Determine the springs needed to absorb the energy:

A vehicle weighing 28 kN and running at 2.5 m/sec is to be brought to rest by a buffer springs. Determine the number of springs needed to absorb the kinetic energy if n = 20

Compression of each spring = 200 mm

Diameter of wire = 30 mm

Radius of coil = 100 mm

G = 80 GPa

Solution

KE = 1 mV ² = 1 (28 × 10³ /9.81) × 2.5²  = 8919.5 N-m

Δ= 64 W R³ n / Gd ⁴

⇒         200 =64 × W × 100³ × 20 / (80 × 10³ ) × (30)⁴

∴          W = 10125 N

For one spring, U = 1 W Δ = 1 × 10125 × (200/1000) = 1012.5 N-m

∴ Numbers of springs, N = KE /U= 8919.5 /1012.5= 8.8 ; 9.0