Teaching Sequence

Work through this resource material in the following sequence:

25 minutes

Part A: Modelling a fall

30 minutes

Part B: Calculating the force of a fall

5 minutes

Reflection

Part A: Modelling a fall

Step 1

Explain to students that, following from the last lesson, where they looked at the forces acting upon someone when punched, they are going to be investigating the effect of the fall on a person’s head. They’re going to do this by dropping different balls onto different surfaces and observing the differences between the balls landing on both surfaces.

In the experiment, the balls being dropped will be:

a basketball
a medicine ball (the weighted type typically found in a gym)
a third ball of a different type (optional), chosen by you or the class.

Alternatively, a sandbag of similar size might be an interesting option because it will much more easily deform to absorb the impact, unlike the other two. If you want to get messy, a watermelon would also be a reasonable analogy (melons are often used in tests as a head replacement), but it’s worth keeping in mind that the smashing of a melon could be triggering for students, given that there might be connotations of a head being broken in a similar manner.

These balls/objects will be dropped on two (or more different surfaces). We suggest concrete and grass to give a very clear difference in terms of reducing the impact via cushioning or elasticity.

So that it’s easier for students to remember the variables being altered in the experiment, we recommend you write the details of ball and surface types on the board.

Step 2

Having established the outline of the experiment, ask students to come up with a suitable aim and hypothesis for the experiment, using the conventions they should, hopefully, be familiar with by now. In this lesson, we really want to focus on the experimental outcomes so, if time permits, you can spend some time revising aims and hypotheses-writing, but if time is of the essence, don’t feel the need to dwell on the aim and hypothesis too much at this stage.

Step 3

Choose a suitable location for dropping the balls (inside your classroom is probably fine, although this can be a nice chance to get your class outside).

Ask student volunteers to hold the balls at the same height, give them a countdown and have them drop them at the same time. Have the students complete the see, think, wonder table on their worksheets. Be clear with students that they are only to drop, not throw, the balls at the ground, as this can be dangerous (for students, observers and any fragile objects in the area) and affect the results.

Step 4

Try and get the class to determine why one ball bounced quite a bit higher than the other, as well as what made them fall. Here are some sample questions (and answers) ranging from easiest to hardest - choose the questions most suitable for your class:

Force questions:

Which force caused the balls to fall?
The force due to gravity.
What is gravity?
The force of the Earth’s mass pulling other masses towards it.
Were there any forces acting against the movement of the ball?
Yes, air resistance.
Which ball had the larger force acting on it?
The heavier one.
What did you notice about the time that they hit the ground?
They hit around the same time.
Why didn’t the ball with more force (or mass) move faster than the other?
Inertia - heavier things take more force to accelerate.

If you want to explore how the shapes of the balls change when dropped, ask if any students have a camera capable of slow-motion video recording on their phone and ask them to record the impact. The slow motion should allow you to see in greater detail how the balls deform on impact and there’s a reasonable chance that there is at least one student with slow-motion recording capabilities. Ideally, they’ll record both balls hitting the ground for comparison. You might like to refer to these resources for support:

Step 5

Repeat this process, but by dropping just the basketball on two different surfaces (i.e. concrete and grass, brick and sand, etc.; any sufficiently different surfaces will do). Perform the drops and get the students to see, think, wonder, then draw out the concepts using this comparison:

Between the drop on the hard surface and the drop on the soft surface, what things stayed the same and what things changed?

Stayed the same:

Conditions: starting height, wind conditions, temperature
The ball: mass, size, shape, texture, internal pressure
Forces: force due to gravity, downward acceleration, air resistance value
Energy: initial gravitational potential energy, kinetic energy (speed) as the ball hit the ground

Changed:

Conditions: the surface of the ground
Energy: more energy was 'used' in changing the ground (squishing soft dirt or grass, moving sand particles, etc.) and so less of that initial energy was available to provide kinetic energy (movement) of the ball back up.

Step 6

Have the students draw a simplified force diagram for a basketball falling on concrete on their worksheets. Go over solutions on the board when you are ready. They are given below for your convenience.

Safety first: The following activities might be challenging or triggering for some students. Refer to the Handling Sensitive Topics and Issues Factsheet and allow students to step out or take a break (or anything else they need to do to take care of themselves) as needed.

Step 7

Ask the students if they think the human head would behave more like the basketball or the medicine ball. Since it doesn’t bounce like the basketball, what implications does this have for the magnitude of the force applied to the skull - how might the skull, or the brain, respond to such forces? Also, what do they think the difference is for someone falling on concrete versus grass or another, softer surface?

