Ideal speed given radius and angle

In summary, the ideal speed to take a 70 m radius curve banked at a 30.0° angle can be found using the equation v= √ g*r* tan Θ, but it is important to ensure that the calculator is set to degrees instead of radians to avoid errors.
  • #1
Mariesa Yeoman
14
3

Homework Statement


What is the ideal speed to take a 70 m radius curve banked at a 30.0° angle?

Homework Equations


tan θ = v2/r g

The Attempt at a Solution


This has me stuck, when I attempted this I came to the equation v= √ g*r* tan Θ
But when I substitute in the variables, I enter then into the calculator and it show answer undefined? Is this not the correct formula? or am I simply doing it wrong?
 
Physics news on Phys.org
  • #2
It has nothing to do with the formula. Be sure your calculator is set to degrees. In radians tan(30) is negative and trying to take the square root of that will cause an error.
 
  • #3
I guess I am just unsure of how to do the problem?
 
  • #4
Mariesa Yeoman said:
I guess I am just unsure of how to do the problem?
I would say @kuruman has almost surely identified what you are doing wrong.
Do you not know how to set your calculator to degrees instead of radians? If so, enter the angle in radians. 30° is π/6. Its tan should be 1/√3, about 0.5774.
 
  • #5
Ok that took care of it, Thank you so much!
 

What is the ideal speed for a given radius and angle?

The ideal speed for a given radius and angle depends on various factors such as the weight of the object, the surface on which the object is moving, and the force applied. However, as a general rule, the ideal speed for a given radius and angle can be calculated using the formula: V = √(r x g x tanθ), where V is the ideal speed, r is the radius, g is the acceleration due to gravity, and θ is the angle.

How does the radius affect the ideal speed?

The radius plays a significant role in determining the ideal speed for a given angle. The larger the radius, the higher the ideal speed required to maintain a stable motion. This is because a larger radius requires a greater centripetal force to keep the object moving in a circular path, which in turn requires a higher speed.

What is the relationship between angle and ideal speed?

The angle of an object's trajectory also affects the ideal speed. The steeper the angle, the higher the ideal speed required to maintain the object's motion. This is because a steeper angle requires a greater force to overcome the pull of gravity and maintain the object's circular motion.

How does weight affect the ideal speed for a given radius and angle?

The weight of an object can affect the ideal speed for a given radius and angle. A heavier object will require a higher ideal speed to maintain its motion compared to a lighter object. This is because a heavier object will have a greater inertia, and therefore, a higher speed is needed to overcome this inertia and maintain a stable circular motion.

What happens if the ideal speed is not maintained for a given radius and angle?

If the ideal speed is not maintained for a given radius and angle, the object may lose its circular motion and either slow down or veer off its path. This can result in the object falling or colliding with other objects, causing potential damage or injury. It is essential to carefully calculate and maintain the ideal speed for a given radius and angle to ensure safe and stable motion.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
893
  • Introductory Physics Homework Help
Replies
15
Views
1K
  • Introductory Physics Homework Help
Replies
22
Views
1K
  • Introductory Physics Homework Help
Replies
15
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
832
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
104
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
Back
Top