Pirate ship!

When I was in the Sixth Form, we were sent to escort a group of new Year 7s on a trip to Alton Towers, which had far fewer ride sin the those days. I tried the Pirate Ship and hated it. The trouble was that I knew I had to outlast the Year 7s, so I had to stay on 10 consecutive times. What was the big problem? I don't think that the forces were large. I'm estimating the radius as about 12m. Using the rapid repeat photograph mode on the camera, I estimate that the ship moved 1.2m in 0.3 seconds through its equilibrium position. That gives a maximum speed of 4 metres per second. So the centripetal acceleration will be vsquared/r = 16/12 = 1.3 m/s/s. That's nowhere near g. But the problem came at the top. For a split second you and the ship stop. The you are in free-fall against the barrier which I found unnerving!

When seagulls follow the trawler: bow waves

I was watching this fishing boat at Silloth and ended up thinking about the way that bow waves form at the front. The boat was moving at a steady speed on a reasonably calm sea. It was almost low tide so the current would have been small so it wouldn't be unreasonable to think of the sea water as stationary with a moving boat on it. So the front of the boat pushes on the water. Molecules in water are close together. You can't compress water very much. So the large mass of water in front of the boat (in tis case all the way to Ireland) gets in the way of the water that is being pushed forward by the boat. Hence the water mounts up. They will gain gravitational potential energy and will then try to lose that by falling. I think this will be why the wave them spreads out.

Year 10: Specific Heat Capacity using liquid nitrogen

I went to a lecture last week at which a piece of iron of mass 469 grams was placed in an insulated tub of liquid nitrogen. Liquid nitrogen boils at -196 degrees Celsius so a block of iron at room temperature (24 degrees Celsius) will seem stupidly hot to it. Thermal energy from the iron block went into the liquid nitrogen by conduction and made it boil.

 This next picture shows you a murky looking iron block below the surface of the liquid nitrogen.

The scales had been zeroed with the tub of nitrogen on top and then the block of iron was added so that the reading on the scales was 469.00 grams. As the liquid nitrogen boiled, nitrogen gas went off into the air and the reading on the scales went down. Here is the final reading.

Now the iron loses 200 Joules of thermal energy for every gram of nitrogen that goes into the air.

1. Calculate the mass of liquid nitrogen that boiled off into the air.

2. Show that 48064 Joules of energy must have gone out of the iron and into the liquid nitrogen to make that much boil away.

3. Use energy = mass x c x change in temperature  to calculate the specific heat capacity of the iron. (Hints: the iron cooled from room temperature to the temperature of liquid nitrogen, and you need to put the mass of the iron into kg to get a decent answer)

4. Look up the true value from the specific heat capacity. We were very close. Explain why that means we can say that the experiment was accurate and give a reason why it is impossible for this experiment to give a perfect answer.

Apples float and pears sink

I went to an excellent cookery demonstration last night. It was said that the way you tell the difference between apples and pears is that apples float and pears sink.  The Internet agrees. This picture shows what I found in my kitchen. The pear is a sweet desert pear. We are wondering if it is a cross with an apple. It is also quite ripe so maybe that makes a difference. Further research is required. Internet answers say that apples continue to "breathe in oxygen". That doesn't sound scientific to me. For a start, breathe is a word used for mechanical ventilation by lungs. Plants absorb gases by diffusion. Perhaps apples do continue to do respiration, for which oxygen would be needed. I will try to find an answer. But respiration would create carbon dioxide gas which would pass out by diffusion. I'm not convinced that the apple ends up pumped with oxygen but I'll try to find a definitive answer.

Things float in water if they are less dense than water. The pear is almost under water so it must be very close to 1 gram per cubic centimetre. The apple sits higher in the water.

Archimedes says upthrust = weight of water displaced. Since the volume of water displaced is almost equal to the volume of the pear, density is almost water. Upthrust has to equal 0.098kg x g.

Upthrust = 0.129kg x g but say 10% of the apple is above the water. Then perhaps the density is 0.9 grams per cubic centimetre.

Bass: how low can you go?

It was Rock Night last night. Thanks to those who came and to those who made it happen! I was looking at the bass bins. Speaker cones are meant to spread out the sound waves in all directions by diffraction. In other words, it would be bad if you could only hear the sound if you were stood directly in front of that speaker cone. What if you were slightly off to one side? Diffraction takes sound waves and makes them into semi-circular wavefronts going in all directions. But it works best if the size of the hole is the same as the wavelength. Take the stop speaker. Diameter is roughly 30cm. For waves, speed = wavelength x frequency. The speed of sound is roughly 330 m/s. If the wavelength is 0.3m, then frequency = 1100 Hz. I've never done the calculation before. That's a surprisingly high frequency for bass. The slightly smaller cones below will work best for even higher frequencies. So if you want to hear the very lowest frequencies best, you'd probably need to stand more or less in line with the speaker.

Sixth Form question: how far away is Blackpool Tower?

You might need to enlarge this picture to see Blackpool Tower!
Imagine a triangle that goes from my eye to the top of my little finger, down to the bottom of my little finger and then back to my eye. Show that the angle at my eye end is about 0.5 degrees. Then compare Blackpool Tower with my little finger and use similar triangles to work out how far away I was stood from Blackpool Tower. You might even be able to tell me where I was!

Sky Mirror at Nottingham Playhouse

Sky Mirror is a work of art by Anish Kapoor outside Nottingham Playhouse. It is a polished silver bowl. We'd say that the sky is at infinity as far as the study of Optics is concerned. That's because all the rays of light coming from the sky to the mirror will be parallel. Those hitting the top of the mirror are reflected downwards. Those hitting the bottom of the mirror are reflected upwards. Standing this far away, the rays coming down from the top cross over with the ones going up from the bottom and the picture is upside down. If the mirror is parabolic, there should be a single focal point. If you stand closer than the focal point, the rays don't cross and your reflection is the right way up.

The convex side was harder to see due to building works.

This diagram shows why the image is the right way up, because the rays never cross over.

You see a virtual image - you behind the mirror. If it is the same distance behind as you are in front, the fact that your brain thinks the rays get closer together behind the mirror makes you look smaller.

Of course, you can test all of this with a spoon.