The blocks A and B are connected by a piece of spring. Block B rests on an inclined plane of 40° and block A hangs vertically. The coefficient of kinetic friction between block A and the inclined plane is 0.29. Calculate the acceleration of the system if the mass of block A is 0.15 kg and that of block B is 7.5 kg.
To calculate the acceleration of the system, we need to consider the forces acting on each block individually and then apply Newton's second law of motion.
First, let's analyze the forces on block B, which rests on the inclined plane of 40°. We have the force of gravity acting vertically downwards, which can be split into two components: one along the inclined plane and the other perpendicular to it. The component along the inclined plane opposes motion and is given by mg * sin(40°), where m is the mass of block B and g is the acceleration due to gravity. The perpendicular component does not affect the motion along the plane and is given by mg * cos(40°).
Since there is kinetic friction acting on block A, there is also a frictional force acting on block B along the inclined plane. The frictional force is calculated by multiplying the coefficient of kinetic friction (μ) by the perpendicular component of the weight of block B. So the frictional force is μ * mg * cos(40°).
Considering the forces on block A, we have only the force of gravity acting downwards. The weight of block A is given by m * g, where m is the mass of block A and g is the acceleration due to gravity.
To find the net force acting on each block, we subtract the opposing forces from the forces that drive motion. For block B, the net force is (mg * sin(40°)) - (μ * mg * cos(40°)). For block A, the net force is m * g.
Now, we can apply Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration. So, we can set up the following equations:
For block B: (mg * sin(40°)) - (μ * mg * cos(40°)) = 7.5 kg * acceleration
For block A: m * g = 0.15 kg * acceleration
Substituting the values and solving these two equations simultaneously will give us the acceleration of the system.