Wind drag problem with a ball hanging on a rope

In summary: DanYou have too many forces on your diagram. The force from the wind is the force of the drag. So you only have the force from the wind acting to the right.-Dan
  • #1
crememars
15
2
Homework Statement
A 1.2 kg ball is hanging from the end of a rope. The rope hangs at an angle of 25 degrees from the vertical when a 15.0m/s horizontal wind is blowing. If the wind’s force on the rope is negligible, what drag force does the wind exert on the ball?
Relevant Equations
the answer is 5.84 N
1665924593232.png

I drew a FBD but I feel like it's wrong because there are too many missing values. I tried this:

Fy = 0
Tcosθ - Fg = 0
Tcosθ = mg
T = (1.2)(9.8) / cos(25)
T = 12.98 N

Fx = ma
Fwind - Tsinθ - Fdrag = ma
Fwind - (12.98)(sin25) - Fdrag = ma

I don't know how to find these missing values. I feel like I'm approaching the situation wrong? I saw one solution solve it like this:

g(tanθ) = a
(9.8)(tan25) = 4.57

Fx = ma
Fx = (1.2)(4.57)
Fx = 5.48 N

but this doesn't make any sense to me.

any help would be appreciated, thank you !
 
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  • #2
crememars said:
Homework Statement:: A 1.2 kg ball is hanging from the end of a rope. The rope hangs at an angle of 25 degrees from the vertical when a 15.0m/s horizontal wind is blowing. If the wind’s force on the rope is negligible, what drag force does the wind exert on the ball?
Relevant Equations:: the answer is 5.84 N

View attachment 315675
I drew a FBD but I feel like it's wrong because there are too many missing values. I tried this:

Fy = 0
Tcosθ - Fg = 0
Tcosθ = mg
T = (1.2)(9.8) / cos(25)
T = 12.98 N

Fx = ma
Fwind - Tsinθ - Fdrag = ma
Fwind - (12.98)(sin25) - Fdrag = ma

I don't know how to find these missing values. I feel like I'm approaching the situation wrong? I saw one solution solve it like this:

g(tanθ) = a
(9.8)(tan25) = 4.57

Fx = ma
Fx = (1.2)(4.57)
Fx = 5.48 N

but this doesn't make any sense to me.

any help would be appreciated, thank you !
You have too many forces on your diagram. The force from the wind is the force of the drag. So you only have the force from the wind acting to the right.

-Dan
 
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  • #3
topsquark said:
You have too many forces on your diagram. The force from the wind is the force of the drag. So you only have the force from the wind acting to the right.

-Dan
I think I understood, thank you! so the drag would be equal to the x component of the tension.
 
  • #4
crememars said:
I think I understood, thank you! so the drag would be equal to the x component of the tension.
Yes.

-Dan
 
  • #5
topsquark said:
You have too many forces on your diagram. The force from the wind is the force of the drag. So you only have the force from the wind acting to the right.

-Dan
Would that not make it 4.97 N if it is equal to the x-component of the tension in the string?
 
  • #6
No.
But if you show how you get this value, someone may figure out the error.
 
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  • #7
It helps to draw your diagram approximately to scale. Then you can tell if the answer you came up with is in the ballpark (sanity check). If you draw the correct arrangement of the 1.3kg force vector on the ball, the drag vector you are solving for, and the 25-degree angle in the right place, that will be everything you need.
 
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Related to Wind drag problem with a ball hanging on a rope

1. What is wind drag and how does it affect a ball hanging on a rope?

Wind drag is the force exerted by air resistance on an object moving through the air. When a ball is hanging on a rope, it is subject to wind drag because it is being pulled by gravity and is also moving through the air. This can cause the ball to sway back and forth, affecting its trajectory and stability.

2. How does the weight and size of the ball impact wind drag?

The weight and size of the ball can greatly impact wind drag. A heavier and larger ball will experience more wind drag than a lighter and smaller ball. This is because the larger surface area of the ball creates more air resistance, and the weight of the ball determines how much force is needed to overcome this resistance.

3. Can wind speed affect the wind drag on a ball hanging on a rope?

Yes, wind speed can greatly affect the wind drag on a ball hanging on a rope. The higher the wind speed, the greater the force of wind drag on the ball. This can cause the ball to sway more and potentially alter its trajectory.

4. Is there a way to reduce the impact of wind drag on a ball hanging on a rope?

There are a few ways to reduce the impact of wind drag on a ball hanging on a rope. One way is to increase the weight of the ball, as this will help to stabilize it against the force of wind drag. Another way is to decrease the surface area of the ball by making it more streamlined, which will reduce the amount of air resistance it experiences.

5. How does the length of the rope affect wind drag on a ball?

The length of the rope can affect wind drag on a ball in two ways. A longer rope will create more surface area for the wind to push against, increasing the overall wind drag on the ball. However, a longer rope also allows for more movement and flexibility, which can help to reduce the impact of wind drag on the ball's trajectory.

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