Question

Consider a bucket of mass equal to 13 kg suspended as shown in the figure below. Determine the pull on the ED, EB, BA and BC ropes so that the system is in balance. The maximum tension that the rope can hold is 230 N

Answer 1

Solution :

Given :-

A bucket of mass 13kg is suspended as shown in figure.

The maximum tension that the rope can hold is 230N

To Find :-

Determine the pull(tension) on the ED, EB, BA and BC ropes so that the system is in balance.

Concept :-

This question is completely based on concept of Force equilibrium in 2D.

Calculation :-

• Force eq. at E point :

✳ In x-direction

▪ T1cos30° = T2cos53°

▪ T1(√3/2) = T2(3/5)

▪ T1 = 2√3T2/5

✴ In y-direction

▪ T1sin30°+T2sin53°=13g

▪ T1(1/2)+T2(4/5)=13g

▪ √3T2/5+4T2/5=13g

▪ T2(√3+4)=65g

▪ T2 = 65g/5.73

▪ T2 = 113.43N

▪ T1 = 2√3(113.43)/5

▪ T1 = 78.49N

• Force eq. at B point

✴ In y-direction

▪ T2sin53° = T3sin30°

▪ 113.43(4/5) = T3(1/2)

▪ T3 = 181.48N

✴ In x-direction

▪ T4=T3cos30°+T2cos53°

▪ T4 = 181.48(√3/2)+113.43(3/5)

▪ T4 = 156.98 + 68.058

▪ T4 = 225.03N