Find Acceleration of Wedge & Mass on Incline | Incline Problem Solution

[fresh]

Question is:

A wedge makes an angle theta to the horizontal. it has a mass M2 and can slide along the horizontal. A mass M1 slides along the frictionless surface of the incline. What are the expressions for the acceleration of the wedge and the mass M1?

I am just puzzled. Any suggestions to get me started is great.

 

[maverick280857]

1. What happens to the wedge as the mass on it moves down the incline?

2. Can you draw a freebody diagram to see the interplay of forces?

3. Apart from forces, what approach can you think of to solve this problem? What are the constraints of the system? What are its dynamic variables?

 

[wais]

To find the acceleration of the wedge and mass M1, we can use Newton's Second Law, which states that the net force on an object is equal to its mass times its acceleration (F=ma). We can break down the forces acting on both the wedge and mass M1 separately and then use them to find their individual accelerations.

For the wedge, the forces acting on it are its weight (mg) and the normal force (N) from the incline. The normal force is perpendicular to the incline and can be found by taking the component of the weight in the direction perpendicular to the incline, which is mgcosθ. This means that the net force on the wedge is mgcosθ - mg = mg(cosθ - 1). We can then use this net force and the wedge's mass (M2) to find its acceleration using F=ma. So, the expression for the acceleration of the wedge is a = (mg(cosθ - 1))/M2.

For the mass M1, the forces acting on it are its weight (mg) and the normal force (N) from the incline. The normal force in this case is equal to the weight of the mass, since it is on a frictionless surface. This means that the net force on mass M1 is mg - mg = 0. Therefore, the acceleration of mass M1 is zero.

In summary, the expression for the acceleration of the wedge is a = (mg(cosθ - 1))/M2 and the acceleration of mass M1 is 0. This means that the wedge will accelerate down the incline while mass M1 will remain at rest.