A block of mass M slides along the smooth wedge mass M.what will be the acceleration of centre of mass of block and wedge system?
To find the acceleration of the center of mass of the block and wedge system, we can consider the forces acting on the system.
1. Gravity: Both the block and the wedge experience a gravitational force pulling them downwards. The block experiences a force of mg (mass of the block multiplied by the acceleration due to gravity), and the wedge experiences a force of Mg (mass of the wedge multiplied by the acceleration due to gravity).
2. Normal force: The block exerts a normal force on the wedge, and the wedge exerts a normal force on the block. These normal forces cancel each other out and do not contribute to the acceleration of the system's center of mass.
3. Friction force: There will be a friction force acting between the block and the wedge, opposing the relative motion between them. This friction force will be dependent on the coefficient of friction (μ) and the normal force between the block and the wedge.
Considering all these forces, we can use Newton's second law to calculate the acceleration of the center of mass:
ΣF = Ma
ΣF = Force on the block - Force on the wedge
Force on the block = mg - friction force
Force on the wedge = Mg + friction force
Plugging these values into the equation, we have:
mg - friction force - (Mg + friction force) = Ma
Simplifying further:
(a + g) = (m - M)g / (m + M)
Therefore, the acceleration of the center of mass of the block and wedge system is (m - M)g / (m + M), where m is the mass of the block and M is the mass of the wedge.