Difficulty: Medium

Average Score: 52%

A carpenter saws a wooden board into three large pieces. As the saw cuts the wood, sawdust forms.

What must be true about the cut pieces, sawdust, and original uncut board, according to the law of conservation of matter?

Rationale

The mass of the uncut board equals the mass of the large pieces plus the mass of the sawdust.

According to the law of conservation of matter, the total mass before and after a physical change must remain constant. In this scenario, the original uncut board's mass is equal to the combined mass of the cut pieces and the sawdust produced during the sawing process.

A (The mass of the uncut board equals the mass of the large pieces plus the mass of the sawdust.) CORRECT

This statement accurately reflects the principle of conservation of matter. When the carpenter saws the board, the mass of the original board is distributed between the cut pieces and the sawdust created. Therefore, the total mass remains unchanged.

B (The total mass of the sawdust equals the mass of the large pieces.) YOUR ANSWER

This statement is incorrect because it disregards the mass of the original uncut board. The sawdust does not account for the entire mass of the wood; it is simply a byproduct of the cutting process, and thus cannot equal the mass of the large pieces alone.

C (The mass of the uncut board equals the total mass of the large pieces.) YOUR ANSWER

This choice is also incorrect because it ignores the mass of the sawdust produced during the sawing. The mass of the uncut board must equal both the mass of the large pieces and the mass of the sawdust combined.

D (The total mass of the sawdust equals the mass of the large pieces minus the mass of the uncut board.) YOUR ANSWER

This statement is nonsensical as it suggests a scenario where the mass of the sawdust relates negatively to the mass of the uncut board, which violates the conservation of matter. The sawdust is a component of the total mass and cannot be subtracted in such a manner.

Conclusion

In conclusion, the law of conservation of matter dictates that the total mass remains constant during physical changes. Thus, the mass of the uncut board must be equal to the combined mass of the large pieces and the sawdust produced during the cutting process. This understanding highlights the importance of considering all components in a system when analyzing changes in mass.

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