Most of us know intuitively that in a head-on collision between a large dump tru

Question

Most of us know intuitively that in a head-on collision between a large dump truck and a subcompact car, you are better off being in the truck than in the car. Why is this? Many people imagine that the collision force exerted on the car is much greater than that exerted on the truck. To substantiate this view, they point out that the car is crushed, whereas the truck is only dented. This idea of unequal forces, of course, is false; Newton's third law tells us that both objects are acted upon by forces of the same magnitude. The truck suffers less damage because it is made of stronger metal. But what about the two drivers? Do they experience the same forces? To answer this question, suppose that each vehicle is initially moving at 7.80 m/s and that they undergo a perfectly inelastic head-on collision. Each driver has mass 76.0 kg. Including the masses of the drivers, the total masses of the vehicles are 800 kg for the car and 4,000 kg for the truck. If the collision time is 0.110 s, what force does the seat belt exert on each driver?

force on truck driver    ____ N

force on car driver      _____N

Explanation / Answer

mass of the car m1 = 800 kg

mass of the truck m2 = 2000 kg

the collision time is t = 0.110 s

let V be the common velocity of the two vehicles after the collision

we know that

m1u1 + m2u2 = (m1 + m2) x V

or V = [m1u1 + m2u2/(m1 + m2)]

where u1 = +7.80 m/s and u2 = -7.80 m/s

force on truck driver

F2 = m2 x a

where a = (V/t)

force on car driver

F1 = m1 x a

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