Foam rubber ball hanging in a string - Forces

[Norway]

Homework Statement

Okay, so I'm not originally an English speaker, so this may be silly reading for some of you, especially a lot of the words here, which isn't to find in the dictionaries either, but hopefully you'll at least get a picture of the task and help me solve it.

The drag (air resistance) of a ball made of foam rubber, is:
$$L = (8,7 \cdot 10^{-4} Ns^2 / m^2)v^2$$
The ball has a mass of 8,0 g.

We attach the ball to a piece of string hanging from the ceiling, and in front of a reversed vacuum cleaner. LOL. I have no idea what to call that machine in English, but it creates an air flow the affects the ball when it's hanging there in midair.

The air flow makes the ball move to the side, so that the string makes an angle of 38 degrees compared to straight down.

Draw an illustration showing the forces affecting the ball. Find the speed of the air when it passes the ball.

Homework Equations

I mentioned the only equation earlier, I think.

The Attempt at a Solution

No idea how to start. As for the drawing, I've written the gravitational force G straight down, the wind force V directly right and the string force parallel to the string, going from the ball. Is that correct? Anything else?

Thanks a lot.


Edit: I guess I could have called that "machine" a fan, and made it easy for myself. Lol.

 

[kuruman]

You have drawn the forces correctly. Now all you have to do is add them as vectors and say that their sum is zero. Don't forget to convert the mass from grams to kilograms.

** Edit **

A "reverse vacuum cleaner" is perfectly understandable.

 

[tomcue]

I would like to provide the following response:

Firstly, it is important to understand the concept of forces and how they act on objects. In this case, we have three main forces acting on the foam rubber ball: the gravitational force (G), the wind force (V), and the string force (T). The gravitational force is always directed downwards towards the center of the earth, while the wind force and string force can vary in direction depending on the conditions.

In order to understand the motion of the ball, we must consider the net force acting on it. This can be calculated using the formula F=ma, where F is the net force, m is the mass of the object, and a is the acceleration. In this case, the acceleration is caused by the wind force, as it is the only force acting on the ball in the horizontal direction.

Next, we can use the given equation for drag (air resistance) to calculate the wind force. This equation takes into account the velocity of the ball, which we can find using trigonometry and the angle of the string. Once we have the wind force, we can plug it into the F=ma equation to find the acceleration of the ball.

Finally, to find the speed of the air passing the ball, we can use the equation for drag again, but this time solving for the velocity (v). By rearranging the equation and plugging in the values for the drag coefficient, mass of the ball, and acceleration, we can find the speed of the air.

As for the drawing, you have correctly identified the three main forces acting on the ball. However, it is important to also consider the direction of these forces and how they balance each other out to determine the motion of the ball. I would recommend drawing a free body diagram to better visualize the forces and their directions.

I hope this helps in solving the problem and understanding the concept of forces. As always, it is important to carefully consider all given information and equations, and to double check calculations for accuracy.