The eleven year old sat a nationwide science test recently (he did exceptionally well but you will be glad to hear that the parental boasting section of this post is now over). He was able to bring the paper home. One of the questions he got “wrong” - which sounds slightly familiar except it involves no monkeys - was as follows:
What answer is correct or what answers could be correct, based on the question as asked? Needless to say I don’t agree with the “official” answer but I won’t bias you by telling what it was.
Aren’t their weights identical and therefore the pull of gravity equal on both sides, regardless of how the two weights are situated with respect to each other? Each acts as a counterweight to the other.
If one side gets heavier when the two weights are at different heights, then counter-weighted elevators wouldn’t work, would they?
I say B). The force acting on each mass is gravity - equal for each mass, and the effect of gravity on the other mass transferred through the string - again equal for each. This ignores the mass of the string and the reduction in gravity due to the upper mass being further from the Earth.
Not really because the question is carefully phrased to ensure that each phase starts with all items stationary, and what happens from there is a function purely of gravity and friction, where the monkey problem is dynamic.
Counter-weighted elevators have motors to overcome any slight imbalances. This must be true as, for a start, consider that sometimes elevators have people in them and sometimes they don’t.
The monkey problem starts with all items stationary, too. I think they are the same problem and share the same physics. I also think that friction is not intended to be a factor.
Yes but then the monkey moves. Anyway, this thread is about the precise question in the OP, not the monkey problem. Let’s keep this clean and not hijack off into another question.
What is the answer a person doing the test should give to this particular question?
B or D, depending on which is the more negligible, the friction in the pulley or the extra mass of the mass of the extra mass of the longer (but “light” string on one side. If the string is entirely weightless, then B.
I suppose with a perfectly frictionless pulley it might matter that the lower mass is slightly closer to the Earth’s center of mass, thus leading gravity to pull on it infinitesimally more strongly. So, in that case, D.
The problem statement said nothing about friction.
The problem statement did say the string was light, the implication of which is that its mass can be safely disregarded. This means the mass on either side of the pulley is the same, regardless of what height the masses are at.
With negligible string mass, the correct answer is B.
Poorly worded question. Depending on what weight values of “light string” you assume, and how much pulley friction is input for “easily moved up and down”, the answer can be either B) or D). Although since this is test is geared at 5th grade level, and they specified “light” string the answer they were looking for is probably B).
Concur - the question is a little vague in that the specification of the string being ‘light’ may be intended to mean “to be ignored”. I’d go for D, on the basis that ‘light string’ is not explicitly massless.
To me, “light piece of string” implies that the mass of the string is negligible compared to the mass of the, um, masses. And given the real-world description of the pulleys (rather than “frictionless”), I would assume the friction is non-zero. So my best guess would be that B is the intended answer.
Also, if the pulley were frictionless and the string had non-zero mass, none of these answers would be true. What would happen is, the masses would move past the original point, move twice as far and stop, then start moving back. It would oscillate forever, with the original point as the center of the oscillation. (Well, unless we factor in air resistance, in which case it would eventually come to a stop at the original point.)
Was this really in a science test for 11 year olds? Are they actually expected to calculate the answer or is it just taught? Is it one of those tests that just gets harder and harder, or do you have a particularly smart 11 year old?
I don’t remember any real calculation of mass, gravity, friction etc. at school until a few years after 11.
Given massless inextensible string and frictionless pulleys, available from all good mathematical axiom shops, and neglecting the difference in gravitational attraction due to height, the masses will stay right where they are. They don’t need to “return to equilibrium”; they are in (neutral) equilibrium already. Option B. Next!
Enlarging: Object A with mass m has force mg acting on it vertically downwards. Also object B. They’re therefore both applying the same tension to the string and so each object is experiencing a force of -mg exactly balancing the force of gravity. (I should be using vectors here, but eh.) Therefore each mass experiences a net force of zero, so it doesn’t move.
There is no particular reason why the two masses need to have equal potential energies, and there is no scope for the system as a whole to reach a lower-energy state.