Question

A Volkswagen bug is moving to the right with a speed of 20 m/s. A large SUV is moving to the left at a speed of 20 m/s. The SUV has a mass three times that of the small car. They have an totally inelastic head-on collision in an intersection. There are two passengers in each vehicle, one seat-belted and the other not seat-belted. All the passengers weigh the same. The non-seat-belted passengers both collide with the dashboard of their respective cars. Use the following codes to refer to each of the passengers: SB = SUV, belted SN = SUV, non-belted VB = Volkswagen, belted VN = Volkswagen, non-belted
1. Rank the magnitude of the impulse experienced by the four passengers in this collision from smallest to largest. If two impulses are equal, then show an equals sign between them.

a. SB = SN < VB = VN
b. VB = VN < SB = SN
c. SB < SN < VB < VN
d. SB < VB < SN < VN

2. Rank the magnitude of the forces experienced by the four passengers in this collision, from smallest to largest. If two forces are equal, then show an equals sign between them.

a. SB = SN < VB = VN
b. VB = VN < SB = SN
c. SB < SN < VB < VN
d. SB < VB < SN < VN

Answer 1

Answer:

For part 1) correct answer is : a) SB=SN<VB=VN

For part 2) correct answer is :  a) SB=SN<VB=VN

Explanation:

We will use the following formula of momentum

momentum after collision =momentum before collision

$(m+3m)*v$=m*u1-(3*m*u2)

As we know u1 = u2 = 20 m/s

Hence,

-2*m*20 = 4*m*v

v = -10 m/s

v being the  common velocity of the SUV and car after the collision

As we know that impulse is J = change in momentum = m*(v-u)

And u being initial velocity which is same for the SUV and car

non belted passengers collide with dashboards with a force which is called as a internal force  and due to that internal forces the momentum remains constant heance impulse is also same experienced by seatbelted and non seat belated

As mass of SUV is 3 times the mass or car.

Hence the correct option is a) SB=SN<VB=VN

2) There is the same order of rant for force and impulse

As we know that impulse j = F*dt

Hence correct answer. is a) SB=SN<VB=VN