Final answer:
To find the magnitude of acceleration of the wedge, we need to consider the forces acting on the block and the wedge and use Newton's second law. Once we have calculated all the forces, we can determine the magnitude of the acceleration.
Step-by-step explanation:
To find the magnitude of acceleration of the wedge, we can use Newton's second law, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration. In this case, we need to consider the forces acting on the block and the wedge.
The force due to gravity acting on the block can be calculated using the equation F = m * g, where m is the mass of the block and g is the acceleration due to gravity. The normal force acting on the block is equal to its weight, and the force of friction is given by the equation Ffriction = μ * N, where μ is the coefficient of friction and N is the normal force.
On the wedge, the forces acting are the normal force and the component of the force due to gravity parallel to the incline. The normal force can be calculated using the equation Nwedge = m * g * cos(theta), where theta is the angle of the incline. The component of the force due to gravity parallel to the incline is given by Fparallel = m * g * sin(theta).
Once we have calculated all the forces, we can use Newton's second law to determine the magnitude of the acceleration of the wedge.