IB Physics 2015 Higher level Paper 2 Question 2

Question: Students have to explain why the resultant force acting on a skier moving at constant velocity must be zero. The purpose of this question is to assess students’ knowledge of Newton’s first law of motion. 

Mark Scheme: 
(1) Newton’s first law states that a body remains at rest or moves with) constant velocity / steady speed / uniform motion unless external / net / resultant / unbalanced force acts on it. (2) A clear link between constant velocity and no resultant force.

Comments: 

This question is about using Newton’s first law of motion to explain why the resultant force acting on an object that is moving at constant velocity must be zero. Students are expected to state Newton’s first law and to relate “constant velocity” to “no resultant force.” However, in Physics for the IB diploma, Newton’s first law of motion is stated as “[w]hen no forces act on a body, that body will either remain at rest or continue to move along a straight line with constant speed (Tsokos, 2008, p. 69).” This version of Newton’s first law does not use the term such as “external force,” “net force,” “unbalanced force,” and “resultant force” that are specified in the mark scheme.

On the other hand, another version of Newton’s first law is “a free particle always moves with constant momentum relative to an inertial frame of reference: p = constant (Alonso & Finn, p. 100).” However, the mark scheme does not state Newton’s first law in terms of linear momentum. Currently, very few textbook authors state Newton’s first law in this form. In addition, this version of Newton’s first law adopts the term “free particle” instead of “resultant force.” Thus, it is unclear how the mark scheme could be interpreted by physics teachers. Importantly, the three Newton’s laws of motion can be consistently related to the linear momentum as summarized below: 

1. Newton’s first law: A free particle always moves with constant linear momentum. 

2. Newton’s second law: Force is defined as the rate of change of linear momentum. 

3. Newton’s third law: The principle of conservation of linear momentum.

In schools, physics teachers may use an air-track experiment to show that an object can be moving at a constant velocity for a short period of time. Strictly speaking, Newton’s first law cannot be exactly demonstrated by this experiment. That is, we cannot completely eliminate frictional forces or gravitational forces on an object experimentally. In The Nature of the Physical World, Eddington (1928) criticizes Newton’s first law, and rephrases it as “[e]very body continues in its state of rest or uniform motion in a straight line, except in so far as it doesn’t (p. 124).”

Feynman insights?: 

Newton’s first law of motion is also known as the principle of inertia. Historically speaking, Newton (1687) states that “[e]very body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon (p. 19).” The term resultant force is not used in the original formulation of Newton’s first law as well as many later versions of the principle of inertia. For example, in Volume I of The Feynman Lectures on Physics, Feynman states that “if an object is left alone, is not disturbed, it continues to move with a constant velocity in a straight line if it was originally moving, or it continues to stand still if it was just standing still (Feynman et al., 1963, section 9–1 Momentum and force).” Essentially, Feynman is conceptualizing an isolated body that is left alone and it is not disturbed by external forces.

In Volume II of The Feynman Lectures on Physics, Feynman proposes a broader definition of straight line: “ ‘Straight-line’ motion — the analog of ‘uniform velocity along a straight line’ — is then that motion which takes a watch from one place at one time to another place at another time in the way that gives the longest time reading for the watch. This will be our definition for the analog of a straight line in space-time (Feynman et al., 1964, section 42-4 Geometry in space-time).” In a similar sense, modern formulation of the principle of inertia may be stated as: “[t]here is a special class of observers, relative to whom all free objects appear to either be at rest or to move along geodesics in spacetime. These are observers who are in free fall in a gravitational field (Smolin, 2013, p. 341).” However, in this version, the term “free objects” does not necessarily mean that the objects are not acted upon by a resultant (gravitational) force.

Note: 
1. In Newtonian Mechanics, French (1971) writes that “Moreover, there is the far from trivial question of defining a straight line in a real physical sense: it is certainly not intuitively obvious, nor is it an abstract mathematical question. (How would you define a straight line for this purpose?) (p. 164).”

2. About 2000 years before Newton has formulated his three laws of motion, Mozi (墨子) writes that, “止，以久也。止，無久之不止”; it means that “if there is no such force, the motion will never stop (Needham, 1962, p. 58).”

3. You may want to take a look at this website:
http://feynman-answer.blogspot.sg/2016/04/newtons-first-law-of-motion.html

References:
1. Alonso, M., & Finn, E. J. (1992). Physics. Wokingham: Addison-Wesley.
2. Eddington, A. (1928). The Nature of the Physical World. New York: Cambridge University Press. 
3. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley. 
4. Feynman, R. P., Leighton, R. B., & Sands, M. (1964). The Feynman Lectures on Physics, Vol II: Mainly electromagnetism and matter. Reading, MA: Addison-Wesley. 
5. French, A. (1971). Newtonian Mechanics. New York: W. W. Norton. 
6. Needham, J. (1962). Science and Civilisation in China: Volume 4, Physics and Physical Technology, Part 1, Physics. Cambridge: Cambridge University Press.
7. Newton, I. (1687/1995). The Principia. (A. Motte, Trans.). New York: Prometheus.
8. Smolin, L. (2003). The Principle of Inertia. In J. Brockman (ed.), This explains everything. New York: Harper Perennial.
9. Tsokos, K. A. (2008). Physics for the IB Diploma (5th ed.). Cambridge: Cambridge University Press.