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

In summary, the problem involves a system with a frictionless floor between objects B and C, and a static coefficient of friction of 0.2 between objects B and D. The mass of object A is 5kg, the mass of object B is 10kg, and the mass of object D is 2kg. The goal is to determine the value of the mass of object C that will keep object D in a static position. The maximum acceleration must be found first, and then the two cases of M_c being greater or less than M_total must be solved for. The answer in the book is 1.333 < M_c < 10.5, which was confirmed by the other participants in the conversation.
  • #1
sedaw
62
0
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 !:smile:
 
Last edited by a moderator:
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  • #2
?
 
  • #3
somebody ?

PLZ ...
 
  • #4
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.)
 
  • #5
Doc Al said:
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 .
 
Last edited:
  • #6
sedaw said:
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.
 
  • #7
yes... that is right !
i think this is what i did .
 
  • #8
sedaw said:
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.
 
  • #9
Now it makes sense! :wink: :cool:

(I also confirmed the book's answers.)
 
  • #10
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.)
 
  • #11
look at my effort this is exactly what i did , i know that i need to find the max acceleration .

where is my mistake ?
 
  • #12
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!
 

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

1. What are Newton's Laws?

Newton's Laws are a set of three physical laws that describe the relationship between an object's motion and the forces acting upon it. They were developed by Sir Isaac Newton in the 17th century and are considered fundamental principles in the study of mechanics.

2. How do Newton's Laws help to find the center of mass for a static object?

Newton's Laws provide a framework for understanding the forces acting on an object, which are necessary for calculating its center of mass. By analyzing the forces and their corresponding moments acting on the object, one can determine the position of its center of mass.

3. What is meant by "static position" in the context of Newton's Laws?

In the context of Newton's Laws, static position refers to a state of equilibrium where an object's velocity and acceleration are both zero. This means that all forces acting on the object are balanced, resulting in a stable and stationary position.

4. What is the significance of finding the center of mass for a static object using Newton's Laws?

Finding the center of mass for a static object using Newton's Laws allows for a better understanding of the object's overall behavior and stability. It is also essential for solving problems involving the distribution of mass in an object and determining its rotational motion.

5. Can Newton's Laws be used to find the center of mass for a moving object?

Yes, Newton's Laws can also be applied to moving objects to determine their center of mass. However, the calculations become more complex as the object's velocity and acceleration must be taken into account along with the forces acting on it.

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