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

In summary, the question requires finding the velocity of a car without assistance from friction. The equation ncos(15) - w = 0 is used to determine the y component, and n is isolated and substituted in the x component to solve for v. This is necessary due to the system of two equations and two unknowns, n and v.
  • #1
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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  • #2
Because you have a system of two equations and two unknowns, n and v. You eliminate n in order to solve for v.
 

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

How is speed affected by a banked turn?

The speed of an object on a banked turn is affected by the angle of the bank and the radius of the turn. The greater the angle of the bank, the greater the speed can be without losing traction. The smaller the radius of the turn, the slower the speed must be in order to maintain traction.

What is the relationship between speed and centripetal force on a banked turn?

The centripetal force required for an object to maintain a circular motion is directly proportional to its speed. Therefore, as the speed increases, so does the required centripetal force. This is why a higher speed is possible on a banked turn, as the banking angle helps to provide the necessary centripetal force.

How does the weight of the object affect the speed on a banked turn?

The weight of an object has no direct effect on its speed on a banked turn. However, weight does play a role in determining the necessary centripetal force for the turn. A heavier object will require a greater centripetal force, which can be achieved with a higher speed or a steeper banking angle.

What is the role of friction in finding speed on a banked turn?

Friction plays a crucial role in maintaining traction and preventing the object from slipping or skidding on a banked turn. The banking angle helps to increase the normal force, which in turn increases the friction force and allows the object to maintain its speed without losing traction.

How does the shape and texture of the surface affect the speed on a banked turn?

The shape and texture of the surface can affect the speed on a banked turn by altering the amount of friction between the object and the surface. A rougher surface will provide more friction and allow for a higher speed, while a smoother surface may require a lower speed to maintain traction. The shape of the surface can also affect the banking angle needed for the object to maintain its speed without slipping or skidding.

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