Geometric Vector Diagrams

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I Love Pi

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Hello! I was able to determine where majority of the diagrams with great confidence, however, three of them left me puzzled. I made my best educated guesses for the three circled in green.
-Please, note that the 1st circled diagram has wheels, therefore it does not have friction forces. It also does not have a rope, therefore there is no tension. Additionally, it is seemingly at rest (v=0).
-Please, note that the second circled diagram is not touching the carpet, therefore, friction forces are not acting upon it. Also, there is a rope, therefore tension is involved.
-Please, note that the third circled diagram has wheels, therefore it does not have friction forces. It also does not have a rope, therefore there is no tension. It seems to not to match any of the force diagrams/equations.

Could you help me determine where the three diagrams, circled in green, belong? Thank you so much!
 

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I Love Pi said:
Hello! I was able to determine where majority of the diagrams with great confidence, however, three of them left me puzzled. I made my best educated guesses for the three circled in green.
-Please, note that the 1st circled diagram has wheels, therefore it does not have friction forces. It also does not have a rope, therefore there is no tension. Additionally, it is seemingly at rest (v=0).
-Please, note that the second circled diagram is not touching the carpet, therefore, friction forces are not acting upon it. Also, there is a rope, therefore tension is involved.
-Please, note that the third circled diagram has wheels, therefore it does not have friction forces. It also does not have a rope, therefore there is no tension. It seems to not to match any of the force diagrams/equations.

Could you help me determine where the three diagrams, circled in green, belong? Thank you so much!
Click to expand...
A couple of things:
1) The force of friction always opposes the direction of motion. So the friction force for the + diagram is downhill, not uphill. You've got a couple of these mistakes.

2) For ! there are two forces on the cart, are there not?

3) For the floating ball, yes, there is no friction force.

4) It appears that there are two diagrams with the carts that have the same FBD. These are ! and (cent).

-Dan
 
My car has wheels on them. In fact, they have 4 wheels on them.
My question to you is if there is no friction between my tires and the level street how does my car move?

I asked the above question based on some of your answers.

There is something called rolling friction. Hopefully @topsquark will help me out by explaining that to you.
 
Steven G said:
My car has wheels on them. In fact, they have 4 wheels on them.
My question to you is if there is no friction between my tires and the level street how does my car move?
Click to expand...
The problem explicitly says that this is an ideal physics class cart, not a real car:

Note that there's carpet (friction!), wheels (no friction!) and that one has the ball floating in the air on purpose.​

This cart doesn't move on its own; it just rolls as gravity or the experimenter moves it.
 
I am sorry that I failed to read the whole problem and based my answer solely on the diagram.
 
topsquark said:
A couple of things:
1) The force of friction always opposes the direction of motion. So the friction force for the + diagram is downhill, not uphill. You've got a couple of these mistakes.

2) For ! there are two forces on the cart, are there not?

3) For the floating ball, yes, there is no friction force.

4) It appears that there are two diagrams with the carts that have the same FBD. These are ! and (cent).

-Dan
Click to expand...
Hello Dan!
Thank you for your in-depth advice and for being patient with me. I made some adjustments to my answers in the document attached below. Please let me know if you spot any other issues. Again, thank you!
 

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  • Geometric Vector Diagrams Revised.pdf
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I Love Pi said:
Hello Dan!
Thank you for your in-depth advice and for being patient with me. I made some adjustments to my answers in the document attached below. Please let me know if you spot any other issues. Again, thank you!
Click to expand...
Looks good except for that last one. What are the forces on the cart? The Normal force and it's weight. There is no force acting up the slope. This is a common mistake...many times a student will think a force has to be pointing in the direction of the velocity, but velocity isn't a force. So there is no force acting up the slope.

Break down the normal force and weight into their components again and take a look at the diagrams.

-Dan
 
Hi Dan,
It appears as though you were referring to the % forces diagram where the cart is slowing down. Correct me if I am incorrect in this assumption. Since velocity is not a force, I made adjustments to my free body diagram and placed the % force diagram with the other frictionless carts. My amendments are attached below, once again.
 

Attachments

  • Geometric Vector Diagrams Revision 2.pdf
    622.6 KB · Views: 1
I Love Pi said:
Hi Dan,
It appears as though you were referring to the % forces diagram where the cart is slowing down. Correct me if I am incorrect in this assumption. Since velocity is not a force, I made adjustments to my free body diagram and placed the % force diagram with the other frictionless carts. My amendments are attached below, once again.
Click to expand...
There you go! Good job.

-Dan
 
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