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 experienced by the truck. To substantiate this view, they point out that the car is crushed, whereas the truck in only dented. This idea of unequal forces, of course, is false. Newton's third law tells us that both objects experience 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 9.0 m/s and that they undergo a perfectly inelastic head-on collision. (In an inelastic collision, the two objects move together as one object after the collision.) Each driver has a mass of 70.0 kg. Including the drivers, the total vehicle masses are 870 kg for the car and 4070 kg for the truck. The collision time is 0.160 s. Choose coordinates such that the truck is initially moving in the positive x direction, and the car is initially moving in the negative x direction.

(a) What is the total x-component of momentum BEFORE the collision?

(b) What is the x-component of the CENTER-OF-MASS velocity BEFORE the collision?

(c) What is the total x-component of momentum AFTER the collision?

(d) What is the x-component of the final velocity of the combined truck-car wreck?

(e) What impulse did the truck receive from the car during the collision? (Sign matters!)

(f) What impulse did the car receive from the truck during the collision? (Sign matters!)

(g) What is the average force on the truck from the car during the collision? (Sign matters!)

(h) What is the average force on the car from the truck during the collision? (Sign matters!)

(i) What impulse did the truck driver experience from his seatbelt? (Sign matters!)

(j) What impulse did the car driver experience from his seatbelt? (Sign matters!) (k) What is the average force on the truck driver from the seatbelt? (Sign matters!)

(l) What is the average force on the car driver from the seatbelt? (Sign matters!)

Final thoughts on this problem: Note that Newton's 3rd Law is valid: the force the truck exerts on the car is equal and opposite to the force the car exerts on the truck. In terms of momentum, the impulse the truck gives the car is equal and opposite to the impulse the car gives the truck. But, this does NOT mean the forces exerted on the individual drivers is equal and opposite! The force the seatbelt exerts on the truck driver is much less than the force the seatbelt exerts on the car driver. But that is okay; these two forces are NOT part of a Newton's 3rd Law force pair.

Explanation / Answer

the force acting on the truck is equal to the force acting on the car . since car is smaller and not as strong as the truck is , the car gets crushed under the large equal force . the force transferred to driver of the car is also greater as the car is not not strong enough to resist the effect of the force due to collision , on the other hand , truck is stronger and resists the force applied by the car and the driver feels less force as truck increases the time for the effect of force to reach the driver.

a)

total momentum before collision = 870 x 9 - 70 x 9 = 7200 kgm/s

b)

V = (870 x 9 - 70 x 9) / (870 + 70) = 7.65 m/s

c)

using conservation of momentum

momentum after collision = momentum before collision = 7200 kgm/s

d)

V = 7200 / (870 + 70) = 7.65 m/s

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