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 8.40 m/s and that they undergo a perfectly inelastic head-on collision. Each driver has mass 79.0 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 0.140 s, what force does the seat belt exert on each driver? (Enter the magnitude of the force.)

force on truck driver N ?

force on car driver N?

Answer 1

By applying momentum conservation,

Pi = Pf

m1*v1i + m2*v2i = (m1+m2)*v

here, v = combined velocity = ??

m1 = total mass of car = 800 kg (Let initial direction of motion of car is positive)

m2 = total mass of truck = 4000 kg

initial speed of car(v1i) = 8.40 m/sec.

initial speed of truck(v2i) = -8.40 m/sec.

So, 800*8.40 + 4000*(-8.40) = (800+4000)*v

v = (800*8.40 - 4000*8.40)/4800

v = -5.6 m/s

here, negative sign represents that after collision both mass moves in initial direction of truck.

now, by impulse momentum theorem,

I = F*dt = dP

So,

average force on truck driver = F2 = dP/dt = m*(v- v2i)/dt

here,m = mass of driver = 79.0 kg

v = final velocity = -5.6 m/s

dt = time interval = 0.140 s

So, F2 = 79*(-5.6 - (-8.40))/0.140

F2 = 1580 N

Magnitude = |F2| = 1580 N

average force on car driver = F1 = dP/dt = m*(v- v1i)/dt

here, v = final velocity = -5.60 m/s

m = mass of car driver = 79.0 kg

dt = time interval = 0.140 s

So, F1 = 79.0*(-5.60 - 8.40)/0.140

F1 = -7900 N

Magnitude = |F1| = 7900 N

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