A View Into Our Days: Newton’s Laws

Following on from this post delving into science in our homeschool and in particular, our first few physics lessons from the year, here’s the next instalment, highlighting how we investigated Newton’s three fundamental laws of motion.

The Discussion

To start this set of three lessons, we sat in a group on the floor and the children took it in turns to read through the descriptions of Newton’s three laws from these two books: 1) Physics for Edexcel International GCSE (Nick England) and 2) CGP Edexcel International GCSE Physics, The Revision Book.

At this point, there was an extremely lengthy discussion about each law in turn. Not content with merely accepting the rules at face value, they each asked many questions, dissecting the examples, looking at other factors at play and drawing on their own life experience in order to get a solid understanding of the theory being discussed.

My friend and I did our best to answer their queries, explaining each concept in as many different ways as we could think of, encouraging them to think of their own examples, and if that failed, bringing in MrJ, a physics fan, to help.

Following our long discussion, they each wrote up the laws in their journals in a way that best helped them remember, and memorised each one. Then, we spent a couple of weeks conducting a variety of hands-on experiments to further investigate each law and aid their comprehension.

Newton’s First Law of Motion

“When the resultant force acting on an object is zero, the forces are balanced, and the object does not accelerate. It remains stationary or continues to move in a straight line at a constant speed.”

Or alternatively put, “A body at rest will stay at rest and a body in motion will continue at constant velocity, unless acted upon by an external unbalanced force.”

For example, if a runner is moving at their top pace, their thrust forward is equal to the air resistance pushing them back, i.e. the opposing forces are balanced, and so their speed remains constant until one of the forces changes and become unbalanced – e.g. the runner tires and their thrust drops or a headwind picks up slowing them down.

Experiment One – Crash Test Dummy

Firstly, to test this law, we started with an extremely simple Crash Test Dummy experiment from this Junk Drawer Physics book.

They found a plastic action figure, placed it on top of a toy car and pushed the car into a wall. We discussed what happened to the dummy – i.e. when the car stopped, the action figure kept moving until it too hit the wall, encountering an unbalanced force.

In step two, they added an elastic band to attach the figure to the car, and we discussed how, on impact, it was this rubber band (seatbelt) which provided the unbalanced force to stop the forward motion of the figure.

Finally, they added in a marshmallow just to simulate an airbag. And then they got to eat one each, which always makes for happy Beans!

Newton’s Second Law of Motion

“If there is an unbalanced force acting on an object, it accelerates in that direction. The object could speed up, slow down or change direction.”

So, when the burner flame heats the air in a hot air balloon, the upward force is greater than the downward pull of gravity. The resultant force is an upwards acceleration of the balloon.

His second law also states that when an unbalanced force acts on an object:

• “the magnitude of the object’s acceleration varies in direct proportion with the size of the unbalanced force” – so as the force increases, so does the acceleration.
• “the magnitude of the object’s acceleration varies inversely with the mass of the object” – so the heavier an object, the slower the acceleration for the same force.

This gives rise to the formula, force = mass x acceleration.

Experiment Two – Testing How Mass and Force Affect Acceleration

The following experiment tests the relationship between force, mass and acceleration, and Newton’s second law, F = ma.

The Set Up

This is how the experiment should have been set up:

But as our budget didn’t stretch to light gates and data loggers to calculate acceleration, instead we used human timers, some assumptions and calculations! We attached the car to a piece of string and on the other end, tied it to a hook of masses, suspended over the edge of the kitchen worktop on a pulley like in the picture above.

We marked a starting line and then two other lines, at set intervals. Human timers were positioned at these latter two positions and they measured the time taken from when the car was released to when it passed their particular line. Thus, we had measurements for how long it took for the car to reach positions 1 & 2 from the starting point, and simply subtracted one from the other to work out the time taken to go from point 1 to point 2.

Our plan was to calculate the car’s acceleration in two steps. Firstly, we used the distance travelled between points 1 & 2 divided by the time taken to calculate the velocity of the car across this section. We then made a massive assumption that the velocity between points 1 & 2 would be the same as the velocity at point 1.

