Block A has a mass of 27 kg and block B has a mass of 44 kg. The two blocks are
ID: 1873019 • Letter: B
Question
Block A has a mass of 27 kg and block B has a mass of 44 kg. The two blocks are stacked on the ramp with an incline of =27.3. Determine the largest horizontal force F that can be applied to block B without either block moving for each of the following two cases:
a.) The friction coefficient for the contact between blocks A and B is s1 = 0.6 and the friction coefficient for the contact between block A and the ramp is s2 = 0.24.
b.) The friction coefficient for the contact between blocks A and B is s1 = 0.6 and the friction coefficient for the contact between block A and the ramp is s2 = 0.60.
The maximum force before either block A or B slips is N
Part b)
The limiting slip condition occurs at Select an answer the contact between A and B or the contact between A and the ramp
The maximum force before either block A or B slips is N
Explanation / Answer
given
ma = 27 kg
mb = 44 kg
theta = 27.3 deg
let the largest horizontal force on B be F
a. friction coefficient between A and B is k1 = 0.6
friciton coefficeint between A and ramp is k2 = 0.24
hence from force balance
let friction between two blocks be f
Fcos(theta) - ma*g*sin(theta) - f = 0
also,
let friction between A and floor be f'
then
from force balance
f = ma*g*sin(theta) + f'
f' = k2*((ma + mb)*g*cos(theta) + Fsin(theta))
hence
Fcos(theta) = ma*g*sin(theta) + ma*g*sin(theta) + k2((ma + mb)*g*cos(theta) + Fsin(theta))
Fcos(27.3) = 196.02859158 + 0.24(618.93078 + Fsin(27.3))
F = 442.5873799N
the limiting slip condition between contact of A and ramp
b. when k1 = 0.6, k2 = 0.6
then
f = k1*ma*g*cos(theta)
F = 295.6316012 N
the limiting slip condition between contat of blockjs A and B