acting on it. The force of gravity is pulling it downward, and the tension in the rope is pulling it upward.
The force of gravity acting on the hanging block is given by m*g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, the net force acting on the hanging block is:
Net force = m * g - tension
Using Newton's second law again, you can set up the equation:
m * g - 18 N = m * acceleration
Since the acceleration is already known (3 m/s^2), you can rearrange the equation to solve for m:
m = 18 N / (g - 3 m/s^2)
Substituting the value of g (approximately 9.8 m/s^2), you find:
m = 18 N / (9.8 m/s^2 - 3 m/s^2) ≈ 2.64 kg
So, the mass (m) of the hanging block is approximately 2.64 kg.