Most students have, or can at least sympathize with, the intuition that upward m

Question

Most students have, or can at least sympathize with, the intuition that upward motion requires an upward force, in which case the upward rope force must “beat” the downward gravitational force to make the child move up. Can we reconcile that intuition with the Newtonian conclusion that the upward force merely equals the downward force? A. (Work together) Consider the child, initially at rest, right when the rope first starts to pull him upward. During that initiation stage of the motion, is the upward force from the rope greater than, less than, or equal to 250 newtons (the child’s weight)?

1. What does Newton’s Second Law say about this question? (Hint: Is the child accelerating during the initiation of the motion?)

2. Does the Newtonian answer here agree with common sense? B. (Work together) Now consider the child’s motion after the initiation stage of the motion, once he is already moving. 1. Intuitively, if the rope’s force remains larger than the child’s weight (like during the initiation stage), does the child continue speeding up, or does he slow down, or rise with constant speed? Briefly explain.

2. Does Newton’s second law agree with your answer? Explain.

3. Intuitively, if the rope force became smaller than the child’s weight, would the child speed up, slow down, or rise at steady speed? Briefly explain.

4. Does Newton’s second law agree with your answer? Explain.

Explanation / Answer

(A)

(1) When it is at rest, upward force is equal to downwnard force

it means applied upward force is equal to its weight

and when we try to accelerate it from its velocity 0 then it need some extra force

So according to Newton's second law there should be some net force to give acceleration and net force = upward force - downward force

Hence upward force should be more than its weight to start pulling thisin upward direction

(2) Common sense also says that we need some force to move this up but we sometimes ignore that weight is also acting in downward direction

(B)

(1) is applied force is larger that the weight then it should accelerate in upward direction we can say this using common sense also because clearly there is large force in upward direction due to which it will accelerate

(2) Newton's second law also agree with this as upward force is larger it means we have net force in upward direction so object will accelerate.

(3)Intuitively we can ignore its weight and we might think that upward force become less so amount of speeding up also become less but it is still speeding up with less acceleration

(4) Newtn's second law say that now downward force is more than upward force so net force will be in downward direction so acceleration will be in downward direction or we can say deceleration (negative acceleration) in upward direction

Due to this it will slow down

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