IP3 03 Dynamics

05 April

Simulation of Projectile Motion with Air Resistance

Seng Kwang Tan 02 Kinematics, 03 Dynamics, IP3 03 Dynamics, Simulations 0 Comments
Open in new tab 🔗 This simulation offers a hands-on and dynamic way to explore the physics of projectile motion with and without air resistance. By adjusting parameters such as launch velocity, angle, and air resistance, users can visualize how these factors affect the shape and reach of a projectile’s trajectory. The app provides real-time changes including motion paths, velocity vectors, and a velocity-time graph showing horizontal and vertical components separately. It also calculates and displays key quantities such as maximum height and range under ideal and non-ideal conditions (based on an arbitrary coefficient of drag. Through interactive experimentation and visual reinforcement, learners gain a deeper understanding of concepts the effect of air resistance, and the difference between theoretical and real-world motion. This is suitable for JC1’s topic on projectile motion. It can also be used for Upper Sec, if you change the launch angle to 90 degrees.
15 March

Interactive System Schema Generator

Seng Kwang Tan 03 Dynamics, IP3 03 Dynamics, Simulations, Student Learning Space 0 Comments

I built this web app to help students draw system schemas, having blogged about this before.

It is also available and optimised for download for SLS.

Basic Instructions

To add Bodies:

  • Click the “Add Body” button.​
  • Click on the canvas to place the body at your desired location.​
  • Label the Body.

Add Forces:

  • Click the “Add Force” button.​
  • Click on two bodies that exert the force on each other.​
  • Label the Force.

Using System Schema to Understand Newton’s Third Law

Newton’s Third Law states that when Body A exerts a force on Body B, Body B exerts an equal and opposite force on Body A. While this principle is conceptually simple, many students struggle to apply it consistently across different physical scenarios. The System Schema approach provides a powerful way to visualise and analyse these interactions. It is a representation tool developed by The Modeling Instruction program at Arizona State University (Hinrichs, 2004).

A system schema is a diagram that represents objects (as circles) and interactions (as lines) between them. Instead of focusing on individual forces, a system schema helps students see the relationships between objects before applying force diagrams. This method emphasizes Newton’s Third Law by explicitly showing how forces come in pairs between interacting objects.

To correctly identify action-reaction force pairs, consider the following guidelines:​

  1. Forces Act on Different Objects: Each force in the pair acts on a different object. For example, if Body A exerts a force on Body B, then Body B simultaneously exerts an equal and opposite force on Body A.​
  2. Forces Are Equal in Magnitude and Opposite in Direction: The magnitudes of the two forces are identical, but their directions are opposite.​
  3. Forces Are of the Same Type: Both forces in the pair are of the same nature, such as gravitational, electromagnetic, or contact forces.

The steps to applying System Schema to Newton’s Third Law are as follow:

  1. Identify the bodies in the system – Draw each object as a separate circle.
  2. Represent interactions – Draw lines between bodies to indicate forces they exert on each other (e.g., a box on the ground interacts with Earth through gravitational force).
  3. Label force pairs – Each interaction represents an action-reaction force pair (e.g., a hand pushes a wall; the wall pushes back).
  4. By mapping forces this way, students can easily recognize that forces always act between bodies and in pairs, reinforcing the symmetry of Newton’s Third Law.

One of the most common misconceptions of students is that normal contact force and gravitational force acting on a body are action-reaction pairs because they are equal and opposite in a non-accelerating system. By using the system schema, they can see that the two forces involve interaction with different bodies, e.g. the floor of an elevator for normal contact force, and the Earth for gravitational force.

28 March

Use of System Schema to Visualise Action-Reaction Pairs

Seng Kwang Tan 03 Dynamics, IP3 03 Dynamics 0 Comments

It is a common misconception for students to assume that when a book is placed on a table, its weight and the normal contact force acting on it are action-reaction pairs because they are equal in magnitude and opposite in direction.

While we can emphasise the other requirements for action-reaction pairs – that they must act on two different bodies and be of the same type of force – I have tried a different approach to prevent this misconception from taking root. After reading this article on the use of the system schema representational tool to promote understanding of Newton’s third law, I tried it out with my IP3 students.