Once we had our velocity at point 1, we calculated the acceleration using the formula (final velocity at point 1 – initial velocity at point 0)/time taken from point 0-1, using the final velocity of point 1 as calculated in step one above.

Now we could calculate a rough acceleration, we could vary the force, by changing the number of 100g of weights on the end of the hook, and the overall mass of the system, by affixing weights to the top of the car.

We conducted four different tests as follows (repeating each one five times and then calculating an average timing for each test):

1. 300g on the pulley (all other tests were compared to this one)
2. 100g on the car and 200g on the pulley (so the mass of the system remained constant at 300g, but the force decreased as there were less weights on the hook pulling the car down)
3. 200g on the car and 300g on the pulley (so an increase in mass of the system – 500g vs. 300g – but the same force as in test 1)
4. 400g on the pulley, nothing on the car (an increase in mass and force compared to test 1)

The Results

Although our method of measuring the acceleration in the experiment was very inaccurate due to our assumptions and the human error in timing (it would have been much more accurate had we light gates at our disposal), we did find the right relationship between force, acceleration and mass, i.e. that F=ma, or if we flip the formula around, a = F/m.

Acceleration in test 1 was higher than for test 2, which we would have expected as there was a higher force in test 1 – 300g of weight on the hook, equating to 0.3kg x 10 (gravitational pull) = 3N (Newtons) of downward force, as compared to 200g or 2N of force in test 2.

Similarly, the acceleration in test 3 was lower than that of test 1, which again we would have predicted from Newton’s a = F/m second law, because although the force was constant in both (at 3N), the mass in test 3 was higher (500g + the mass of the car) versus that of test 1 (300g + the mass of the car).

Finally, the acceleration for test 4 was the highest of them all as it had the greatest force (400g of weight on the hook, or 4N of downwards pull).

Although a lack of light gates made this a more complicated experiment, having an opportunity to play around with force and mass and seeing the impact on the acceleration of the car was a really helpful way of embedding the formula in their minds. And all I had to buy was a cheap pulley, a hook and some weights.

Experiment Three – Catapulting Projectiles

Bean10 (can’t believe he’s double figures now) already had this Engino Newton’s Laws Set. Within this was a simple experiment to build a catapult and test Newton’s second law by firing projectiles of varying mass to see the impact on the acceleration. Please note it’s a great set, but you don’t need to purchase for this experiment. Instead you could make your own simple catapult.

Once the catapult was constructed, we conducted three different tests to see how far it could propel one wheel, two attached wheels and finally a three-wheel construction (each wheel had a mass of 25g).

Each time, the force was the same – they pulled the catapult back to the same starting position each go and the tension of the rubber band also remained constant – but the masses were obviously different (25g, 50g and 75g), resulting in varying accelerations (as measured by how far each wheel construction was projected).

They repeated each test four times and worked out an average distance.

As predicted, the lightest projectile had the highest acceleration, travelling the furthest across the room, and the heaviest, with the lowest acceleration, was propelled the least far.

This was a super easy experiment to teach them about the relationship between force, mass and acceleration and it involved shooting things across the room, which seems to go down very well with children and adults alike!

Newton’s Third Law of Motion

“For every force, there is an equal and opposite force.”

So, if two children of the same mass stand on two skateboards (lined up end to end), holding hands over the ends of their boards, and skateboarder A pushes skateboarder B (a good experiment to try), she will feel an equal and opposite force from skateboarder B’s hand. Both should experience the same force but in opposite directions, pushing them both backwards, accelerating away from each other.

Experiment Four – Balloon Rocket

This is such an easy experiment to set up and shows Newton’s third law in action. Firstly, set up two chairs a distance away from each other and tie a string to one of the chairs. Secondly, thread a straw along the string and attach the other end of the string to the second chair. You should now have a piece of string with a straw able to freely move along its length if pushed.

Next, blow up a balloon, hold the end rather than tying it shut and, whilst not letting any air escape, Sellotape it to the straw. Position your balloon rocket at the end of the string where the balloon opening is nearest to a chair. Then, let go and watch the balloon shoot along the string!

Finally, discuss with them how the air shooting out of the balloon creates a force in one direction – backwards – which thus experiences an equal and opposite force in the alternative direction – forwards along the string to the other chair. A fun way of demonstrating his third law!

