Question

Consider the head-on collision between a water molecule, mass 18u and a nitrogen molecule mass 28u. Prior to the collision, the nitrogen moving to the right at +0.4390 km/s and the water molecule is moving to the left at -0.7570 km/s. Immediately after the collision, the velocity of the water molecule is v = 0.6990 km/s. A positive sign indicates a molecule moving to the right and a negative sign indicates a molecule moving to the left. The atomic mass unit (u) is commonly used to indicate the mass of atoms and molecules: 1u=1.66×10^-27kg.

What is the velocity of the nitrogen molecule immediately after the collision? (in m/s)

A: -0.3976

B: -0.4970

C: -0.6212

D: -0.7766

E: -0.9707

F: -1.2134

G: -1.5167

H: -1.8959

Tries 0/20

If the collsion described above is an elastic collision, which of the following MUST conserved?
I. Momentum
II. Kinetic Energy

A

B

C

D

A	I only
B	Neither I nor II
C	Both I and II
D	II only

Answer 1

In any kind of collision, if we consider both the particles as a system, then the forces acting between them becomes the internal forces.

And we can observe that there are no external forces on the system,

Hence, we know that momentum of the system is conserved. That is, initial momentum of the system is equal to the final momentum of the system.

Therefore,

(P​​​​​​w)i + (P​​​​​​n)i = (P​​​​w)f + (P​​​​​​n)f

momentum is the product of mass and velocity vector of the particle. So using the given data, and assuming v as the velocity of nitrogen molecule just after collision.

(P​​​​​​w)i = 18*(-0.7570)

(P​​​​​​n)i = 28*(0.4390)

(P​​​​w)f = 18*(0.6990)

(P​​​​​​n)f = 28*v

Now substituting values in the above equation,

18*(-0.7570) + 28*(0.4390) = 18*(0.6990) + 28*v

Solving the equation, we get,

v = (-0.4970) km/s. (Velocity of nitrogen molecule after collision)

Part B) Answer is C) option, if the collision is elastic, that means initial kinetic energy of the system is equal to the final kinetic energy of the system. And momentum is always conserved,

Hence we can say, both kinetic energy & momentum of the system is conserved between the initial and final situation.

P.s. kinetic energy is not conserved through out the collision, it is only conserved between just before & just after collision in case of elastic collision.

The actual fact is when we observe the part of during collision, although very less time, the system gets deformed and the kinetic energy gets converted to deformation potential energy, which again gets restored as kinetic energy only if collision is elastic, otherwise some of complete part of that energy remains as deformation potential energy of the system.