Question

In this problem, we will consider a collision of two moving objects such that after the collision, the objects stick together and travel off as a single unit. The collision is therefore completely inelastic.
You have probably learned that "momentum is conserved" in an inelastic collision. But how does this fact help you to solve collision problems?
The following questions should help you to clarify the meaning and implications of the statement "momentum is conserved."

1) What physical quantities are conserved in this collision?

a) the magnitude of the momentum only
b) the net momentum (considered as a vector) only
c) the momentum of each object considered individually

2) Two cars of equal mass collide inelastically and stick together after the collision. Before the collision, their speeds are V1 and V2. What is the speed of the two-car system after the collision?

a) V1+V2
b) V1-V2
c) V2-V1
d) (V1V2)^(1/2)
e) (1/2)(V1+V2)
f) (V1+V2)^(1/2)
g) The answer depends on the directions in which the cars were moving before the collision.

3) 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+P2
b) P1-P2
c) P2-P1
d) (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.

4) Two cars collide inelastically and stick together after the collision. Before the collision, their momenta are p1 and p2. After the collision, their combined momentum is vector p. Of what can one be certain?

a) Vector P = p1+p2
b) Vector P = p1-p2
c) Vector P = p2-p1

Answer 1

1)

Answer:

b) the net momentum (considered as a vector) only

Explanation:

As we know that momentum is a vector quantity and since there is no external force on this system

So here momentum of the system will remain conserved for complete system

so correct answer will be

b) the net momentum (considered as a vector) only

2)

Answer:

e) (1/2)(V1+V2)

Explanation:

As we know that there is no external force on the system of two cars

So we will have

$mv_1 + mv_2 = (m + m)v$

$v = \frac{mv_1 + mv_2}{m + m}$

$v = \frac{v_1 + v_2}{2}$

3)

Answer:

a) $P_1 + P_2$

Explanation:

As we know that there is no external force on the system of two cars

So we will have

$P_1 + P_2 = P_f$

4)

Answer:

a) $\vec P = P_1 + P_2$

Explanation:

As we know that there is no external force on the system of two cars

So we will have

$P_1 + P_2 = P_f$