I got this wrong on a quiz and have to correct it to get points back. I have to explain why.
Which of the following is true concerning a system of objects?
a. if the total momentum is conserved, then the total energy is definitely conserved
b. if the total energy is not conserved, the total momentum is is definitely not conserved
c. if the total energy is conserved, the total momentum is definitely conserved
d. the total energy and total momentum may be conserved independently of each other
the answer is d. Now I realize that the first three are basically the same :/
Please help me understand why they can be conserved independently. Example? Please put it in simple terms.
THanks!
Which of the following is true concerning a system of objects?
a. if the total momentum is conserved, then the total energy is definitely conserved
b. if the total energy is not conserved, the total momentum is is definitely not conserved
c. if the total energy is conserved, the total momentum is definitely conserved
d. the total energy and total momentum may be conserved independently of each other
the answer is d. Now I realize that the first three are basically the same :/
Please help me understand why they can be conserved independently. Example? Please put it in simple terms.
THanks!
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What a bad question. Whoever wrote this question and designated the answer as d either didn't understand physics, or didn't understand logic, or both.
Total energy and total momentum are ALWAYS conserved, if it is a closed system. The question is confusing because it doesn't clarify if you're supposed to assume a closed or open system. Even in a closed system, kinetic energy might not be conserved, but the question asks about total energy not total kinetic energy.
a and b are logically equivalent. c is different. If the second part of c is always true (it is for a closed system), then c is true, regardless of what the first part is. Total momentum is conserved if total energy is conserved. Total momentum is conserved if total energy is not conserved. Each is true. The only way c is not right is if it's possible for momentum not to be conserved, which requires an open system.
Now even in an open system it's a bit hard to come up with a scenario where a is wrong. If momentum is conserved, it's a little hard to get something outside the system to carry away any energy without carrying away any momentum. But say you fire two equal wedges at each other, and they both wedge between two equal blocks, which fly away at 90 degrees to the motion of the wedges. But the blocks are considered outside your system. Then the momentum of your system will be conserved but energy will leave it.
Total energy and total momentum are ALWAYS conserved, if it is a closed system. The question is confusing because it doesn't clarify if you're supposed to assume a closed or open system. Even in a closed system, kinetic energy might not be conserved, but the question asks about total energy not total kinetic energy.
a and b are logically equivalent. c is different. If the second part of c is always true (it is for a closed system), then c is true, regardless of what the first part is. Total momentum is conserved if total energy is conserved. Total momentum is conserved if total energy is not conserved. Each is true. The only way c is not right is if it's possible for momentum not to be conserved, which requires an open system.
Now even in an open system it's a bit hard to come up with a scenario where a is wrong. If momentum is conserved, it's a little hard to get something outside the system to carry away any energy without carrying away any momentum. But say you fire two equal wedges at each other, and they both wedge between two equal blocks, which fly away at 90 degrees to the motion of the wedges. But the blocks are considered outside your system. Then the momentum of your system will be conserved but energy will leave it.