In: Civil Engineering
A lightweight rope is wrapped around a 100-lb
drum, passes over a frictionless pulley, and is
attached to a weight W (see figure). The
coefficient of friction between the drum and
the surfaces is 0.50. Determine the maximum
amount of weight that can be supported by
this arrangement.
Ans) Let,
Weight of drum (W) = 100 lb
Coefficient of friction between drum and surface () = 0.50
Friction force between drum and horizontal surface = F1
Friction force between drum and vertical surface = F2
Reaction force between drum and horizontal surface = R1
Reaction force between drum and vertical surface = R2
Tensile force in rope = T
We can see that their are 5 unknowns so we need 5 equations of equilibrium to solve the problem,
Equating forces in X direction we get, Fx = 0
=> Fa - Nb + T = 0 .................................(1)
Equating forces in Y direction we get, Fy = 0
=> Na + Fb - 100 = 0................................(2)
Also, using Coulomb law,
Fa = Na
=> Fa = 0.50 Na...........................................(3)
Fb = Nb
=> Fb = 0.50 Nb.............................................(4)
Now, taking moment about center of drum with diameter 'd' , M = 0
=> Fb (d/2) + Fa (d/2) - T (d/2) = 0
=> Fb + Fa - T = 0 ........................................(5)
On solving these equations we get,
Fa = 25 lb
Nb = 100 lb
T = 75 lb
Na = 50 lb
Nb = 50 lb
Hence, maximum weight that can be supported = T = 75 lb