## Running down hill and mechanical working

Physics Narrative for 14-16

#### Filling and emptying stores by working

Here is a particular, but common, example where energy sloshes from store to store as a result of the actions of forces on mass. And, as it's physics, we start off with a simple world: no frictional forces, so no thermal stores. Only two stores are involved: a kinetic store and a gravitational store. And you can keep it simple by focusing on snapshots – just look at the start and end points.

You can increase the complexity whilst still keeping the idea of snapshots – add friction to the imagined world, and so a thermal store. Explore this to see how the height, speed and temperature are affected by how the energy is shared out amongst the stores.

In both cases, energy is shifted to or from the stores by mechanical working – that is, by forces acting on the object that's moving up and down the hill.

- The gravity force shifts energy to or from the gravity store.
- The gravity force shifts energy to or from the kinetic store.
- The slipping forces and drag forces shift energy to the thermal store.

You might remind yourself, in passing, that the frictional forces are dissipative precisely because they act only to shift energy to the thermal store.

#### Rates of change

Figuring out the rate at which the energy is shifted adds another degree of complexity altogether: one that is best left to post-16 studies, even if the situation is frictionless.

However, some semi-quantitative reasoning may help you get a feel for how the quantities interact, so developing more confidence in situations where the conversations in the classroom take a tricky turn. All the evidence points towards a sound understanding resting on this style of thinking, rather than on the ability to substitute numbers into equations.

The general pattern is easy to judge as it's just mechanical working. Where the force and velocity are largest, the power in the pathway will also be largest.

For the linear hill, as you might imagine, this is likely to be near the bottom of the hill, where the velocity is largest, because the force driving the ball down the slope is constant.

For the other two hills, the situation is not so simple, because the force driving the object down the hill also varies – the steeper the slope of the hill, the greater the driving force. For the convex hill, the driving force and velocity will both be largest near the bottom, and so here the power in the pathway will definitely be the largest. The concave hill will have the largest driving force at the top of the hill, but the largest velocity at the bottom. You'd need more precise data about the shape of the hill to say where the power is greatest.

You can begin to reason about situations which aren't frictionless by making connections between the power in the pathway that fills the thermal store and the velocity. Drag forces increase with velocity: sliding forces may do so as well.