Experiment Five – Catapulting Bags of Sugar

For this experiment, we used the same catapult from experiment three although this time, we removed its wheels and placed it on a very slippery surface. The children prepared three little plastic bags of sugar sellotaped up into small parcels making them easier to catapult (and let’s face it, to stop sugar getting sprayed across my living room!). The three bags contained 50g, 100g and 200g of sugar.

Next, as per the instructions, we positioned a ruler running away from the back of the catapult with zero lined up to its very back edge as in this photo:

Our aim was to see how far the catapult was forced backwards when it projected the bag of sugar forwards, i.e. to see the equal and opposite forces highlighted in Newton’s third law, in action.

For all of the tests we conduct, I ask the children to predict the outcomes. Here, like they had predicted, as the projectile’s (the bag of sugar) weight increased, the forward acceleration of the projectile decreased (as proven in F=ma, or a=F/m) and likewise, so did the backwards acceleration of the catapult. The sugar travelled less far forward and the catapult less far backwards.

We also discussed why the catapult didn’t move back as far as the projectile was shot forward. They could explain that, whilst there were equal and opposite forces at play as in Newton’s third law, the catapult itself was heavier than the bag of sugar being projected, and so its acceleration for the same force was lower, meaning that it moved less far. They also thought the friction of the catapult along the ground would have been higher than the air resistance slowing the projectile down, reducing the distance moved backwards by the catapult more than the forwards motion of the bag of sugar.

Again, another simple experiment stimulating some good discussion about Newton’s laws.

Experiment Six – Playing with Marbles

Another super simple experiment to set up. All you need are some marbles and a large picture book.

We opened the book out into the centre page and along the crease, we laid out a group of marbles (of the same size) touching each other. We then rolled one marble directly into the group to see what would happen. The result: our rolled marble joined the group of stationary touching marbles, and a different marble popped out the other end.

We repeated with two marbles and this time, two popped out the other end.

As each marble hits the row of stationary marbles with a force A, it encounters an equal and opposite force B, stopping its forward motion. But the forward force A continues to travel through the system, the row of marbles, until it reaches the last marble which is free to move, and so accelerates out of the pack.

With the higher force of two marbles travelling through the system, two marbles are forced out the other end.

Next, we tried varying the sizes of the marbles. Firstly, we rolled in a large marble comparative to the row of touching marbles in the crease. The result: the big marble stopped, and three little marbles rolled out the other end.

In a collision, there is a force on both objects that causes acceleration of them both. According to Newton’s third law, the forces are equal in magnitude and opposite in direction, but according to his second law, that F = ma, if the two objects are unequal in size, the lightest object will receive the greatest acceleration for this same force.

Thus, in the last experiment, there is a greater acceleration of the lighter marbles, and so three of them roll away for the one large marble rolled in.

Finally, they repeated the experiment by this time rolling one small marble into a row of large marbles. This time, as the small marble hit the row of large ones, it bounced off and accelerated backwards faster than one large marble rolled out the other end.

Again this proved that although the forward force of the small marble onto the row of large ones was the same and opposite to the force pushing it backwards, the small and large marble at either end experienced unequal accelerations due to their size inequalities and the smallest accelerated the most.

Exactly as would happen if a lighter skater pushed a heavier skater away – they would move back further than their heavier friend.

The Beans found this experiment really fascinating and played around with many permutations testing out the basic principles of Newton’s laws.

The Practice

They wrote up each experiment in their science journals and finally, to check their understanding of the topic, we completed a whole gamut of practice and exam-style questions from the two books mentioned above along with some from this CGP exam practice book.

For this, they took it in turns to answer questions verbally in our group, always cross-referencing with the answers to ensure they were using the correct terminology.

Here are some examples:

Next, we’re reviewing mass, weight and gravity; Galileo’s famous experiments; and the concept of terminal velocity.

On the basis that I truly believe the very best way to learn a concept is to teach it to someone else, we’re handing over the reins to the children… I’ll be giving them my lesson plans and asking them to work together to teach me and my friend how it all works!

Should be very interesting 😊 I’ll report back on how it goes in our next physics post.