Block moving around in a semi cricle

[arrax]

Homework Statement

A cylinder is cut out of a large block with mass M=4kg sitting on a table. A small block of negligible size and mass m=0.5kg is placed within the hole. All the surfaces are frictionless. The radius of the cut is R=0.80m and the angle is 25 degrees.

Basically there's a block with a semi-circle cut into it. Inside the semi circle is a block that is positioned 25 degrees to the left from bottom dead center. And there is a force F pushing this big block with a semi-circle cut to the right. So when you push the block, the little block in the half pipe moves. I'm supposed to find the FORCE on the big block that makes the small block move 25 degrees and the force of the block on the mass m (the small block)

Homework Equations

F=ma, Circumference = 2∏r

The Attempt at a Solution

i have no idea where to start, but for the small block i tried using tanθ = a/g, but I came out with 4.575 m/s^2 for my a which seems way too fast.

 

[tms]

Start where one should always start: by writing down the forces acting on the blocks (separately). There are two on the small block: one is gravity and the other is ...

 

[arrax]

The other is the M block acting on the small block, and So gravity does act on the small block so I do end up using tan25 deg = a/g I think because of the force of the big block acting on the small block on the x axis.

 

[tms]

Recall that the small block is very small. The force of the big block on the small will be the same as the force of an inclined plane tangent to the hole would be.

 

[asteriatic]

I would approach this problem by first identifying the key variables and their relationships. The main variables in this problem are the masses of the two blocks (M and m), the radius of the semi-circle (R), the angle at which the small block is positioned (25 degrees), and the force applied to the large block (F).

To find the force on the big block that makes the small block move 25 degrees, we can use the equation F=ma, where F is the force we are looking for, m is the mass of the small block, and a is the acceleration of the small block.

To find the acceleration, we can use the formula for circular motion, a=v^2/r, where v is the velocity of the small block and r is the radius of the semi-circle. Since the small block is moving at a constant speed in a circular path, we can also use the formula for linear velocity, v=ωr, where ω is the angular velocity.

To find ω, we can use the relationship between linear and angular velocity, v=rω, where v is the linear velocity and r is the radius.

Putting these equations together, we can find the acceleration of the small block, and then use that to find the force on the big block.

To find the force of the big block on the small block, we can use Newton's third law, which states that for every action, there is an equal and opposite reaction. Therefore, the force of the big block on the small block will be equal in magnitude but opposite in direction to the force of the small block on the big block.

Overall, it is important to identify the key variables and their relationships in order to solve this problem. By using the appropriate equations and principles, we can find the forces on both blocks and understand the motion of the system.