Figure shows blocks connected by a light string placed on the two inclinded parts of a triangular wedge. The coefficients of static and kinetic friction are 0.28 and 0.25 respectively at each of the surfaces. Find the minimum and maximum values of m for which the system remains at rest. Find the acceleration of either block if m is given the minimum values calculated in the first part and is gently pushed up the inclined for a short while g = 10 m/s2 .
Answers
Coefficient of friction: A coefficient of friction is a mathematical value thatdemonstrate the relationship between the force of friction between two objects and the effective normal reaction in between the objects that are involved in committing friction.
It is a scalar quantity, meaning the direction of the force is independent of the physical quantity.
Solution: Consider right hand side block has a weight 2 kg and the system shown in the figure below:
The forces on this block are shown in figure with M= 2kg.
It is assumed that m has its minimum value so that 2kg block has a tendency to slip down.
As the block is in equilibrium resultant force will be zero
.Applying Lemi’s theorem: Mg/sine900 =T+f/sin (900+450)=N/sine (900 +450) or N=Mg/ √2 and,
N=2X10/√2 = 10√2=10X3.14=32.4: T = Mg/√2-f=Mg/√2 –μkN =Mg/√ 2-μxMg/√ 2