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banked track watch

1. Car travels round banked, circular track. Diagram states:

R cos theta = mg (Bostock & Chandler Applied Maths Vol 1, p. 277)

This makes R greater than mg. The diagram in question includes no centrifugal force increasing the pressure of the car on the track, and R is only equal to mg on a horizontal surface.

Can any one explain how a component can be greater than the force whose component it is?

I must finally be getting senile.
2. (Original post by graham fyfe)
...
Hint:

If the car is not moving, then what's stopping it from slipping sideways on the banked track?

Edit: I've not got the book or seen the picture, so this is partly guess work based on your description.
3. Many thanks for answering so quickly. It's a standard block-on-slope
situation except that the centripetal acceleration is horizontal, so that whereas the reaction force R (often called N) is usually mg cos theta, things are now the other way round with mg = R cos theta, making the reactive force larger than mg, which doesn't seem to make sense.
4. (Original post by graham fyfe)
Many thanks for answering so quickly. It's a standard block-on-slope
situation except that the centripetal acceleration is horizontal, so that whereas the reaction force R (often called N) is usually mg cos theta, things are now the other way round with mg = R cos theta, making the reactive force larger than mg, which doesn't seem to make sense.
Sarcasm at its best
5. (Original post by graham fyfe)
Many thanks for answering so quickly. It's a standard block-on-slope
situation except that the centripetal acceleration is horizontal, so that whereas the reaction force R (often called N) is usually mg cos theta, things are now the other way round with mg = R cos theta, making the reactive force larger than mg, which doesn't seem to make sense.
Can you scan/photograph the page and supporting text. In low res. if possible - some of the pictures on here are over 3Meg! Any comments I make will otherwise just be guesswork.

I had the impression that the object was stationary from your first posting, though that no longer looks to be the case from this latter post.
6. Thanks again, Ghostwalker. I (will try to) append a copy of the relevant page with my understanding (?) of it writ large at the bottom. G. Fyfe

I bet it doesn't work. There's nothing to tell you how.

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