Fall Speed Based on Angle: 0°, 45°, 90°

In summary: That seems to be a 3d problem.How am I going to do that?I haven't studied that yet.Can you give me a step by step?
  • #36
Yes.
 
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  • #37
So the total kinetic energy = potential energy at the top?
But that does not give any increase in speed at any given point on the path AD
 
  • #38
No. Total mechanical energy at any point = total mechanical energy at the top.
 
  • #39
voko said:
No. Total mechanical energy at any point = total mechanical energy at the top.

Really?
Shouldn't it be total kinetic+ total potential energy (At that position)= Total potential energy at the top.
 
  • #40
What is total mechanical energy? And what is it at the top?
 
  • #41
Mechanical energy is sum of Potential and kinetic energy
(I will be learning those names in Gr.11)

Now back to the question
##P_E=mg\sin\gamma x##
##E_K=\frac{1}{2}mv^2+\frac{Mv^2}{4}##
so,
##mg0.6=mg\sin\gamma x+\frac{1}{2}mv^2+\frac{Mv^2}{4}*2##
 
  • #42
If I say something you do not know, say that right away :)

I think you are using two variables for the same thing, mass of the system: ## m = M ##. Use just one for simplicity. Then, why do you have *2 in the final equation, which you did not have in the equation for ##E_K##? ##E_K## already includes the energy of both wheels.
 
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  • #43
voko said:
If I say something you do not know, say that right away :)

I think you are using two variables for the same thing, mass of the system: ## m = M ##. Use just one for simplicity. Then, why do you have *2 in the final equation, which you did not have in the equation for ##E_K##? ##E_K## already includes the energy of both wheels.

m=M/2 So linear kinetic energy + rotational kinetic energy
Rotational kinetic energy is ##\frac{Mv^2}{2}##
And you said m =M/2
So mass of two wheels should be 2M
 
  • #44
adjacent said:
m=M/2 So linear kinetic energy + rotational kinetic energy
Rotational kinetic energy is ##\frac{Mv^2}{2}##
And you said m =M/2

I could have been sloppy in my notation. I used ##m## as a dummy variable when talking about the moment of inertia of an abstract cylinder. So it is not the ##m## that we have in the linear kinetic energy. I used ##M## to denote the total mass of the system, which is the ##m## in the linear kinetic energy. It is the mass of the entire system, i.e., the two wheels and the infinitely light rod. The total rotational kinetic energy is ## mv^2 \over 4## or ## Mv^2 \over 4## depending on whether you prefer ##m## or ##M## for the total mass of the system; whichever your preference is, use it in the linear kinetic energy and the potential energy.
 
  • #45
Oj.Then it's ##mg0.6=mg\sin\gamma x+\frac{1}{2}mv^2+\frac{Mv^2}{4}##?
 
  • #46
Like I said, ##m = M##. Just choose one of them and use it everywhere! Then simplify.
 
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  • #47
Oh.My problem is solved now.Did you have all this in mind from the beginning? or Did you solve the problem at first?
-Just curious-
Time to thank you.
 
  • #48
adjacent said:
Oh.My problem is solved now.Did you have all this in mind from the beginning? or Did you solve the problem at first?

Let's put it this way: I knew the general character of motion (uniformly accelerated motion in a straight line - did you get that?) when I initially responded. Then as you were getting stuck at various points I made sure that I had a clear picture of the relevant details.

I suggest that you pay attention to the following: how the 3D problem was reduced to the 2D problem. That is very important in physics! Then how it was simplified further by the choice of the coordinate ##x##. And finally, how conservation of energy was used instead of the tedious force/torque analysis. Reduction of dimensionality, convenient coordinates and conservation laws are the most powerful tools in physics, master them.
 
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  • #49
Ok.Thank you.Since you are so intelligent, What's your education level?
 
  • #50
adjacent said:
What's your education level?

Masters in maths.
 
<h2>What is fall speed based on angle?</h2><p>Fall speed based on angle refers to the rate at which an object falls to the ground when dropped from different angles. This can be affected by factors such as air resistance and gravity.</p><h2>How does the angle affect fall speed?</h2><p>The angle at which an object is dropped can greatly affect its fall speed. When dropped at a 0° angle, the object will experience the maximum force of gravity and will fall straight down at a constant speed. At a 45° angle, the object will have a combination of vertical and horizontal motion, resulting in a slower fall speed. At a 90° angle, the object will experience the least amount of force from gravity and will have a slower fall speed due to increased air resistance.</p><h2>Does the weight of the object affect fall speed based on angle?</h2><p>Yes, the weight of an object can affect its fall speed based on angle. Heavier objects will generally fall faster at a 0° angle due to the increased force of gravity, while lighter objects may fall slower. However, at a 45° or 90° angle, the weight of the object may have less of an impact on fall speed as air resistance becomes a more significant factor.</p><h2>How does air resistance impact fall speed based on angle?</h2><p>Air resistance can greatly affect fall speed based on angle. As an object falls, it will experience air resistance, which increases with the surface area of the object. This means that at a 0° angle, the object will have a smaller surface area and will fall faster due to less air resistance. At a 90° angle, the object will have a larger surface area and will experience more air resistance, resulting in a slower fall speed.</p><h2>Are there any real-world applications for understanding fall speed based on angle?</h2><p>Understanding fall speed based on angle is important in various fields such as physics, engineering, and sports. In physics, it can help predict the motion of objects and in engineering, it can be used to design structures that can withstand different angles of impact. In sports, it can be useful for athletes to understand the trajectory of objects, such as a baseball or football, to improve their performance.</p>

What is fall speed based on angle?

Fall speed based on angle refers to the rate at which an object falls to the ground when dropped from different angles. This can be affected by factors such as air resistance and gravity.

How does the angle affect fall speed?

The angle at which an object is dropped can greatly affect its fall speed. When dropped at a 0° angle, the object will experience the maximum force of gravity and will fall straight down at a constant speed. At a 45° angle, the object will have a combination of vertical and horizontal motion, resulting in a slower fall speed. At a 90° angle, the object will experience the least amount of force from gravity and will have a slower fall speed due to increased air resistance.

Does the weight of the object affect fall speed based on angle?

Yes, the weight of an object can affect its fall speed based on angle. Heavier objects will generally fall faster at a 0° angle due to the increased force of gravity, while lighter objects may fall slower. However, at a 45° or 90° angle, the weight of the object may have less of an impact on fall speed as air resistance becomes a more significant factor.

How does air resistance impact fall speed based on angle?

Air resistance can greatly affect fall speed based on angle. As an object falls, it will experience air resistance, which increases with the surface area of the object. This means that at a 0° angle, the object will have a smaller surface area and will fall faster due to less air resistance. At a 90° angle, the object will have a larger surface area and will experience more air resistance, resulting in a slower fall speed.

Are there any real-world applications for understanding fall speed based on angle?

Understanding fall speed based on angle is important in various fields such as physics, engineering, and sports. In physics, it can help predict the motion of objects and in engineering, it can be used to design structures that can withstand different angles of impact. In sports, it can be useful for athletes to understand the trajectory of objects, such as a baseball or football, to improve their performance.

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