A uniform log with a mass of 90 kg, a length of 4 m, and a radius of 12 cm is he
ID: 2251396 • Letter: A
Question
A uniform log with a mass of 90 kg, a length of 4 m, and a radius of 12 cm is held in an inclined position, as shown below. The coefficient of static friction between the log and the horizontal surface is 0.53. The log is on the verge of slipping to the right. Find the tension in the support wire and the angle the wire makes with the vertical wall.
A uniform log with a mass of 90 kg, a length of 4 m, and a radius of 12 cm is held in an inclined position, as shown below. The coefficient of static friction between the log and the horizontal surface is 0.53. The log is on the verge of slipping to the right. Find the tension in the support wire and the angle the wire makes with the vertical wall.Explanation / Answer
let tension T,frictional force f,normal N,mass m,theta=$
Balancing horizontal force:
f=Tsin$; 0.53N=Tsin$ -(1)
Balancing vertical force:
N + Tcos$ = mg ; N + Tcos$ = 882 N -(2)
Balancing moment(torque) about point where f & N are acting:
mg*2cos20 + Tsin$*(4sin20 +0.12cos20) = Tcos$*(4cos20-0.12sin20) -(3)
solving 3 equations:
Put Tsin$ & Tcos$ from (1) & (2) in (3)
N=0.517 kN
T=0.661 kN
tan$=0.4557; $=24.5
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