Question

Two cars collide inelastically and stick together after the collision. Before the collision, the magnitudes of their momenta are P1 and P2 . After the collision, what is the magnitude of their combined momentum?a) P1+P2b) P1-P2c) P2-P1d)(P1P2)^(1/2)e) (1/2)(P1+P2)f)(P1+P2)^(1/2)g)The answer depends on the directions in which the cars were moving before the collision.

Answer 1

a. P₁ + P₂

Step-by-step explanation:

Let the mass of first car be m moving with velocity u. Consider another car having m' moving with velocity u'. Their momentum will be:

P₁ = m u

P₂ = m' u'

Total initial momentum = P₁ + P₂

Momentum remains conserved when no external force acts on the system. It does not depend on the type of collision (elastic/inelastic). Thus, momentum after the inelastic collision would be equal to the momentum before the collision i.e. P₁ + P₂

Thus, correct option is a.

Answer 2

The correct answers are A, B, C

Step-by-step explanation:

In the problems of the moment, the most important thing is to define those who form the system so that the forces during the crash have been internal, the moment can be conserved. In this case the system is made up of the two cars. We write the equations just before and after the crash

Before the crash

p₀ = P1 + P2

After the crash

pf = (m1 + m2) v

p₀ = pf

P1 + P2 = (m1 + m2) v = Pf

Let's analyze the possible initial diversions of cars

-Car 1 travels to the right

Car 2 to the right

Pf = P1 + P2

Car2 to the left

Pf = P1-P2

-Car 1 to the left

Car 2 to the right

Pf = -P1 + P2

Car 2 to the left

Pf = -P1 -P2

The correct answers are A, B, C