Compute the total force which shall be acting on the springs:

An automobile of mass 1300 kg, travelling at a speed of 60 kmph hits a depression in the road that has a radius of curvature of 15 m. Compute the total force which shall be acting on the springs.

Solution

The speed of the car is 60 kmph, i.e.

(60 × 1000)/3600

 = 16.67 m / sec

The car is travelling along with a curve of radius 15 m. Hence, acceleration

a_n   = v² / r  .

∴ a_n = (16.67)²/ 15

 = 18.52 m / sec

 The inertia force F_i = - m a_n shall be acting as illustrated.

∴ F_i  = - m . a_n = 1300 × 18.52

= 24076 N

Considering equilibrium of forces as illustrated in Figure (b), we obtain following

∑ Fy  = 0  ∴ N = F_i  + mg

= 24076 + 12753 = 36829 N ;

 where mg = 1300 × 9.81