## September 18, 2011

### 4.11 Gravitational Potential Energy

Recall and use the relationship:

$\small Gravitational\, potential\, energy\, =\, mass\times gravitational\, field\, strength\times height$
$\small GPE=m\times g\times h$

Increasing either your mass, height or gravitational field strength (going to another planet is the easiest way to do this) will give you a higher GPE, and vice versa, lower your weight/height and you lower your GPE.

Example:

If a 750kg car is at the top of a 50m slope with a vertical height of 10m, how many Joules of GPE does the car have? (g on earth is 10N/kg)

$\small GPE=m\, g\, h$
$\small GPE=750kg\times 10N/kg\times 10m$
$\small GPE=75,000J\, or\, 75kJ$

Note: we use the vertical height (10m) appose to the slope height (50m) because weight acts in straight line from the ground.

Important: we often say that an object has no GPE when it is on the ground, but if we were to have a swinging pendulum it obviously wouldn’t touch the ground so we say that it has 0J of GPE when it is at its lowest point. Basically during experiments we say that the object has 0J of GPE when it is at the lowest point possible, this is because theoretically we could measure all objects GPE from the centre of the earth, but it is not convenient to do so.