Question

Suppose that each vehicle is initially moving at 7.0 m/s and that they undergo a perfectly inelastic head on collision. Each driver has a mass of 80.0 kg. Including the drivers, the total vehicle masses are 800 kg for the car and 4000 kg for the truck.

(a) if the collision time is 0.150 s, what average forces does the seatbelt exert on the truck driver? N

(b)What average force does the seatbelt exert on the car driver? N

Answer 1

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suppose each vehicle is initially moving at 10.0 m/s and they undergo a perfectly inelastic head-on collision. Each driver has mass 90.0 kg. Including the drivers, the total vehicle masses are 810 kg for the car and 4010 kg for the truck.

If the collision time is 0.140 s, what force does the seatbelt exert on the truck driver?
_______N

What average force does the seatbelt exert on the car driver?
_______N

Mass of the car with driver, m1 = 810 kg

Mass of the truck with driver, m2 = 4010 kg

Initial velocity of the car, v1 = 10 m/s

Initial velocity of the truck, v2 = - 10 m/s

In the perfectly inelastic collision,

Common velocity of the system, v = ( m1 v1 + m2 v2 ) / (m1+m2)

                                                    = (8100 - 40100)/(810+4010)

                                                    = - 6.64 m/s

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Mass of each driver, M = 90 kg

Collision time, t = 0.140 s

(a)

Force exerted by belt on the truck driver:

Ftruck= M (v-v2)/t

        = 90 * (-6.64+10)/0.140

        =2.16 x 10^3 N

(b)

Force exerted by belt on the car driver:

Fcar = M (v-v1)/t

        = 90 * (-6.64-10)/0.140

        =1.07 x 10^4 N