Sticks

2009-May-07, 01:30 PM

This one is inspired by large bridges, such as the Humber Bridges.

It is known that in real long bridges, they need to take into account the curvature of the Earth, so that the distance between the towers at the top is greater than the distance at the base of the towers.

Suppose you had a very long bridge and so the towers are built so that they are both tracing a line that leads to the centre of the Earth. (See attached diagram)

The bridge deck however is perfectly flat and frictionless. In fact it is parallel to a line through the centre of the Earth. It is perpendicular to the line from the centre of the Earth that bisects the angle the line of the bridge towers make at the centre of the Earth.

The Bridge deck is made of a fictional material that keeps it rigid and does not flex. Assume no issues with weather.

Again see diagram.

Now suppose we take two bowling balls, place one at a bridge tower and one at the centre of the bridge deck.

When the balls are released, will the ball at the tower roll, if so which direction. It is the same question with the one in the centre of the bridge deck. The one in the centre of the bridge deck, if it is placed slightly off centre in either direction towards either tower, what should happen.

Explain your reasoning.

I will wait before I give my thoughts.

:think:

It is known that in real long bridges, they need to take into account the curvature of the Earth, so that the distance between the towers at the top is greater than the distance at the base of the towers.

Suppose you had a very long bridge and so the towers are built so that they are both tracing a line that leads to the centre of the Earth. (See attached diagram)

The bridge deck however is perfectly flat and frictionless. In fact it is parallel to a line through the centre of the Earth. It is perpendicular to the line from the centre of the Earth that bisects the angle the line of the bridge towers make at the centre of the Earth.

The Bridge deck is made of a fictional material that keeps it rigid and does not flex. Assume no issues with weather.

Again see diagram.

Now suppose we take two bowling balls, place one at a bridge tower and one at the centre of the bridge deck.

When the balls are released, will the ball at the tower roll, if so which direction. It is the same question with the one in the centre of the bridge deck. The one in the centre of the bridge deck, if it is placed slightly off centre in either direction towards either tower, what should happen.

Explain your reasoning.

I will wait before I give my thoughts.

:think: