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# Physics, centripetal force and resolving watch

1. So if we were given r and v and had to find the the angle needed on a smooth bank for a car to counteract the tendency of the car to slip up the slope. I've formed 2 different equations, the second one works but the first doesn't.

I don't understand why?

Ncos(#) = mg resolving one way and the other mg=cos(#). Why does mg≠cos(#)?
2. (Original post by BDunlop)
So if we were given r and v and had to find the the angle needed on a smooth bank for a car to counteract the tendency of the car to slip up the slope. I've formed 2 different equations, the second one works but the first doesn't.

I don't understand why?

Ncos(#) = mg resolving one way and the other mg=cos(#). Why does mg≠cos(#)?

You are mixing two “different” coordinates systems. The component of forces along the normal force direction is not Nmg cosθ = 0.

When you are writing the following Netwon 2nd law equations,

N cosθmg = 0

N sinθ = mac

you are using the coordinate system shown in blue.

If you are writing the following Newton’s 2nd law equations,

Nmg cosθ = mac sinθ

mg sinθ = mac cosθ

you are using the coordinate system shown in red.

ac is the centripetal acceleration.

3. (Original post by Eimmanuel)
You are mixing two “different” coordinates systems. The component of forces along the normal force direction is not Nmg cosθ = 0.

When you are writing the following Netwon 2nd law equations,

N cosθmg = 0

N sinθ = mac

you are using the coordinate system shown in blue.

If you are writing the following Newton’s 2nd law equations,

Nmg cosθ = mac sinθ

mg sinθ = mac cosθ

you are using the coordinate system shown in red.

ac is the centripetal acceleration.

Okay, thank you very much. One thing, where you say N-mgcos(theta) =ma sin(theta), should this not be N+ma sin(theta) =mg cos(theta) because ma and N are both acting in the same direction?

Cheers
4. (Original post by BDunlop)
Okay, thank you very much. One thing, where you say N-mgcos(theta) =ma sin(theta), should this not be N+ma sin(theta) =mg cos(theta) because ma and N are both acting in the same direction?

Cheers
No. You may want to revise how to do vector addition to give resultant vector.
mac sinθ is the resultant force.

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Updated: October 29, 2017
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