Questions on Forces & Friction: Analyzing Plate & Block Motion

[Pipsqueakalchemist]

Homework Statement

Questions below

Relevant Equations

Newton’s 2nd law

So I have questions on two separate questions. The first question is about the fbd of the plate attached to the pin. How can there be an Ax since there’s no other force in the horizontal direction wouldn’t the plate start moving on the x-direction due to imbalanced forces.

Second question about the elevator question. I knew how to do the problem but I do have some confusion. I have my work below and for the 0.4Nb=100*1.5*alpha part, I’m confused bc since friction is the only force horizontal force acting on the block wouldn’t the block move and slip?

 

[Lnewqban]

Without the pin restricting movement along the x-axis, the center of mass of the block will move vertically down.
The pin provides the centripetal acceleration that deviates the mass from the more natural straight vertical trajectory.

 

[Pipsqueakalchemist]

But when you write Equation of motion in the x direction. Ax is the only force so wouldn’t that imply it’s accelerating in the x direction. I originally thought the FBD would just be W and Ay

 

[PeroK]

But when you write Equation of motion in the x direction. Ax is the only force so wouldn’t that imply it’s accelerating in the x direction. I originally thought the FBD would just be W and Ay

The diagram shows the CoM of the plate moving in a circle in the x-y plane and not initially in the y-direction. There must, therefore, be a force on the plate (from the hinge) in the x-direction.

 

[PeroK]

Second question about the elevator question. I knew how to do the problem but I do have some confusion. I have my work below and for the 0.4Nb=100*1.5*alpha part, I’m confused bc since friction is the only force horizontal force acting on the block wouldn’t the block move and slip?

I'm not sure where the confusion lies. If a block is resting on a surface and the surfaces accelerates in the horizontal direction, then the friction may accelerate the block with the surface; or, if the friction is insufficient, the block will slide backwards relative to the surface.

 

[Pipsqueakalchemist]

The diagram shows the CoM of the plate moving in a circle in the x-y plane and not initially in the y-direction. There must, therefore, be a force on the plate (from the hinge) in the x-direction.

Oh so the Ax acts as the centripetal force right?

 

[PeroK]

Oh so the Ax acts as the centripetal force right?

The centripetal force has an x-component, yes.

 

[Pipsqueakalchemist]

The centripetal force has an x-component, yes.

So the pin A is the centripetal force causing the plate to rotate around A

 

[Pipsqueakalchemist]

Without the pin restricting movement along the x-axis, the center of mass of the block will move vertically down.
The pin provides the centripetal acceleration that deviates the mass from the more natural straight vertical trajectory.

Wait how do you it would move down. Why couldn’t it move up or stay in static equilibrium?

 

[PeroK]

So the pin A is the centripetal force causing the plate to rotate around A

The centripetal force is a component of the net force: the vector addition of gravity and the reaction force at the pin.

 

[Lnewqban]

Wait how do you it would move down. Why couldn’t it move up or stay in static equilibrium?

Because the direction of the represented force (24 Kg x 9.8 m/s^2).