2024 A/L Physics Past Paper · Question 05 (English Medium)

Answer: (5) all (A), (B) and (C) are true.

What the question asks

What we know:

A bullet hits a wooden block and stays inside it.

The block stands on a smooth horizontal surface, so there is no friction.

We want: which of the statements (A), (B) and (C) are true for this collision.

What each letter means:

$m$, $M$ ($\text{kg}$): the mass of the bullet and of the block.

$u$ ($\text{m s}^{-1}$): the velocity of the bullet before the hit.

$v$ ($\text{m s}^{-1}$): the velocity of the bullet and the block together after the hit.

Relevant theory

For a system of interacting objects, the momentum remains constant, provided no external force acts on the system.

The total energy of a closed system remains constant. However, within a system one form of energy can get converted into another form of energy.

Reading the options

The first quote says that the total momentum of a system stays constant when no external force acts on it. The second quote says that the total energy of a closed system stays constant, but one form of energy can change into another form. We use these to test the three statements.

For example, a lump of wet clay is thrown at a toy cart and sticks to it. The cart and the clay roll off together, more slowly than the clay flew.

You hear a soft thud and the clay gets a little warm. That is where the missing kinetic energy went.

Reasoning and calculation

The law of conservation of linear momentum is valid for the collision.

The surface is smooth, so no external horizontal force acts. The pushes between the bullet and the block are inside the system. So the total momentum before and after is the same: $mu = (m + M)v$.

A

The law of conservation of energy is valid for the collision.

The total energy of a closed system stays constant. In the hit some kinetic energy becomes heat and sound, but kinetic energy plus heat plus sound is the same as before. So the law holds.

B

A part of kinetic energy of the system is lost due to the collision.

Take $m = 1$, $M = 9$ and $u = 10$. Then $v = 1$. The kinetic energy before is $50$ and after it is $5$. The bullet stays stuck in the wood, so $45$ became heat and sound. Part of the kinetic energy is lost.

C

Statement (A) is true, because no external force acts along the smooth surface.

Statement (B) is true, because the total energy never changes.

Statement (C) is true, because part of the kinetic energy became heat and sound.

So all three are true.

Why the other options fail

(C) is also true. The pair moves off slower, and part of the kinetic energy turns into heat and sound.

(B) is also true. The lost kinetic energy is still there as heat and sound, so the total energy stays.

(A) is also true. No external force acts on the smooth surface, so the total momentum stays.

(B) and (C) are also true. The energy only changes form, and part of the kinetic energy is lost to heat and sound.

Conclusion

Momentum and total energy are both conserved, and part of the kinetic energy is lost as heat and sound. (A), (B) and (C) are all true.

The answer is (5).

When two bodies stick together, momentum is always conserved but kinetic energy is not.

The total energy is still conserved: the lost kinetic energy is now heat and sound.

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