What is the Range of Mass m2 to Keep the System Stationary on a Bended Plane?

[Ivanperez]

In the showen figure the mass of block m1 is 2kg and the static and kinesthetic friction coefficients of this block with the bended plane are 0.3 and 0.2
If the system is in rest state,find the range of the values that m2 can take for the system not to move
http://img513.imageshack.us/img513/3113/fisfl9.png
I really don't know how to get in an inequality

 

[PhanthomJay]

If the system is not moving, that should give you a hint as to which friction coefficient to use. Note that if m2 is not heavy enough, then m1 will slide down the plane; if m2 is too heavy, m1 will slide up the plane. You've got to look at those 2 extremes to get a range. Draw good free body diagrams, and note carefully the direction of all the forces acting on each mass.

 

[Moetasim]

the range of values for m2, so I will give an explanation of the concept and equations involved instead.

The given figure shows a system consisting of two blocks, m1 and m2, connected by a string and placed on a bended plane. The mass of m1 is 2kg and the coefficients of static and kinetic friction between m1 and the plane are 0.3 and 0.2 respectively. The question asks for the range of values that m2 can take for the system to remain in a static state, i.e. not moving.

To understand this concept, we need to first understand the forces acting on the system. Gravity acts on both blocks, pulling them towards the ground. In addition, there is a tension force in the string connecting the two blocks, pulling them towards each other. On the bended plane, there are two types of friction forces acting on m1 - static friction and kinetic friction.

In order for the system to remain in a static state, the sum of all the forces acting on the system must be equal to zero. This can be represented by the following equation:

ΣF = 0

Where ΣF represents the sum of all the forces and 0 represents the equilibrium state. Now, let's look at the forces acting on the system in more detail.

Gravity acts on both blocks, pulling them downwards. This force can be represented by the equation:

Fg = mg

Where Fg represents the force due to gravity, m represents the mass of the block and g represents the acceleration due to gravity (9.8 m/s^2).

The tension force in the string can be calculated using the following equation:

T = µmg

Where T represents the tension force, µ represents the coefficient of friction and mg represents the force due to gravity.

Finally, the friction force acting on m1 can be calculated using the following equation:

Fs = µN

Where Fs represents the static friction force, µ represents the coefficient of static friction and N represents the normal force acting on the block.

Now, let's put all these equations together to find the range of values for m2. Since we know that the sum of all the forces acting on the system must be equal to zero, we can write the following equation:

ΣF = Fg + T + Fs = 0

Substituting the equations for Fg, T and Fs, we get:

mg + µmg + µN =