The internet is awash with recorded fights or assaults where a victim is knocked over or is unconscious after the punch before falling onto a hard surface and this is oftentimes the most deadly part. Massive deceleration when hitting the ground causes almost all of the force to be applied to our head in a very short space of time and this is deadly. By changing the drop surface, we can show that softer surfaces will reduce the impact on the head and cause less injury. Additionally, we’re demonstrating to students that the vast majority of the force of the fall is absorbed by our head and it is this force that causes the most significant damage, not the initial blow to the head that caused the fall. This is a perfect time to remind students to always wear a helmet, and wear it properly when on their bike, skateboard or scooter: helmets absorb the impact that would otherwise be transferred to our skull. It’s better to 'look silly' than it is to be in the hospital with head injuries.

As the brain is inside our skull, we often think of it as being static or fixed in position, but this is not the case. In a collision, the brain will continue to move in the same direction as the rest of the head until an unbalanced force is applied to it. In this case, it will be the skull pushing back in the opposite direction once the head hits the ground. To conceptualise this, ask students to consider what happens when they’re in a car that brakes suddenly: they continue moving forward until the seat belt pulls them back into place. In a fall, our brains will act like the body in a car and the skull acts like the seatbelt.

Part B: Calculating the force of a fall

Step 1

Inform the students that now you will be looking at what happens after the initial punch - the fall. Since it is a complicated system, you will make the following assumptions and simplifications (these are also on their worksheets for reference throughout the task):

The victim is unconscious and will not attempt to break their fall with their arms
The head of the victim will be considered as a free-body (neck and body not considered)
Take the mass of a human head m_head = 5.0 kg
Consider the victim’s height to be 175 cm, or h_victim = 1.75 m
Take acceleration due to gravity as g = 10 ms^-2
Take the force of the initial punch to be F_punch = 2000 N
Assume the fist is in contact with the head for 20 ms, t_punch = 20 x 10^-3 s
Air resistance can be assumed to be negligible.

Required formulae can be found on the initial mind map!

Step 2

Working alone, have each student work through the problems on their worksheet regarding the motion of the head during the fall and upon impact.

Question 1: What is the initial gravitational potential energy of the victim’s head?

U_g= mgh
= 5.0 x 10 x 1.75
= 87.5 J

Question 2: If the head was to fall straight down, what speed will the head be travelling when it hits the ground?

U_g = E_k
87.5 = ½ mv²
87.5 = ½ x 5.0 x v²
v = 5.92 ms^-1

Question 3: What momentum does this represent?

p = mv
= 5.0 x 5.92
= 29.6 kgms^-1

Question 4: In reality, it wouldn’t fall straight down - why not?

Because the punch would impart an initial horizontal velocity in addition to the vertical acceleration caused by gravity, the head would travel in an arc.

Question 5: What is the magnitude of the downward force acting on the head as it falls?

F = ma
= 5.0 x 10
= 50 N

Question 6: What will be the sideways acceleration of the head during the punch?

Question 7: What will be the sideways speed of the head immediately after the punch?

Question 8: What is Newton’s First Law?

Inertia (any valid explanation will suffice).

Question 9: Use Newton’s First Law to explain how the brain gets damaged directly during the initial punch and when hitting the ground.

Due to inertia, the brain will initially try to remain stationary as the skull moves sideways. This means that the skull will accelerate into the brain causing trauma. When the head hits the ground, the brain will continue to accelerate downwards due to gravity until acted upon by the skull, applying an upwards force and decelerating the brain suddenly. This can cause twisting and bleeding in the brain, as well as damaging the brain stem and neural pathways.

Step 3

To conclude, you may wish to collect these at the end of the lesson to correct and use as a formative assessment task for feedback or have students self-correct by displaying solutions on the board.

Reflection

Ask students to offer insight on what they learned today and what today’s lesson made them wonder about (there are prompts on the Student Worksheet if you want them to record these thoughts).

In dot points or a couple of sentences, outline what you learned from today’s lesson. These can be things that are new, or things you have remembered today that you learned in the past.
What is one thing today’s lesson made you want to know more about? How will you find this out?

Differentiated Learning

Extension

This reference material is a guide to the mathematics of simple kinematics written for teachers. It contains examples, questions and solutions along with good explanations similar to a student textbook. Content from pages 6 - 26 is suitable for Year 10 students and will provide a good foundation for skills should they enter VCE Physics later on. From page 17 is the straight-line motion equations content which can be applied to today’s context using values from Part B.

Provisions for Learning Support

The calculations in this lesson can be challenging for some students. Consider grouping students with varying skill levels together for that part of the lessons or modelling some of the calculations on the board with students.
Consider giving clues or the relevant formula to students to focus more on the application of mathematics, or conversely require only a formula to be stated as a solution to focus more on the application of physics concepts.

Coward Punch - The Physics of Falling

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