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 10.0 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 100.0 kg. Including the drivers, the total vehicle masses are
900 kg for the car and 4100 kg for the truck. The collision time is
0.080 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.

Answer #1

**let m1 = 4100 kg, v1 = 10 m/s**

**m2 = 900 kg, v2 = -10 m/s**

**a) Px_Before = m1*v1 + m2*v2**

**= 4100*10 + 900*(-10)**

**= 32000 kg.m/s**

**b) vcm_before = (m1*v1 + m2*v2)/(m1+m2)**

**= (4100*10 + 900*(-10))/(4100 + 900)**

**= 6.40 m/s**

**c) Px_after = Px_Before**

**= 32000 kg.m/s**

**d) vx_f = 6.40 m/s**

**e) impulse on the truck = change in momentum of the
truck**

**= m1*(vf - v1)**

**= 4100*(6.4 - 10)**

**= -14760 N.s**

**f) impulse on the car = m2*(vf - v2)**

**= 900*(6.4 - (-10))**

**= 14760 N.s**

**g) on truck, Favg = impulse on truck/time**

**= -14760/0.08**

**= -184500 N**

**h) on car, Favg = impulse on car/time**

**= 14760/0.08**

**= 184500 N**

**i) impulse on the truck driver = change in momentum of
the truck driver**

**= m*(vf - v1)**

**= 100*(6.4 - 10)**

**= -360 N.s**

**j) impulse on the car driver = m*(vf - v2)**

**= 100*(6.4 - (-10))**

**= 1640 N.s**

**k) on truck driver, Favg = impulse/time**

**= -360/0.08**

**= -4500 N**

**l) on car driver, Favg = impulse/time**

**= 1640/0.08**

**= 20500 N**

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...

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...

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...

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