## Module 5 Class Activities

## Reconciling common sense and Newton’s laws

### I. “Timmy’s fallen down the well!”

To rescue a child who has fallen down a well, rescue workers fasten him to a rope, the other end of which is then reeled in by a machine. The rope pulls the child straight upward at steady speed. The child weighs 250 newtons, which means gravity pulls him downward with 250 newtons of force.

A. (*Work together*) Draw a diagram of this situation that you can refer to during subsequent discussions.

B. (*Work individually*) As the child is pulled upward at constant speed, does the rope exert an upward force greater than, less than, or equal to 250 newtons? Explain. If you have competing arguments, write them both down!

C. (*Work together*) If you didn’t do so in part B, give an intuitive argument that the rope exerts a force greater than 250 newtons.

D. (*Work together*) If you didn’t do so in part B, use Newton’s second law to determine whether the rope exerts a force greater than, less than, or equal to 250 newtons. (*Hint:* The rope pulls the child with constant velocity. So what’s the acceleration?)

E. (*Work together*) Are you 100% comfortable with your understanding of this scenario, or is there still something that needs to be reconciled? Explain.

### II. Refining intuition to reconcile Newton’s laws with common sense

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?

F. (*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)?

- What does Newton’s second law say about this question? (
*Hint:*Is the child accelerating during the initiation of the motion?) - Does the Newtonian answer here agree with common sense?

G. (*Work together*) Now consider the child’s motion *after* the initiation stage of the motion, once he is already moving.

*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.- Does Newton’s second law agree with your answer? Explain.
*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.- Does Newton’s second law agree with your answer? Explain.
- Let’s tie this all together. It makes sense that, if the rope force remains greater than the gravitational force, the child keeps speeding up; and if the rope force becomes less than the gravitational force, the child slows down. By this line of intuitive reasoning, what happens to the child’s motion if the rope force
*equals*the child’s weight,*i.e.,*if the rope force “compromises” between being greater than and being less than the child’s weight? Explain. - Does Newton’s second law agree with your answer?

### Check in with your LA before moving on to the next part.

H. (*Work together*) Consider this *intuition refinement diagram*.

- Which of those two refinements were you using (perhaps unconsciously!) in part B above?
- Which of those two refinements agrees with Newton’s second law?
- Which of those two refinements were you using (perhaps unconsciously) back in part I B and I C?

I. (*Work together*) Way back at the start of this tutorial, we saw what Newton’s second law says about the child and the rope: To keep the child moving upward at steady speed, the rope force must equal (not beat) the child’s weight. Given that you’d already figured out the answer to this question in part I, what was the point, if any, of part II of this tutorial?

- What do you think your professor (Dr. Formica) would say?
- What’s your own opinion? (Be honest: It’s OK if you disagree with your professor, and we want to hear what you think.)