The blocks A and B are connected by a piece of spring. Block B rests on a smooth inclined plane of 35° and block A hangs vertically. Calculate the acceleration of the system if the mass of block A is 1.06 kg and that of block B is 6.4 kg

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To calculate the acceleration of the system, we need to consider the forces acting on both blocks A and B.

Let's start by analyzing block A. The only force acting on it is the force of gravity, which can be calculated using the formula:

Force of gravity = mass × acceleration due to gravity

Given that the mass of block A is 1.06 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the force of gravity on block A:

Force of gravity on block A = 1.06 kg × 9.8 m/s²

Next, let's consider block B. Since it rests on a smooth inclined plane, there are two forces acting on it: the force of gravity and the component of gravity parallel to the inclined plane. The force of gravity on block B can be calculated as:

Force of gravity on block B = mass × acceleration due to gravity

Given that the mass of block B is 6.4 kg, we can calculate the force of gravity on block B:

Force of gravity on block B = 6.4 kg × 9.8 m/s²

To find the component of gravity parallel to the inclined plane, we need to resolve the force of gravity into its components. The component of gravity parallel to the inclined plane can be calculated using the formula:

Component of gravity parallel to inclined plane = Force of gravity on block B × sin(θ)

Where θ is the angle of the inclined plane, which is given as 35°. Let's calculate the component of gravity parallel to the inclined plane:

Component of gravity parallel to inclined plane = Force of gravity on block B × sin(35°)

Now, let's find the net force acting on the system. Since block B is resting on a smooth inclined plane, the frictional force can be ignored. Therefore, the only force causing acceleration is the component of gravity parallel to the inclined plane.

Net force = Component of gravity parallel to inclined plane

Now, we have the net force acting on the system. To calculate the acceleration, we can use Newton's second law of motion:

Net force = mass × acceleration

Since both blocks A and B move together, we can consider the total mass of the system as the sum of the masses of block A and block B:

Total mass of the system = mass of block A + mass of block B

Finally, we can calculate the acceleration of the system using the formula:

Acceleration of the system = Net force / Total mass of the system

Plug in the calculated values to find the acceleration of the system.