Solve Newton's Laws to Find Mc for Static Position of MD

[sedaw]

http://img237.imageshack.us/img237/5499/22gj5.jpg

the floor frictionless
between D and C : MUs = 0.2
mA=5kg
mB=10kg
mD=2kg

what is the value for Mc keepin MD in static position ?


my effort :
http://img389.imageshack.us/img389/9196/hwscan00010zf3.png

the answer in the book 1.333<m<10.5 not as my .

what is wrong ?


TNX !

 

[sedaw]

?

 

[sedaw]

somebody ?

PLZ ...

 

[Doc Al]

I don't understand the problem. What's frictionless? The friction coefficient is given for what surfaces? What is being held static? (If the entire system is static, the acceleration would be zero.)

 

[sedaw]

I don't understand the problem. What's frictionless? The friction coefficient is given for what surfaces? What is being held static? (If the entire system is static, the acceleration would be zero.)

NO ! the entire system is not static .
the surface that object B placed on is frictionless .
The friction coefficient between the objects B and D is 0.2 .
need to determine the value of the mass of object C that hold object D static .

 

[LowlyPion]

the floor frictionless
between D and C : MUs = 0.2
mA=5kg
mB=10kg
mD=2kg

what is the value for Mc keepin MD in static position ?

the answer in the book 1.333<m<10.5 not as my .

I believe I understand the problem. The surface between B and the floor it's on is frictionless. The surface between D and B however has a static coefficient of .2.

What they are asking, if I am reading your effort correctly, is to identify the domain of values for the mass of C, such that whatever motion ensues, D does not get displaced on the top of B.

That said I would suggest a simpler approach. First identify what acceleration D will tolerate without being displaced relative to B.

Then using that value construct the two cases: one where C is greater than A, that will cause the system to accelerate TOWARD C, the tipping point as it were of the BD contact. And the other case where the system will be set in motion accelerating TOWARD A without disturbing D.

Solving these 2 cases then will set the limit of the domain for the mass of C.

 

[sedaw]

yes... that is right !
i think this is what i did .

 

[LowlyPion]

yes... that is right !
i think this is what i did .

Without checking your algebra for what you did do, I got the answers you gave from the book.

 

[Doc Al]

Now it makes sense!

(I also confirmed the book's answers.)

 

[Doc Al]

The first step is to find the maximum acceleration, as LowlyPion suggests. What did you get for that? (No need for complicated calculations for that, since friction is the only relevant force on the top block.)

 

[sedaw]

look at my effort this is exactly what i did , i know that i need to find the max acceleration .

where is my mistake ?

 

[Doc Al]

Your work looks OK to me, but you didn't finish. You have M_c in terms of M_total, but M_total contains M_c. Solve for both values of M_c!