IP Topics

Hydraulic Press Simulation

This simulation can be used for O-level Physics, for the topic of Pressure. I created it as it was relevant to our school’s IP3 physics as well.

It demonstrates the working principle of a hydraulic press. By adjusting the cross-section areas (A) of the two cylinders, you only need a small amount of force at the narrow piston to exert a large amount of force at the wider piston. This is how, when driving, the force applied by one’s foot is enough to supply a large force to apply the brake pads on a car’s wheels.

The advantage of using GeoGebra is that one can create such simple simulations within a couple of hours and it can be readily embedded into SLS – a wonderful tool to have during this period of full home-based learning.

Tensegrity Explained

There is a new internet trend called “tensegrity” – an amalgamation of the words tension and integrity. It is basically a trend of videos showing how objects appear to float above a structure while experiencing tensions that appear to pull parts of the floating object downwards.

In the diagram below, the red vectors show the tensions acting on the “floating” object while the green vector shows the weight of the object.

The main force that makes this possible is the upward tension exerted by the string from which the lowest point of the object is suspended. The other tensions are downward and serve to balance the moment created by the weight of the object.

This is a fun demonstration to teach the principle of moments, and concepts of equilibrium.

These tensegrity structures are very easy to build if you understand the physics behind them. Some tips on building such structures:

  1. Make the two strings exerting the downward tensions easy to adjust by using technic pins to stick them into bricks with holes. You can simply pull to release more string in order to achieve the right balance.
  2. The two strings should be sufficiently far apart to prevent the floating structure from tilting too easily to the side.
  3. The centre of gravity of the floating structure must be in front of the string exerting the upward tension.
  4. The base must be big enough to prevent the whole structure from toppling.

Here’s another tensegrity structure that I built: this time, with a Lego construction theme.

Forces in Equilibrium

While preparing for a bridging class for those JAE JC1s who did not do pure physics in O-levels, I prepared an app on using a vector triangle to “solve problems for a static point mass under the action of 3 forces for 2-dimensional cases”.

For A-level students, they can be encouraged to use either the sine rule or the cosine rule to solve for magnitudes of forces instead of scale drawing, which is often unreliable.

For students who are not familiar with these rules, here is a simple summary:

Sine Rule

If you are trying to find the length of a side while knowing only two angles and one side, use sine rule:

$$\dfrac{A}{\sin{a}}=\dfrac{B}{\sin{b}}$$

Cosine Rule

If you are trying to find the length of a side while knowing only one angle and two sides, use cosine rule:

$$A^2 = B^2 + C^2 – 2BC\cos{a}$$

Newton’s 2nd Law Questions

Here are the steps to solving a problem involving Newton’s 2nd law.

Step 1: Draw a free body diagram – where possible, sketch a free body diagram to represent:

  1. the body isolated from other objects
  2. the forces acting on the body (ignore all internal forces) along the line of motion.
  3. the direction of acceleration.

Step 2: Write down the equation: $$F_{net}=ma$$

Step 3: Add up the forces on the left-hand side of the equation, making sure that forces acting opposite to the direction of acceleration are subtracted.

Step 4: Solve the equation for the unknown.

For example,

A horizontal force of 12 N is applied to a wooden block of mass 0.60 kg on a rough horizontal surface, and the block accelerates at 4.0 m s-2. What is the magnitude of the frictional force acting on the block?

Step 1: Free-body diagram

Newton's 2nd law

Step 2: Write down the 2nd law equation

By Newton’s 2nd law, $$F_{net}=ma$$

Step 3: Add up the forces making up the net force

$$12 – f = 0.60 (4.0)$$

Step 4: Solve for unknown

$$ f = 12 – 2.4 = 9.6 N$$

Free-Body Diagrams in Two-Body Motion


Students are often confused about the forces in drawing free-body diagrams, especially so when they have to consider the different parts of multiple bodies in motion.

Two-Body Motion

Let’s consider the case of a two-body problem, where, a force F is applied to push two boxes horizontally. If we were to consider the free-body diagram of the two boxes as a single system, we only need to draw it like this.

two-body
Considering both boxes as a single system

For the sake of problem solving, there is no need to draw the normal forces or weights since they cancel each other out, so the diagram can look neater. Applying Newton’s 2nd law of motion, [latex]F=(m_A+m_B) \times a[/latex], where [latex]m_A[/latex] is the mass of box A, [latex]m_B[/latex] is the mass of box B, F is the force applied on the system and a is the acceleration of both boxes.

You may also consider box A on its own.

DYNAMICS2
Considering box A on its own

The equation is [latex]F-F_{AB}=m_A \times a[/latex], where [latex]F_{AB}[/latex] is the force exerted on box A by box B.

The third option is to consider box B on its own.

DYNAMICS3
Considering box B on its own

The equation is [latex]F_{BA}=m_B \times a[/latex], where [latex]F_{BA}[/latex] is the force exerted on box B by box A. Applying Newton’s 3rd law, [latex]F_{BA}=F_{AB}[/latex] in magnitude.

Never Draw Everything Together

NEVER draw the free-body diagram with all the forces and moving objects in the same diagram, like this:

wrong freebody diagram

You will not be able to decide which forces acting on which body and much less be able to form a sensible equation of motion.

Interactive

Use the following app to observe the changes in the forces considered in the 3 different scenarios. You can vary the masses of the bodies or the external force applied.

Multiple-Body Problems

For the two-body problem above, we can consider 3 different free-body diagrams.

For three bodies in motion together, we can consider up to 6 different free-body diagrams: the 3 objects independently, 2 objects at a go, and all 3 together. Find the force between any two bodies by simplifying a 3-body diagram into 2 bodies. This trick can be applied to problems with even more bodies.