What Angle Does the Plumb Bob Make with the Vertical on a Sliding Frame?

[Jstew]

Homework Statement

A plum bob suspended from a frame settles to a steady position as the frame slides down a frictionless inclined plane. What is the angle the plumb bob makes with the vertical during the slide?
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Homework Equations

The problem is from a section introducing Newton's Laws. I assume this problem is about inertia.

The Attempt at a Solution

Utterly no idea how to go about this, although I assume the answer is alpha=theta since that's the clean way the answer could come out.

 

[Jstew]

I figured it out. Set T to Fg and the T and m cancel out, leaving tan(theta)=tan(alpha)

 

[baba89]

I would approach this problem by first understanding the concept of inertia and how it relates to this scenario. Inertia is the tendency of an object to resist changes in its state of motion. In this case, the plumb bob is initially at rest and as the frame slides down the inclined plane, it will continue to remain at rest unless acted upon by an external force.

Next, I would analyze the forces acting on the plumb bob. The only force acting on the plumb bob is the force of gravity, which is directed downwards towards the center of the Earth. Since the frame is frictionless, there is no force opposing the motion of the plumb bob.

Based on this information, I would conclude that the angle the plumb bob makes with the vertical during the slide is 0 degrees. This is because the plumb bob will remain in its initial position and will not rotate or change its angle with the vertical as the frame slides down the inclined plane.

To confirm this, I would also use Newton's Second Law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, since the plumb bob is not accelerating, the net force must be equal to 0. Therefore, the angle between the plumb bob and the vertical must be 0 degrees.

Overall, I would approach this problem by understanding the concept of inertia and analyzing the forces acting on the plumb bob. By using Newton's Laws, I would conclude that the angle the plumb bob makes with the vertical during the slide is 0 degrees.