## Shifting energy between gravitational and kinetic stores

Classroom Activity for 14-16

What the Activity is for

This demonstration allows you to calculate the energy shifted between kinetic and gravity stores. Several different starting points are easy to arrange, depending on whether the mass starts off up or down, and the trolley starts off moving or stationary. Adapt the possibilities to suit the class and the evolving discussion. You can and should calculate the efficiency of the system.

What to Prepare

- 3 retort stands
- 6 bosses and clamps
- 2 glass rods
- 1 single pulley
- some Blu-tack
- 1 sturdy platform (approximately 5 centimetre by 15 cm)
- a 30 cm ruler
- a 1 m ruler
- 1 high-quality dynamics trolley (low friction – runs a long way from a moderate shove)
- some stiff card (about 13.5 centimetre by 10 cm) to attach to the top of the trolley
- 1.5 m of 15 lb breaking strain fishing line
- 1 light gate and timer
- 1 10 g mass holder
- 2 10 g and 1 5 g masses to fit holder

**Safety note: **Take care to anchor the retort stands carefully so that the glass rods are not inadvertently stressed.

What Happens During this Activity

The photograph shows one way to set up the equipment that works. If you have a low-friction pulley wheel then hook it over the top glass rod and fix it in place using a small amount of Blu-tack. If the pulley wheel is not so good, you may be better off just using the glass rod itself as a pulley. Arrange it so that the 10 gram mass holder falls 30 centimetre. Pull the trolley 80 centimetre back from the bottom glass rod. Place the light gate 30 cm from the bottom glass rod so that when the trolley passes through it the 10 g mass has landed on the platform, allowing the fishing line to go slack. As you pull the trolley back, look down the length of the equipment to aim the line of sight of the trolley through the light gate – you don't want to miss.

#### Opening up the discussion

Teacher: Here we have a demonstration where we can calculate energy shifted. There's a small mass of 10 g, which will fall when I release it. This is attached to a dynamics trolley by some fishing line. The trolley has very free-wheeling wheels and the bench is very smooth. Why do you think that's important?

Bill: To minimise the energy wasted by frictional forces on the car wheels.

Teacher: Good, but can anyone suggest a clearer idea than just wasted? Neil?

Neil: Dissipated, Miss…

Teacher: That may be a more helpful description than wasted

, but can you tell me a bit about the thinking that lies behind it? Yes, Judy…

Judy: The energy is spread out, Miss.

Teacher: Yes Judy, that's along the right lines. Can you remember where we look for energy?

Sharran: In stores, Miss. It's always stores.

Teacher: Now let's pull our suggestions together. Lower frictional forces result in less energy being shifted to many stores, and more energy being kept in fewer stores. Keep that in mind as we go back to the apparatus. Now, as I let the mass fall like so, you'll see that the trolley will begin to move. Picture the energy being shifted. The gravity store is emptied. Which store is filled?

Jess: The store to do with movement… what is it called?

Teacher: Yes – the kinetic store. Now this system, as you know, can't be 100 % efficient: not all of the energy is shifted from the gravity store to the kinetic store. We can calculate the energy shifted from the gravity store and the energy shifted to the kinetic store. How can we do this?

Emil: one store of energy is mass (0.01 kilogram) × g (9.8 metre^{second-2}) × height (0.3 metre), which is 0.029 J, and the other store of energy is 12 × *m* (0.25 kg) × *v*^{ 2}.

#### Discussing the experiment

Teacher: Good. Energy is shifted from the gravity store to the kinetic store. But does it all end up there? Yes, Katy?

Katy: No, Miss, some stuff gets warm.

Teacher: Yes. Some energy is shifted to different thermal stores. You can see that the potential energy lost by the mass is easy to find (0.029 joule). The final speed of the trolley once the mass has fallen 30 cm is more difficult to find. The way that we'll do it is by using a light gate. You can see that the trolley has a piece of card (0.135 m long) attached to it. When this card passes through the gate, the time taken to do so is recorded. We can then find the speed of the trolley as speed = distanceduration. So speed = length of the cardtime taken (in seconds). In fact, if we let the mass fall three times and then find the average time of the card through the light gate, this would be a more reliable method, so let's do that.

Now let the mass fall three times and write on the board the potential energy lost by the mass (0.029 J) and the average velocity and average energy in the kinetic store of the trolley.

The time displayed on the light gate will be in millisecond and you should be sure that the students know how to convert milliseconds into seconds (divide by 1000). For the relationship to work the time must be in seconds.

Teacher: Now we will use these to find the efficiency of this system. efficiency = average energy gained by the trolleyenergy lost by the falling mass × 100 %.

(The efficiency from trial data was around 60 %.)

There is at least one other possibility worth exploring – the energy starts in the kinetic store, is shifted to the gravitational store and then returned to the kinetic store. You'll need to adjust the set-up to make the measurements, but it is worth exploring several possibilities as energy is shifted to and fro between the stores.