Solving Friction Problems: Calculate Coefficient & Height

[JoanF]

Homework Statement

mass of the body: 1,0 kg
A is the minimum height that the body must be abandoned to describe a circular path.

there is friction ONLY between A and C

the circular path has radius 1,0 m

1. Calculate the coefficient of kinetic friction between A and C.

2. Calculate the height from the ground that the body will leave the circular path, if left in B. (use as coefficient of friction the value of question 1.)





I had already tried but I can't do it =S please help me

 

[Doc Al]

The problem description is incomplete--there is key information missing. Please provide the full statement of the problem, word for word as it was given.

Also, show what you've tried.

 

[JoanF]

The problem description is incomplete--there is key information missing. Please provide the full statement of the problem, word for word as it was given.

Also, show what you've tried.

1) A is the minimum height that a body of 1,0 kg must be abandoned to describe the circular path of the figure. We know that there is friction ONLY between A and C and that the circular path has radius 1,0 m.

1.1) The normal reaction in C is...
A) 50 N
B) 40 N
C) 10 N
D) 60 N

(I had already done 1.1) and it is correct, it's D).)

1.2) The coefficient of kinetic friction between A and C is...
A) 0,33
B) 0,50
C) 0,22
D) 0,15

1.3) Calculate the height from the ground that the body will leave the circular path, if left in B. (use as coefficient of friction the value of question 1.)

I tried and my answer was 0,22 to 1.2) but how do I do 1.3)?

 

[Doc Al]

I tried and my answer was 0,22 to 1.2)

Good.

but how do I do 1.3)?

What would be the criterion for the body leaving the circular path? Express it mathematically. Then realize that the energy the body will have on entering the circular portion will be different than before.

 

[JoanF]

Good.

What would be the criterion for the body leaving the circular path? Express it mathematically. Then realize that the energy the body will have on entering the circular portion will be different than before.

I've done this:

 

[JoanF]

I've done this:

Is it correct??

 

[Doc Al]

Is it correct??

Unfortunately, I'm finding your work a little difficult to follow. My answer differs from yours, so one of us is making an error.

What I did:
Found the total energy of the mass when let go from A.
Found the new total energy of the mass when let go from B.
Found the condition for losing contact with the surface.
Combined the last two to solve for the height at which the mass leaves the surface.

If you summarize the results you get for each of those steps, perhaps I can see where we differ.

 

[JoanF]

using g=10, I got: h=1,64 m

using g=9,8, I got: h=1,4456 m

I've done just like you

 

[Doc Al]

using g=10, I got: h=1,64 m

using g=9,8, I got: h=1,4456 m

OK, my answer agrees with your second result.

If you were to solve the problem symbolically, only plugging in numbers at the last step to get a numerical answer, you'd see that the answer does not depend on g or m. (They cancel out.) Whenever possible, that's the best way to go, since it reduces the chance for arithmetic error.