(c) Because static friction can adjust, the system can be at rest if the mass of block C is between some maximum value and some minimum value. What are these values if the coefficient of static friction between block B and the table is 0.200?
there has to be a picture with this. It makes no sense to me.
To determine the maximum and minimum values for the mass of block C in order for the system to be at rest, we need to consider the equilibrium conditions and the forces acting on the blocks.
First, let's analyze the forces acting on block C. The only force acting on block C is the gravitational force (mg), where m is the mass of block C and g is the acceleration due to gravity.
Next, let's analyze the forces acting on block B. There are two forces acting on block B: the gravitational force (mg), in the downward direction, and the static friction force (fsb) between block B and the table, in the upward direction.
For block C to be at rest, the static friction force between block B and the table should be equal and opposite to the gravitational force on block B. This can be represented as:
fsb = mg
The maximum static friction force (fMax) can be calculated using the equation:
fMax = coefficient of static friction * normal force
The normal force (N) on block B is equal to the gravitational force acting on block B, which is mg.
Therefore, the maximum static friction force (fMax) can be expressed as:
fMax = coefficient of static friction * mg
In this case, the coefficient of static friction is given as 0.200.
So, fMax = 0.200 * mg
To keep block C at rest, the static friction force (fsb) must be less than or equal to the maximum static friction force (fMax). Therefore, we have:
fsb ≤ fMax
mg ≤ 0.200 * mg
Simplifying this inequality, we can divide both sides by mg (assuming m and g are positive values):
1 ≤ 0.200
Since 1 is greater than 0.200, the inequality is satisfied for any positive value of m. Therefore, there are no maximum or minimum values for the mass of block C in this particular scenario. Block C can have any positive mass, and the system will remain at rest as long as the coefficient of static friction remains constant.
In summary, the values for the mass of block C do not have maximum or minimum limits in this situation.