Question

A cable car used for carrying materials in a hydroelectric project is at rest on a track formed at an angle of 30° with the vertical. The gross weight of the car and its load is 60 kN and its centroid is at a point 800 mm from the track half way between the axles. The car is held by a cable as shown in Fig. The axles of the car are at a distance 1.2 m. Find the tension in the cables and reaction at each of the axles neglecting friction of the track.

Answer 1

Let T be the tension in the cable and the reaction at the pair of wheels be R₁ and R₂ as shown in Fig.

Now, ∑ of forces parallel to the track = 0, gives 

T – 60 sin 60° = 0 

T = 51.9615 kN. 

Taking moment equilibrium condition about upper axle point on track, we get 

R₁ × 1200 + T × 600 – 60 sin 60° × 800 – 60 cos 60° × 600 = 0 

R₁ = 23.6603 kN. 

∑ of forces normal to the plane = 0, gives 

R₁ + R₂ – 60 cos 60° = 0 

R₂ = 30 – 23.6603 

R₂ = 6.3397 kN.