Banked road need to find the angle

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To calculate the banking angle for a road designed for a speed of 43 km/h and a radius of 0.075 km, the relevant equation is tan(θ) = v²/(rg), where v is the velocity and r is the radius. The velocity must be converted to meters per second, resulting in 11.944 m/s. Users are unsure about how to derive this equation from the forces acting on the vehicle, particularly the centripetal force, and how to resolve the components of the normal force. Clarification on the relationship between centripetal acceleration and the banking angle is sought, emphasizing the need for a solid understanding of the physics involved. The discussion highlights the importance of understanding the underlying principles to solve for the angle effectively.
LDRshipphysic
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Calculate the angle at which a road should be banked for a design speed of 43 km/h and a radius of .0075 km.

Givens : radius: .075km = 75m
Vt(maybe?): 43 km/h = 11.944m/s

Unknown: angle

Im not shure about what equations to go about solving this for i know in the end I am probly going to have to cancil out mass's because that isn't given to you.. If anyone can help me it would be soooo nice!

 
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What i attempted to do so far was

Fc=(mvt^2)/r i think i know what the diargram should look like, I am unshure on how to solve for the componits that make up the diargram tho such as Fnx, and Fny, if there was some way i could figure out the compents for Fn then i could figure out how to solve for the angle using trig functions
 
But because i don't know the mass of the object I am unshure how to go about solving it
 
How do u get

Ok, in my physics homework i know the equation that i have to use is tan(θ) = v2/rg but i don't know how you get to that, if there is some way to find out, that would be sweet for your assistance. I know that v2/r is equail to the centripital acceleration but you I am not shure the base equations that would be used, If you can help that would be great thanks.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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