Year 10 Acceleration equation experiment

I set up a light gate at the bottom of my ramp. The can was stationary at A and accelerated down the slope to B where the light gate timed how long it took for the can to pass through. The timing works because the can blocks the infra-red light beam for a certain amount of time.
Here's the data we need to work out the speed:
1. I lined up the 0cm end of the ruler with one side of the tin.

2. Then I looked straight down on the reading on the other side of the tin.

Notice that it doesn't look like the 0cm end is lined up correctly anymore. This is an example of parallax error. It is really lined up but doesn't look like it when you change the angle.
3. Here is the time for the diamter of the tin breaking the infra-red beam

4. We can now use velocity = distance/time to calculate the velocity of the tin at B in the original picture, at the bottom of the slope.
5. Next we need an equation:

6. We know the final velocity at B and the initial velocity at A. If we want to calcuclate the acceleration all we need to know is the distance that the tin rolled down the slope. There was a danger of parallax error at the bottom of the slope because the light gate was well above the ruler and I could read it at the wrong angle. So I used a smaller ruler to make sure that 0cm on my big ruler lined up the the light gate.

 Then I looked at the top of the slope and got this reading for the distance the can rolled.

7. I put all of the readings into metres and calculated. I foundout that the acceleration was 1.4 m/s/s.
8. Then I realised that as the tin rolled along the floor it slowed down and stopped. I reaised that I could use the same equation to calculate the deceleration from B to C below.

All I had to do was to measure how far it rolled along the floor. Here's the reading

9. Friction caused it to decelerate and stop. This time I got -0.46 m/s/s. The minus sign means slowing down not speeding up. Acceleration is a vector so it can be negative as well as positive.

Covid graph update and the constant ratio property

This week the 7-day rolling average for Covid deaths reported in the UK is 87. I have added it to the graph. The gradient is the same as last week so the trend continues and the R-squared value is slightly higher so the trend is more certain.

Another way of assessing exponential decay is to look for a constant ratio property. This is when you do the current data point divided by the previous data point. The answer should be the same all the way down. Here's what I got:

The numbers have fluctuated a bit but the current mean ratio is 0.823. If the trend continues the prediction is that the 7-day rolling mean should be 72 this time next week.

Half-life experiment

Radioactive decay is a random process. The nuclei of the atoms of radioactive elements are unstable and can fall apart at any moment sending out radioactivity. This is called radioactive decay. You can't predict which nucleus will decay next in the same way that you can't know for certain whether one coin will come up heads or tails. But if you have a lot of coins or a lot of atoms then you can start to predict what will happen overall.
For this experiment I took 20 identical coins. I scooped them up into both hands and jangled them around to make them random before dumping them on the table.

 I removed any that were "heads". They had "decayed and were no longer radioactive. I counted what was left.

 Then I scooped up what was left and jangled them in both hands before dumping them on the table. I removed the heads and counted the rest and so on. For each throw, I wrote down how many I counted. In theory, you'd expect the number left to halve each throw. So we can't say which coins will be removed - it's random - but we can predict that half of them will be removed. You can't predict for an individual but you can predict for a large group. That's what half-life is for radioactivity.

In class I normally use 6-sided wooden cubes that I call dice. One side of each cube is marked. I do the same experiment but remove the ones that come out marked side up each time.

This time the chance of one being removed is much lower. It takes longer for the numbers to go down - more throws before the numbers halves. We'd say that the dice have a longer half-life than the coins.

A second momentum experiment

I went back and did an experiment with different masses. In the first experiment I rolled a half-sized tin into a full-sized one. They rolled but not far. Half the amount of momentum shared between one and half masses should mean that they move on at about one third the speed of the small tin coming off the slope. 

 I then did the experiment the other way round. You can tell from the photo clipped from a video that the tins are still moving. They ended up out of shot. The big tin leaves the slope with more momentum which it shares with the small tine. The resultant common speed is much larger.

A big tin and a small tin will not leave the same ramp at the same speed. There are several issues there that will need some further exploring.

Momentum experiment

Any moving object has MOMENTUM. Momentum tells you how hard it is to stop a moving object. The higher the momentum, the harder to stop. You calculcate momentum by doing momentum = mass x velocity.

I got two identical tins from the kitchen. The more solid the contents, the better the experiment because if the liquid inside can slosh around, it can affect the movement of the tin.

I put tin A at the top of the slope and let it roll down the slope into tin B. Only tin A was moving before they collided so only tin A had momentum.

 When tin A hit tin B, they both roled on a short way but at half the speed at which tin A was going originally. This is because only tin A brought momentum into the collision and now it has to share the momentum with tin B. Bceuase they are identical tins, each should get half the momentum and thus be going at half the velocity.  After the collision, there is still the same total momentum as there was before but it now shared outl. Keeping the amount of momentum the same before and after is called CONSERVATION OF MOMENTUM. (It doesn't last long because this rule of Physics only works until friction on the carpet acts on the tins)

 Then I set up two ramps at the same height to create a head on collision. Tin A is coming towards us and so we say it has POSITIVE momentum. Tin B is going away so we say it has NEGATIVE momentum. Momentum has a direction so we say that it is a vector.

Now let's say tin A has momentum +10 and tin B has momentum -10. The total momentum means adding them together. +10 + (-10) = 0. So if momentum is conserved, there will be the same total momentum after the collision: ZERO total momentum. What happened was that the tins stopped dead when they hit each other so it turned out to be true.

If we did this with tinsof different mass they would not stop dead because momentum = mass x velocity so one tin would have more momentum than the other. Try it.

Year 10 Cup cake cases experiment

Take one cup cake case and hold it up as high as you can. Time it as it falls to the ground. Do this 3 times to check that the result is REPEATABLE. It should fall at roughly a steady speed because it has a small weight (pull of gravity) and a large surface area so it is easy for the air resistance (drag) to become so large that it is the same size but opposite direction to the weight. When this happens, the resultant force is zero and there is no acceleration so it falls at a steady speed called the TERMINAL VELOCITY.

 Now put a second cup cake case inside the first. Hold it up as high as you can and drop it, timing the fall. The weight has doubled but the area is still the same so the only way the air resistance can double to achieve zero resultant force and terminal velocity is by going much faster.

 Keep adding cup cake cases, stacked inside each other to increase the weight whilst keeping the area the same.

Here is my graph. Notice the small random errors shown by points not quite on the best fit line. This is our third falling forces experiment and the pattern is still the same on the graph. It is further evidence that the theory of weight, air resistance and terminal velocity is true. The findings of the first experiment have turned out to be REPRODUCIBLE - same independent variable, same dependent variable, same control variable but different situation and yet STILL THE SAME PATTERN.

Covid graph update - back to the original gradient

I have been taking the data on a Wednesday for the 7-day rolling average. I used this site to calculate the average for the last 7 days and got 118, exactly the same as last week. I have added it to my graph and got Excel to calculate the trendline. It is now back to almost exactly the same trendline as when I first calculated it 3 weeks ago.

The points are now further from the line but that is often the case if Physics experiments that plot a graph like this for discharging a capacitor. When the current is low and there are fewer significant figures, the uncertainties are higher and points can be further from the line. This explains why the R-squared value is lower this week.