Question

Consider the diagram of the box and bucket. If the coefficient of static friction is 0.5 and the coefficient of kinetic friction is 0.3, find the maximum mass of the bucket in order for the system to be in static equilibrium. If the block was given a slight nudge to get it moving, find the acceleration of the block and bucket.


(NOTE: The block has a mass of 28.0 kg. Also, the block and bucket are connected by a pulley. Block on the table, bucket hanging on the pulley off the end of the table.)

Answer 1

first the static problem
28*9.8 = 274.4 N weight

274.4 * .5 = Tension in cord = 137.2 N

weight of bucket is then 137.2 N
mass of bucket = 137.2/9.8 = 14 kg

now how fast does it accelerate with mu = .3 and bucket weight of 137.2 ?

force of friction = 274.4*.3 = 82.3 N
T - 82.3 = 28 a

bucket weight down = 137.2 N
137.2 - T = 14 a

two linear equations, two unknowns
T -82.3 = 28 a
-T +137.2 = 14 a
-----------------------
54.9 = 42 a
a = 54.9/42