Centripetal/Centrifugal Force and Moment of Inertia

In summary, the conversation discusses a problem involving a forklift and a pallet with a box on top, and the calculation of the required velocity for the box and pallet to flip around a turn. The assumptions made include the forklift's capability to carry the load, the box being latched down to the pallet, and the center of gravity being in the middle of the box. The conversation also explores the use of centripetal and centrifugal forces, and the calculation of the angle and force required for the box to reach a certain angle. The conversation ends with a discussion on the critical speed for the start of tipping and the possibility of reducing the forklift speed to prevent the box from tipping.
  • #1
co0ldood
8
0
Hello all. I have a problem and I’m not sure if my analysis is 100% accurate. I hope this is the correct spot since it deals with dynamics (mechanics).

Here’s my scenario:
I have a forklift and a pallet with a box on top. I’m trying to calculate the required velocity for the box+pallet to flip around a turn.. and at what angle. Pictures have been uploaded to visualize the problem better.

http://img.photobucket.com/albums/v114/Co0lDood/prob.jpg

Here are my following assumptions:
- Forklift is 100% capable of carrying this load (forklift will NOT tilt on the turn and I can neglect the forklift all together)
- Box is latched down to pallet creating a rigid body.
- Center of gravity (CoG) is directly in the middle of the box.
- The fork lift is at constant velocity (acceleration = 0), which makes centripetal force only acting in the normal direction into the curve.
- No slipping will occur between the fork and the pallet + box.

Known
- I can calculate the velocity, radius of curvature, and all dimensions of the box/pallet.

Centripetal force is Fc= (v^2)/r (in the normal direction toward the curve)
Centrifugal force is the same in magnitude but is acting on the opposite direction at the CoG.

I calculated the angle of when my rigid system will fall over by having the CoG align vertically to point P (as seen in picture) in a static situation.

How would I go about calculating how much force is required to have my rigid body reach the angle I calculated? (so my pallet + box will flip)

I have thought about calculating the moment at point P and CoG (Sum of moment at a point in the free body diagram and equaling it to the sum of moments, at the same point, in the mass-acceleration diagram or kinetic diagram), but I can’t seem to relate it with everything else.

I'm not sure how to go about calculating angular acceleration either.

Can't seem to put everything together. I don’t think I have left anything out.

Any theories or comments would be greatly appreciated. Thank you for your time!
 
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  • #2
Maybe this should me moved to the "homework style" question? Could the mods move this thread if you think it is suitable over there. Thank you.
 
  • #3
I am not sure what your unknowns are. The block will start to tip once the torque from the centripetal 'pseudo' force (the inertial force, mv^2/r, applied at the cg, which is the friction force at the base which provides the centripetal force necessary for curved motion), about the lower right corner, overcomes the torque from the gravity force about that corner. If you know the box dimensions, M., and r, then solve for v. Once the box starts to tip, and the same speed v is maintained, its ultimate tip over is inevitable. It doen't have to wait for the cg to be over the tipping corner. I don't generally like using pseudo forces, but it has its place here; be sure to label your FBD as 'FBD with Pseudo Forces'. If this is a homework question, it should be moved by the moderators for further help. Is it?
 
  • #4
It is not a homework question, more of a conceptual problem for work. What is given is the weight and the dimension of the box

Lets say the box starts to tip, but prior to ultimate tip over, the forklift would slow down or straighten out which will lower 'pseudo' force. Ideally, will the box come back down if I were to sum the moments “or torque” at the corner with the tip angle? (assuming the weight moment overcame the moment of the centripetal ‘pseudo’ force)


I really appreciate the help!
 
  • #5
Oh, yes. If the box c.g. is say a horizontal distance 'd' from the corner, and a vertical distance 'h' up from the base, the critical speed for the start of tipping can be calculated from (mv^2/r)(h) = mg(d). Now at just beyond this point, the box starts to rotate and accelerate (angularly) under the net torque , but if you reduce the forklift speed well before the cg is over the corner of tipping, it will bounce back, since the net torque will be in the the other direction, but you've got to act fast, because the box must first come to an angular stop before reversing its rotation, and if the cg goes past the corner, it's too late!
 
  • #6
PhanthomJay said:
Oh, yes. If the box c.g. is say a horizontal distance 'd' from the corner, and a vertical distance 'h' up from the base, the critical speed for the start of tipping can be calculated from (mv^2/r)(h) = mg(d). Now at just beyond this point, the box starts to rotate and accelerate (angularly) under the net torque , but if you reduce the forklift speed well before the cg is over the corner of tipping, it will bounce back, since the net torque will be in the the other direction, but you've got to act fast, because the box must first come to an angular stop before reversing its rotation, and if the cg goes past the corner, it's too late!

Thank you PhanthomJay. That was how I was going about the problem.. just double checking! I really appreciate the help.

This forum seems great, maybe I'll stick around and try to spread some of my knowledge to others!
 
  • #7
If the bottom board(s) were on the pallet it would not tip over!
 

What is centripetal force?

Centripetal force is the force that keeps an object moving in a circular path. It is directed towards the center of the circle and is necessary for an object to maintain its circular motion.

What is centrifugal force?

Centrifugal force is often referred to as a "fake" force because it is not an actual force, but rather an apparent force that is experienced by an object in a rotating reference frame. It is the opposite of centripetal force and appears to push an object away from the center of rotation.

What is the difference between centripetal and centrifugal force?

The main difference between centripetal and centrifugal force is the direction in which they act. Centripetal force is directed towards the center of rotation, while centrifugal force appears to act in the opposite direction, away from the center of rotation.

What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass and distribution of the object's mass around its axis of rotation. Objects with a larger moment of inertia require more torque to rotate at a given speed.

How do centripetal force and moment of inertia relate?

Centripetal force and moment of inertia are related in that they both play a role in an object's rotational motion. Centripetal force is necessary for an object to maintain its circular motion, while moment of inertia determines how difficult it is to change an object's rotational motion. A larger moment of inertia requires a larger centripetal force to maintain circular motion.

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