Ταχύτητα και επιτάχυνση μιας μπάλας που ροβολάει στην πλαγιά

Η μπάλα ροβολάει στην πλαγιά.

Καθώς η ταχύτητά της αυξάνει από το Α μέχρι το Β, η επιτάχυνσή της

1) αυξάνει επίσης

2) ελαττώνεται

3) παραμένει σταθερή

Όταν η μπάλα πάει από το Β στο Γ, η επιτάχυνσή της

4)      αυξάνεται

5)      μειώνεται

6)      παραμένει σταθερή

Αφού το σκεφτείτε, επιβεβαιώστε την απάντησή σας 

( από το περιοδικό Physics Teacher - Δεκέμβριος 2007)

Ένα σχόλιο και μια απάντηση (The Physics Teacher Φεβρουάριος 2008)

Comment on “Rolling Ball”

Essentially, the problem on page 534 is very poorly specified, and the solution on page 565 is just plain wrong for the motion from point B to point C for the shape of the surface drawn in the picture in terms of the language used to ask the question and explain the answer. I know that I have to spend many lectures each semester getting my students to understand that acceleration is a vector that is not generally in the same direction as the motion, especially if the path is curved. The component of the acceleration parallel to the path does decrease from points B to C in the picture, since that component of gravity parallel to the path.

However, the constraint force, which keeps the ball on the surface, is always perpendicular to the path depends on gravity via the slope, but it also depends on the speed of the ball and the instantaneous radius of curvature of the path. Since the path drawn from point B to C looks to be of nearly constant curvature, he magnitude of the acceleration vector actually increases from B to C.

If the ball was released from rest at point B, and the path was a quarter circle, the acceleration at point C would be two times g in the upward direction!

(Meaning the constraint force was 3mg upwards)

If the ball is already moving at point B, the final acceleration at point C is larger.

Please correct me, if I am mistaken.

(Christopher LaSota – Visiting Asst. Prof. of Physics Kenyon College)

Hewitt’s Response

I am wrong and Christopher LaSota is correct. My point was to help students distinguish between velocity and acceleration, and I failed to state “acceleration along the path”

So if you use this Figuring Physics with your students, point out my error to help them distinguish between acceleration in general and components of acceleration when motion is non-linear.

Paul Hewitt – City College of San Francisco