a) Find the minimum coefficient of static friction between block A and the 30 Fi

Question

a) Find the minimum coefficient of static friction between block A and the 30

Find the minimum coefficient of static friction between block A and the 30 degree incline necessary to keep both blocks at rest if the coefficient of friction between B and the incline is zero and the blocks have equal mass. Use this minimum as the value of the coefficient between A and the incline for parts (b) and (c). What is the magnitude of the contact force between the masses in this case? Find the acceleration of the system if the angle of the incline was increased to 45 degree. What is the magnitude of the contact force between the masses in this case? Find the accelerations of the two masses for an angle of 30 degree if block A is moved and placed back on the incline above block B. What is the force of friction on block A in this case?

Explanation / Answer

a)Net friction force on A=kmgcos(30)

SO for no net movement of the system,

mgsin(30)*2=kmgcos(30)

So

k(min)=1.1547

contact force=mgsin(30)=mg/2

b)2mgsin(45)-kmgcos(45)=2ma

So

a=gsin(45)-kgcos(45)/2=2.93m/s^2

c))When block B is ahead then B will accelerate faster

So

a(block B)=gsin(30)=4.9m/s^2

a(block A)=gsin(30)-kgcos(30)=negative (this means friction is more than weight component.)

So

a(block A)=0

So

force of friction (on block A)=mgsin(30)=4.9m

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