The system schema identifies the bodies in a question and represents them with shapes detached from each other to give space to draw the connecting arrows between them. The arrows must be labelled with the type of force, either by coding them (e.g. r for reaction force, g for gravitational force) or in full.

Every force will be drawn as a double-headed arrow between two bodies to represent that they are action-reaction pairs. It is important for students to understand that every force in the universe comes in such a pair, and the system schema can help them visualise that. If there is a force without a partner, it just means the system is not in the frame yet.

The next step to using the system schema is for students to isolate the object in question and draw its free-body diagram. Each force vector in the diagram should be accompanied by a name that includes: 1. the type of force and 2. the subject which exerts that force on the object.

The effectiveness of this method of instruction is clearly presented in the paper mentioned above, as performance on the force concept inventory’s questions on the third law saw an improved average from 2.8 ± 1.2 to 3.7 ± 0.8.

21 April

Unequal masses attached to rod in free fall

Seng Kwang Tan IP3 03 Dynamics 0 Comments

Came across a question recently that many students answered incorrectly.

Close to the surface of the Earth the gravitational field strength is uniform. A pair of unequal masses are joined by a light, rigid horizontal bar and suspended by a string from their centre of gravity as shown. The mass M of the ball on the left is larger than the mass m of the ball on the right.

The supporting string is now cut and the system begins to fall. Air resistance is negligible.

Which statement is correct?

AThe bar will remain horizontal as it falls.
BThe bar will rotate clockwise as it falls.
CThe bar will rotate anti-clockwise as it falls.
DThe bar will first rotate clockwise and then rotate anticlockwise as it falls.

Without air resistance

This question supposes that air resistance is negligible and so the only forces initially acting on the object is weight. The answer that many students gave incorrectly as B because they assume that the larger weight acting on the larger mass will bring about a larger acceleration.

Since the object begins in equilibrium, and the acceleration of both objects is just gravitational acceleration, the bar will remain horizontal.

With air resistance

This then invites a question: What if there is air resistance?

To consider the vertical acceleration on both balls, we need to consider the net force Fnet, which is the vector sum of weight W and air resistance FR, ignoring the tension exerted by the rod at the initial stage of the fall.

Fnet=W–FR=Vρballg–12ρairv2CDA

The volume V of a sphere is proportional to r3 and its cross-sectional area A is proportional to r2,

A larger radius will imply a larger increase in V than A, and hence, a large W than FR. This will then allow the larger mass to experience a larger acceleration than the smaller mass in the initial stage.

30 March

Man in Elevator

Seng Kwang Tan 03 Dynamics, IP3 03 Dynamics 0 Comments

I just took the elevator in my apartment building with the PhyPhox mobile app and recorded the acceleration in the z-direction as the lift went down and up. This was done in the middle of the night to reduce the chances of my neighbours getting into the elevator along the way and disrupting this experiment, and more importantly, thinking I was crazy. The YouTube video below is the result of this impromptu experiment and I intend to use it in class tomorrow.

I used to do this experiment with a weighing scale, and a datalogger, but with smartphone apps being able to demonstrate the same phenomenon, it was worth a try.

To complement the activity, I will be using this simulation as well. Best viewed in original format: https://ejss.s3.ap-southeast-1.amazonaws.com/elevator_Simulation.xhtml, this simulation done in 2016 was used to connect the changes in acceleration and velocity to the changes in normal contact force as an elevator makes its way up or down a building.

17 March

Newton’s 2nd Law Applet

Seng Kwang Tan 03 Dynamics, GeoGebra, IP3 03 Dynamics 0 Comments

For a full-screen view, click here.

<iframe scrolling="no" title="Dynamics Problem" src="https://www.geogebra.org/material/iframe/id/uthszwjq/width/640/height/480/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/true/ctl/false" width="640px" height="480px" style="border:0px;"> </iframe>

This applet was designed with simple interactive features to adjust two opposing forces along the horizontal direction in order to demonstrate the effect on acceleration and velocity.