# How big are newtons and joules?

## An Eccentric Anomaly: Ed Davies's Blog

Previously I've said that a newton is about the weight of a smallish apple and a joule is the potential energy of an apple on a table. A tweet by @UnitFact reminded me to check.

The other day I bought four apples. According to Tesco they have a mass, between them, of 0.575 kg.

Wikipedia gives a formula for the accleration due to gravity at various latitudes which can be turned into Python as:

```def g(Φ):
return 9.780327*(1 + 0.0053024*sin(Φ)*sin(Φ) - 0.0000058*sin(2*Φ)*sin(2*Φ))
```

I'm at 58.25° north so the acceleration due to gravity here is g(58.25) which is about 9.81778 m/s² (or, alternatively, we can say the force of gravity is 9.81778 N/kg) so the weight of the average of those four apples is:

```>>> .575/4 * g(58.25)
1.4113060047880535
```

The apples weigh about 1.411 newtons each. They're not very large apples so, yes, a small apple could weigh a newton.

So what about the potential energy of putting them on a table? Work done is force times distance (as per UnitFact's tweet) so the potential energy is the weight of the apple times the height of the table. We can work out what height table we'd need to have to store a joule by simply taking the reciprocal of the weight:

```>>> 1/(.575/4 * g(58.25))
0.7085635550386379
```

The top of table I'm typing on is about 690 mm high so an average apple from that lot would have just a tiny bit short of one joule of energy relative to on the floor: So there we go: one joule of energy graphically represented. And if anybody wants to prove otherwise they'll have difficulty as I've just archived the data source for dessert.