A. Common sense vs. Newton’s 1st and 2nd laws There are a number of conclusions

Question

A. Common sense vs. Newton’s 1st and 2nd laws There are a number of conclusions one can draw from interpreting Newton’s laws of motion that seem to go against our basic intuitions. In actuality, the contradictions are due to very subtle “kinks” in our intuitive reasoning. The following exercises are intended to help you find these kinks and straighten them out.

1. To rescue a child who has fallen down a well, rescue workers fasten him to a rope and reel him in with a machine. The rope pulls the child straight upward at steady speed. The child weighs 250 N, which means gravity pulls him downward with 250 N of force.

a. To the right, draw a diagram of this situation that you can refer to during subsequent discussions.

2. As the child is pulled upward at constant speed, consider the force exerted by the rope.

a. Intuitively, do you think the rope exerts a force greater than 250 N? Explain. 21

b. Use Newton’s second law to determine the force exerted by the rope on the child. Remember that the rope pulls the child up with constant velocity.

3. If you answered “yes” on 2a, let’s look more closely at the situation.

a. Consider the time before the rope is being reeled in, when the child is hanging on the rope but is still at rest. What is the force of the rope on the child in that case?

b. During the initiation of the motion, when the rope first begins to pull the child upward, how does the force compare to the child’s weight? Think about whether the child is accelerated during this action.

c. Once the child is moving upward, what will happen if the force of the rope remains larger than the weight of the child?

So the intuition that the upward pulling force of the rope should be larger than the weight of the child stems from the fact that the force must be momentarily larger to initiate the motion; yet, if the force were to remain greater than the weight, the child would continue to accelerate upward in accordance with the 2nd law; therefore, after the initiaion of motion, the force must decrease to equally match the weight of the child in order to maintain a constant upward velocity.

Explanation / Answer

There are many points we have to consider to explain the situation by intuitive reasoning.

when we are pulling the boy with the help of rope via reel machine there are few points we can not ignore practically .

1 In practical case rope is not massless .

2 Rope can not be perfectly inextensible

3 Reel must have some moment of inertia

4 We can not vanish the friction force between axel or reel (which is damping the motion)

5. As soon as rope comes up , the part of rope hanging is decreasing so weight of that part is decreasing as soon as boy comes up

So in each case whether boy is moving up or it is held at rest , the tension will be larger than 250N.

Even when boy is moving up with constant velocity , the part of rope hanging is decreasing so tension will be changing

And at the moment when boy is lifted up from ground , an extra force is needed to change momentum of the whole sytem (rope plus boy ). and also friction due to axel of reel is incresing the required tension to move up .

i hope you would understand the logic behind you querry .

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