Question

Two particles collide and stick together. If no external forces act on the two particles, which of the following is correct for the change in total momentum Δp and the change in total kinetic energy ΔK of the two particles?
a. p<0, K<0.
b. p<0, K=0.
c. p=0, K<0.
d. p=0, K=0.
e. p=0, K>0.

Answer 1

Answer:

c.$\Delta p$=0 and $\Delta k<0$

Explanation:

We are given that two particles collide  and stick together.

If there is no external force act on the two particles then ,it is inelastic collision.

Inelastic collision: There is some loss of kinetic energy but the momentum is conserved.

According to law of conservation of momentum

Initial momentum=Final momentum

Change in momentum=Final momentum-Initial momentum=0

Change in momentum=$\Delta p=0$

Initial kinetic energy is greater than final kinetic energy.

Change in kinetic energy=Final kinetic energy-kinetic energy=- negative

$\Delta k<0$

Hence, option c is true.

c.$\Delta p$=0 and $\Delta k<0$

Answer 2

The event resembles an inelastic collision, for which the change in momentum is zero and change in kinetic energy is negative. Hence, option (c) is correct.

The given problem can be solved by using the law of conservation of momentum, which says that, in a frame of reference, the total momentum before the collision is equal to the total momentum after the collision in the absence of any external force.

• It is given that two particles collide  and stick together.  If there is no external force act on the two particles then , it is inelastic collision.

• Inelastic collision is the collision, where there is some loss of kinetic energy but the momentum is conserved.

According to law of conservation of momentum

Momentum before collision = Momentum after collision

And,

Change in momentum = momentum after collision - momentum before collision

momentum after collision - momentum before collision = 0

$\Delta p =0$

 Also, the Initial kinetic energy is greater than final kinetic energy. Because the velocity before collision was greater in magnitude.

So,

Change in kinetic energy = Final kinetic energy - kinetic energy

Change in kinetic energy = negative

$\Delta KE <0$

Thus, we can conclude that the event resembles an inelastic collision, for which the change in momentum is zero and change in kinetic energy is negative. Hence, option (c) is correct.

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