Draw any figures or force diagrams that may be applicable to theproblem. Designe

Question

Draw any figures or force diagrams that may be applicable to theproblem.

Designers of today’s cars have built “5 mi/hr (8 km/hr)bumpers” that are designed to elastically compress andrebound without any physical damage at speeds below 8 km/hr. If the material of the bumpers permanently deforms after acompression of 1.5 cm, but remains like an elastic spring up tothat point, what must the effective spring constant of the bumpermaterial be, assuming the car has a mass of 1400 kg and it istested by ramming into a solid wall.

Explanation / Answer

   Distance travelled before carstops   s   =   1.5   cm   =   0.015   m    initial speed ofcar   u   =   8km/hr   =   8 * 5 /18   =   2.22   m/s    final speed ofcar   v   =   0    v2   =   u2   +   2* a * s    02   =   2.222   +   2* a * 0.015    acceleration   a   =   -164.28   m/s2    - ve sign is due to retarded motion, it canbe dropped.    Force   F   =   m* a   =   1400 *164.28   =   2.30 *105   N    Springconstant   k   =   F/ s   =   2.30 * 105/ 0.015   =   1.53 *107   N/m    - ve sign is due to retarded motion, it canbe dropped.    Force   F   =   m* a   =   1400 *164.28   =   2.30 *105   N    Springconstant   k   =   F/ s   =   2.30 * 105/ 0.015   =   1.53 *107   N/m

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