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November 01, 2025, 09:09:31 am
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Author Topic: Leaning into banked turns  (Read 899 times)  Share 

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cameron_15

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Leaning into banked turns
« on: June 05, 2010, 09:20:57 pm »
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Questions where cyclists are leaning into a corner to turn faster.

I know that part of the reaction force acts towards the center, however thats about all i can find in my textbook...

How do we calculate the force towards the center that is due to the leaning?

Is it F = mg cos Theta?

Where F is the horizontal component of the weight force and Theta is the angle of leaning...

If thats wrong, please, please correct me!
« Last Edit: June 05, 2010, 09:28:02 pm by cameron_15 »
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cameron_15

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Re: Leaning into banked turns
« Reply #1 on: June 05, 2010, 09:56:01 pm »
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Here's a question:

A cyclist rounds a bend of radius 10 meters with a speed of 9 m/s. the surface of the road is horizontal. the cyclist is forced to lean at an angle of 20 degrees to the vertical to make the turn. total sideways frictional force on the tires is 360N. the bike has a mass of 20kg, what is the mass of the cyclist?

At first glance, i thought easy! Lots of info, not to sure where the angle comes into play on this one.

What I did was equated F = MV^2/r to 360, then solved for mass. Which was wrong.

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Stroodle

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Re: Leaning into banked turns
« Reply #2 on: June 05, 2010, 10:33:51 pm »
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I don't think they'd have this question on an exam...



and



but,











Bloody Jacaranda...

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cameron_15

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Re: Leaning into banked turns
« Reply #3 on: June 05, 2010, 10:40:28 pm »
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Wow, awesome, thanks!
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VCE: Biology 42 (43.23)|Chemistry 42 (45.88)|English 43 (42.87)|Physics 45 (47.07)| Maths methods 40 (45.14)|Specialist maths 34 (41.70)

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googoo

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Re: Leaning into banked turns
« Reply #4 on: June 06, 2010, 07:48:06 am »
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Quote from: cameron_15 on June 05, 2010, 09:56:01 pm
Here's a question:

A cyclist rounds a bend of radius 10 meters with a speed of 9 m/s. the surface of the road is horizontal. the cyclist is forced to lean at an angle of 20 degrees to the vertical to make the turn. total sideways frictional force on the tires is 360N. the bike has a mass of 20kg, what is the mass of the cyclist?

At first glance, i thought easy! Lots of info, not to sure where the angle comes into play on this one.

What I did was equated F = MV^2/r to 360, then solved for mass. Which was wrong.



The given data don't add up.
The combined weight=360cot20=989, combined mass=98.9
98.9x9^2/10 not equal 360.
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lachymm

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Re: Leaning into banked turns
« Reply #5 on: June 06, 2010, 11:33:25 am »
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What does the "R" represent?
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Stroodle

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Re: Leaning into banked turns
« Reply #6 on: June 06, 2010, 03:01:25 pm »
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Rsin(20) represents the component of R (the reaction force of the earth pushing back on the cyclist) which contributes to the centripetal force.
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