Answer:
T= 224.01 N
Explanation:
in imminent motion we have to :
- The frictional force reaches its maximum value
- The system is in balance of forces
Data
W= 500 N : weight of the log
μs = 0.5
μk = 0.35
α = 30°above the ground : angle of the cable attached to the log
Newton's first law to the log:
∑F =0 Formula (1)
∑F : algebraic sum of the forces in Newton (N)
Forces acting on the log
T: cable tension for impending movement
N: normal force
W : weight
f: frictional force , f= μsN
We apply the formula (1)
∑Fx=0
Tx-f = 0
Tcosα-μsN=0
Tcos30°-0.5N=0 Equation (1)
∑Fy=0
N+Ty-W=0
N+Tsin30°-500=0
N= 500-Tsin30° Equation (2)
We replace the value of N of the Equation (2) in the equation (1)
Tcos30°-0.5(500-Tsin30°) = 0
Tcos30°+0.5Tsin30° = 0.5*500
T( cos30°+0.5*sin30°) = 250
(1.116) T = 250
T= 250/1.116
T= 224.01 N
