Why isolate n in the x-component for finding speed on a banked turn?

AI Thread Summary
To find the velocity of a car on a banked turn without friction, it is necessary to isolate the normal force (n) in the x-component of the equations. The y-component equation shows that ncos(15) equals the weight (w), leading to the expression n = mg/cos(15). This substitution is crucial because it allows for the elimination of n, creating a solvable system of equations with two unknowns: n and velocity (v). By isolating n and substituting it into the x-component equation, the problem simplifies, enabling the calculation of v. Understanding this process is essential for solving problems involving banked turns in physics.
aron silvester

Homework Statement


The question wants us to find the velocity that the car can take without assistance from friction. The friction, in this case, is the normal friction, weight friction, and the static friction (pointing towards the right). I understand how it got ncos(15) - w = 0 for the y component. What I don’t understand is why do we need to isolate n, which equaled to mg/cos(15), and plug that inside the n for the x-component?
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Homework Equations


It's all in part 1

The Attempt at a Solution


It's all in part 1
 
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Because you have a system of two equations and two unknowns, n and v. You eliminate n in order to solve for v.
 
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