Wind Speed Project

[grigabuoy]

Homework Statement

hello everyone,

Im new to this forum but i really need some help doing a physics assignment. I am trying to use Newtons second law and the equation for wind resistance(click link) to determine the the angle made by a specific velocity. The link to the assignment is http://www.instruction.greenriver.ed...Essay2-201.pdf [Broken] . I've tried two different approaches but I am not sure if those are correct.

First, I did draw my free body diagrams and broke them up into components of x and y axis: Here is what I got

x(axis)=(wind resistance)-(m)(g)sin(theta)
y(axis)=(Force of tension)-(m)(g)cos(theta)

From there I've tried to manipulate both equations by solving for m, or g, and plugging into the other equation and solving for theta but thus far I've gotten non-realistic solutions.

So I thought maybe I was doing this a little to complicated, so instead I tried to solve this as if it were a triangle. I know that FT=mass*gravity if the ball is straight up and down. i also can calculate the force of windspeed using the formula, and then from there use some law of sins to get me an angle from the triangle but I am not sure if that's applicable in this scenerio.

Any and all help is much appreciated and thanks in advance

Homework Equations

The ball is experiencing three forces, the tension in the string which works along the direction of the string, The weight of the ball vertically downwards and the drag acting horizontally on the ball in the direction of the wind. Taking the x-axis horizontally in the direction of the wind and the y-axis vertically upwards the tension in the string will contribute a x- and y-component to the equations, since it is working at an angle w.r.t. this x/y axis system.

What would be the two components and their signs in this system?

 

[hage567]

The link doesn't work.

 

[grigabuoy]

Here it is. I just copied and pasted it.


Essay 2 Measuring Wind Speed
Imagine that you are a scientist and that you have just made the most exciting trip of your
life. You are now camped at the south-pole of the Earth. It is a wonder filled place, but
very cold. However, your thirst for knowledge and the supplies flown in regularly sustain
you. In a storm, one day, you lose you last reliable anemometer (measures wind velocity)
when it is struck by lightning. However being the clever scientist that you are, you decide
that this minor setback was not going to deter you from making a wind speed
measurement. You figure out that you need nothing more than a ball (of known mass), a
piece of string and a protractor to estimate the wind speed.
You know Newton's laws of motion. You also recall from the physics class you took
early in your career that the resistive force felt by an object as it moves through air is
approximately proportional to the square of its speed. The equation that enables one to
calculate this force, R (see chapter 6, page 164 of your textbook), is
Av2
ρ
D
2
1
R =
Here D is a dimensionless constant called the drag coefficient that depends on the shape
of the object (for spheres, D has a value of about 0.50), r is the density of air, A is the
cross-sectional area of the object and v is the speed with which the object is moving
through the air.
You realize that you can use the same equation to calculate the force felt by the ball
irrespective of whether the ball moves through the air or whether the wind blows against
the ball. You have several balls in your possession: a baseball, a ping-pong ball, a tennis
ball and a golf ball.
Wake up! You are not on the continent of Antarctica. You are in Auburn, WA and you
have an essay due. You must devise a way to use all this information, a ball and a string
to measure the speed of the wind.
You must have a final expression which relates the wind speed to some quantity you can
measure. What that quantity (or, quantities) is (are) depends on the method you devise.
You should clearly state what assumptions you make to do your calculation. These
assumptions must be realistic and should not oversimplify the problem.
Using the expression you found above, estimate what these measured quantity
(quantities) will be if you used a tennis ball if you had
1) A gentle wind at 15 mph
2) A strong gale at 50 mph
3) A hurricane at about 75 mph
You can look up the dimensions and the mass of the balls or measure them in class.
Which ball would give you the best measurement for each of the above type of winds?
Explain.

 

[grigabuoy]

Or try this one.

http://www.instruction.greenriver.edu/physics/anarayanan/PHYS202Wi2007/Notes/Essay2-Wind.pdf [Broken]

 

[PhanthomJay]

Looks like you've chosen the y-axis along the line of action of the tension force, in which case your equation along the perpendicular x-axis is not correct. "R" acts horizontally. But there is a much easier way to solve for R without involving the tension force. In which direction will the resultant of the weight and wind forces act??

 

[grigabuoy]

horizontall, right?

 

[PhanthomJay]

horizontall, right?

No. When you hold the ball with the string attached and there is no wind, the string and ball are in a vertical position. Now with a wind blowing horizontally from say right to left, the ball will swing upward and to the left and reach an equilibrium position (stops moving) at a certain angle with the vertical. In this position, the weight is acting down, and the wind force is acting left. Why would you expect the resultant of those 2 forces to be horizontal? You can either draw a free body diagram using x as the horizontal axis and y as the vertical axis, and solve for R using the solution to the 2 equations with 2 unknowns (T and R are the unknowns, theta you can measure, so it is known). This is apparently what you started to do, but you had the wrong FBD. To avoid doing the problem this way, you can look at the resultant direction of the weight and wind forces. HINT: IF the wind force was equal to the weight force, the ball would swing upward at a 45 degree angle.

 

[grigabuoy]

Thanks for your help. But I am so lost. Why would I want to solve for R if my teacher gave me the formula for R?

 

[PhanthomJay]

Thanks for your help. But I am so lost. Why would I want to solve for R if my teacher gave me the formula for R?

If I read the problem correctly, the problem has 2 parts. In the first part, you are asked to determine a method of calculating the unknown wind speed. So you can't calculate v if you don't first measure the angle and calculate R. In the second part, you are given the wind speeds, so you can calculate R right off the bat, but they then want want you to determine which type of ball is best to use for the given wind speed. Like it means if you use a heavy ball with a light wind, the ball won't swing very much, so it won't be easy to measure the angle.