**Saturday 7 ^{th} July**

The first lecture of the day was actually a problem solving activity with Professor Martin Freer.

When we teachers are teaching A level physics we are so wrapped up in getting the syllabus finished that we don’t have much time for getting the students to think more deeply about the physics they are learning. At Birmingham University third year students take a course in critical thinking and we looked at some of the questions that they do.

He started the session off by asking how much kinetic energy is needed to get round the loop of the roller coaster.

Students (and this includes undergraduates) commonly relate the kinetic energy to the potential energy i.e. ½mv^2 = mgh where m is the mass of the cart, v is the maximum velocity of the cart, g is gravity and h is the height of the loop. Of course the problem with this is that the cart would reach the top of the loop and fall directly downwards (and anybody in it would be killed). In fact the cart would need about twice the kinetic energy.

The professor about to demonstrate the answer

The professor about to demonstrate the answer

The Professor about to demonstrate the answer

The answer to question (i) is c (in fact there has been an AS question similar to this). When the slinky is released the tension force caused by the mass of the slinky towards its bottom decreases to zero. The bottom of the slinky stays still until the wave moving down the spring reaches it and it gets the “message” that the tension has gone. The tension in the spring determines the velocity of the wave. How fast the wave travels down the spring determines the time for the spring to “know” the tension has gone.

The answer to question (ii) is c. My initial explanation was that the water and the floating body are not part of the oscillating the system so their inertia (reluctance to move) will keep them relatively in place. The real answer can related to the equivalence principle. See http://en.wikipedia.org/wiki/Equivalence_principle for more information.

The answer to (iii) is a due to the position of the pivot.

We didn’t have time to go through all of these problems. The answer to (i) (1) is that the water level stays the same. When the block of ice is floating on water the upthrust created on the ice by water is equal to the weight of the displaced water. When the ice cube is melting its volume changes but its weight remains the same and its exactly equal to the weight of displaced water when the ice cube was frozen therefore the ‘volume of melted water’ fits exactly to the ‘volume of displaced water when the ice cube was frozen’…

So the water level does not change! Newspapers often go on about the effect of melting ice in the sea and rising sea levels but it is in fact ice melting on land that is the problem. I think the answer to (i)(2) is that the water level decreases because this time, when the air escapes, there is a smaller volume of melted water to fill the gap left by the ice. I think the answer to (i)(3) is that the water level stays the same for the same reason as (i)(1). The answer to (i)(4) is that the water level goes down. The nail falls to the bottom when the ice melts. The nail on the bottom is not putting a force on the water but on the base of the tank. Nail only displaces its volume of water.

If you think I am wrong about any of these don’t hesitate to tell me.

We didn’t have any time at all to look at the above problem. Why don’t you have a go.