Monday, 15 April 2013

Common Misconceptions when using Newton’s 3rd Law of Motion

Newton’s 3rd Law (N3L) presents the greatest challenge to students unlike the first two laws of motion because what it claims is contrary to many daily experiences and hence counter-intuitive. Newton's Laws of motion allows us to break down the problem systematically by first looking at the forces exerted on bodies, compute the resultant force and predict its motion.

Challenges to learners include:
·          N3L only work for specific situations, e.g., system at rest
In using N3L, we are looking only at the forces between two bodies at the point/surface of direct contact (except for the fundamental forces which are action-at-distance[1]). If the two bodies are in contact, the force on each body due to the other body must be equal and opposite. There is no need to look beyond the contact point when using N3L.

·      Object being pushed experience a larger force exerted by the imparter (e.g., a person) while the force exerted on the imparter by the object should “logically” be less.
This is a compromised version of N3L. Students recognized and know that they need to apply N3L but preconceptions compel students to come up with alternate N3L to accommodate daily experiences. The single most difficult misconception to rectify in students since it is contrary to daily experiences.

·           Using N3L to describe the forces acting on the same body
Forces like gravitational force (or weight) and normal force exerted by the table are taken to be the pair of forces in accordance to N3L because they are “equal and opposite”.

·           Dealing with massless string
In basic mechanics, the sole purpose of the string is to connect various bodies so that they behave as a single system yet they are not in contact. N3L is not applicable to the forces between two bodies even though they satisfy “equal and opposite forces on two different bodies” condition because they are not in contact. N3L describe the pair forces between each end of the string with the body. For the string, the forces on both ends must cause it to be taut and have equal magnitude regardless of the state of motion of the system. This is a consequence of Newton’s 2nd Law
     Resultant force on string = mass x acceleration
=>                        Tleft – Tright =     0    x        a

[1] Actually most of the forces we are discussing in Mechanics are action-at-a-distance electromagnetic interactions. We don’t observe this because we perceive only the macroscopic form of the interaction which is the contact between objects.

Sunday, 14 April 2013

Typical problems in Newton's 2nd and 3rd Laws that are difficult for beginners

Complete the following questions for the 3 cases (see pictures)
(a) Identify the forces acting on A and B separately even if they are interacting
(b) Identify which pairs of forces that are a consequence of Newton' 3rd Law.
(c) Calculate the magnitude and indicate the direction of all the forces on A and B separately
(d) Calculate any forces on the rope if applicable

Newton's 3rd Law - The difficulty from learner's perspective

Below is a rather normal textbook example for Newton's 2nd Law:

A person pushes a box, mass xx kg on a frictionless surface with force yy N, determine the resultant force and acceleration of the box.

Very few teachers will spend their time to discuss about the person pushing the box since identifying the forces on the box is sufficient to illustrate the use of F = ma. However if one is to take a closer look at the forces on the person pushing the box, there will be plenty of inconsistencies. This is the kind of textbook problems that plague physics teaching which are the source of confusion among students because it cannot exist in real life. There is no way the person standing on a frictionless floor to push the box for more than an instant! There is a contradiction between actual experience and physics principles. To deal with the discrepancy, students resorted to assimilate the solutions of this kind of problems through mental accommodation rather than through a consistent mental model. Many researches have pointed out that such laymen's preconceptions of how the world functions continue to persist in learners even after years of high quality science education.

What Newton's 3rd Law claims and how we perceive how forces work in the real world can be poles apart. To master it, learners have to stop relying on personal perceptions and use the laws which are unbias and self-consistent. Learners should start to build a consistent mental model from ground up rather than accomodate Newton's Laws with pre-existing perceptions. For the record, it took the ancients (from Aristotle to Newton's) almost 2000 years to realise that over-reliance on the senses lead to inconsistent scientific model. To master Newton's Laws of motion, we may want to take a leaf from a small part in a famous martial art novel 倚天屠龙记.


Finally I appeal to all teachers and anxious parents to allow students the time to struggle with Newton's Laws. The more they struggle, the more they can distil the essence of the laws. Trying to shorten the 2000 years' of journey taken by scientists is not practical. If a teacher can teach the laws [in the textbooks] and the students can understand them with a few examples and assignments, why do we need teachers? We can easily replace teachers with DVDs of lectures and demonstrations (Hewitt or Walter Lewin just to name a few)!

The following conversation may shed some light on the struggle of learners have in order to reconcile real world experience with Physics model.

Student - If I am pushing a box on a frictionless surface, then the box should push back at me with the same amount of force. But if the box is moving in the direction i am pushing it, doesnt that mean that i am exerting a larger force on it?

Teacher - Why do you think you need a larger force to move the box in the direction of motion? Maybe you want to break down the question into the forces acting on the box and the man. Maybe sketch and drop me a pic?

Student - Because there needs to be a resultant force for the box to move? But if that's so then newtons third law doesn't apply... So it only applies for stationary objects?
student's sketch

Teacher - Newton's third law applies 100% of the time! Looking at what you have drawn, the box will accelerate to the right but the person will accelerate to the left! Do you think there is something missing on the person? Can you walk on a frictionless ground?

Student - Then the person should have a force by muscles letting him walk?

Teacher - Nope. No one can walk on a frictionless floor! To walk, you need to be able to exert a force on the floor backward relative to you which gives rise to a force on you by the floor (see diagram). In fact you need to be able to exert a force by your legs larger than what you apply to the box in order for the situation to be possible in real life! Your question is the kind of textbook problems that plague physics teaching which led to confusion among students (You have brought up an excellent problem).  If you look at the box alone, no problem, most students will be able to work out the acceleration of the box easily. However contradiction arises because the person can't accelerate forward with the box unless the floor under him miraculously turn into a rough floor for him to exert a force on it backward!
Teacher's sketch

Student - But then if we use your first question of two boxes as an example, when box A pushes on box B, by N3L box B should push back with the same amount of force. But box B will move, which means its pushing back with less force. then how does N3L apply then? Or rather, why is there even resultant force in the world?
Question that is referred to by student

Student - Oh. Is it cause the amount of force with which B pushes back on A doesn't affect the resultant force of B itself cause it's on A, not B?

Teacher - Yes! Well done!

Wednesday, 3 April 2013

Collision carts simulation for practical on 3/4/13

Please complete the lab assignment P06 by 5/4/13.

The simulation can be downloaded here.

Special thanks for Wee Loo Kang for creating and refining this simulation with and for River Valley High School.

What happens when you drop a spring balance with the measured object still on it?

This video (shot at 120 frame-per-second) can be used to show that the spring balance does not measure the weight/gravitational force of the object hanging below rather it is measuring the force exerted by object.


  • The spring extends because the object exerts a force on the spring balance and the spring balance exerts an equal force on the object (Newton's 3rd Law). The force on the object exerted by the spring balance is equal to the gravitational force on the object when the system is in equilibrium (either at rest or at constant velocity). 
  • When the system is accelerated (or free fall in this video), the force exerted on the spring balance by the object is different (zero at free fall) while the gravitational force on the object remains constant