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# Terminal velocity & angles in triangle of forces watch

1. Hi, I'm a bit confused about a couple of things so I would appreciate some help:

Firstly, is it correct to say that the terminal velocity of an object with a greater mass is larger? My understanding of this is that because drag is proportional to v^2, and when an object reaches terminal velocity drag must = the weight of the object (mg), when the mass increases, drag increases, so terminal velocity must also increase?
If this is right, how do the objects hit the ground at the same time, as Galileo showed?
Also, this will sound like an incredibly stupid question, but it's something I've accepted and never really grasped, how can an object have a velocity if there is no resultant force on it? Like, if it has reached terminal velocity there is no overall force acting on it so how can it be moving? Sorry for asking such a silly question.

My second problem was question (3),(c),(ii) on this paper:http://www.ocr.org.uk/images/62266-q...-mechanics.pdf
I understand how to draw a triangle of forces and how to use Pythagoras' theorem to find the tension, but with this particular example I have no idea how to find the angle between the cable with 70N tension and the weight? As you didn't know the tension in the second cable, you would have to use the other two lines to start drawing the triangle, so you would have to know the angle between them? Unless you worked out the tension in the second cable first and then started drawing the triangle with the 90 degree angle between the two cables. However the question said to draw the triangle first and so find the tension in the second cable, so I don't know how to go about that? I think I'm just missing something really obvious.

Thanks so much if you can help!
2. (Original post by dr-jimmy)
Hi, I'm a bit confused about a couple of things so I would appreciate some help:

Firstly, is it correct to say that the terminal velocity of an object with a greater mass is larger? My understanding of this is that because drag is proportional to v^2, and when an object reaches terminal velocity drag must = the weight of the object (mg), when the mass increases, drag increases, so terminal velocity must also increase?
Drag increases as the velocity increases. That's correct.
The drag force also depends on the shape and size of the object.
So two objects with the same shape and size will experience the same drag force.
If one is heavier (more mass) then the downwards force is greater on it.
The only way you can get the downwards weight to be balanced by the upwards drag is for the heavier object to go faster. This is why heavier objects have a larger terminal velocity if all other things are equal such as shape and size.

If this is right, how do the objects hit the ground at the same time, as Galileo showed?
If the objects are identical they do.
Generally speaking though they don't unless there is no air resistance.
Then their acceleration doesn't depend on mass.

Also, this will sound like an incredibly stupid question, but it's something I've accepted and never really grasped, how can an object have a velocity if there is no resultant force on it? Like, if it has reached terminal velocity there is no overall force acting on it so how can it be moving? Sorry for asking such a silly question.
If there is no resultant force then there is no acceleration. That's it.
So if the object is at rest it stays at rest. If it is already moving it continues to move at the same velocity.

My second problem was question (3),(c),(ii) on this paper:http://www.ocr.org.uk/images/62266-q...-mechanics.pdf
I understand how to draw a triangle of forces and how to use Pythagoras' theorem to find the tension, but with this particular example I have no idea how to find the angle between the cable with 70N tension and the weight? As you didn't know the tension in the second cable, you would have to use the other two lines to start drawing the triangle, so you would have to know the angle between them? Unless you worked out the tension in the second cable first and then started drawing the triangle with the 90 degree angle between the two cables. However the question said to draw the triangle first and so find the tension in the second cable, so I don't know how to go about that? I think I'm just missing something really obvious.

Thanks so much if you can help!
The triangle of forces for this question is a right angled triangle.
You know two of the sides, one is 70N and the other, the hypotenuse, is 120N
Using Pythagoras you can work out the other side. Using trig you can find the angles.
3. (Original post by Stonebridge)
Drag increases as the velocity increases. That's correct.
The drag force also depends on the shape and size of the object.
So two objects with the same shape and size will experience the same drag force.
If one is heavier (more mass) then the downwards force is greater on it.
The only way you can get the downwards weight to be balanced by the upwards drag is for the heavier object to go faster. This is why heavier objects have a larger terminal velocity if all other things are equal such as shape and size.

If the objects are identical they do.
Generally speaking though they don't unless there is no air resistance.
Then their acceleration doesn't depend on mass.

If there is no resultant force then there is no acceleration. That's it.
So if the object is at rest it stays at rest. If it is already moving it continues to move at the same velocity.

The triangle of forces for this question is a right angled triangle.
You know two of the sides, one is 70N and the other, the hypotenuse, is 120N
Using Pythagoras you can work out the other side. Using trig you can find the angles.
Hey, thanks very much for your response! You helped a lot but would you mind if I asked a few more questions to clear stuff up?

'If the objects are identical they do.
Generally speaking though they don't unless there is no air resistance.
Then their acceleration doesn't depend on mass.'

Okay, so if you have two objects of the same shape but different masses, and no air resistance, then they would hit the ground at the same time? (That's very unrealistic I know.) Why is the acceleration independent of mass?

'If it is already moving it continues to move at the same velocity.'
But the force that started it moving in the first place has met a resistive force which has balanced it, how can it still be moving?

'Using trig you can find the angles'
Okay, I see how you would do that, so do you think I was supposed to use trig to find the angle between the first cable and the weight, then draw the triangle, then use Pythagoras to find the tension in the second cable? I was just a bit confused because in the example triangle on the mark scheme there was no labelled angle about from the right angle, and no mention of trig?

Thanks so much for your help, I'm really sorry for asking so many questions.
4. (Original post by dr-jimmy)
Okay, so if you have two objects of the same shape but different masses, and no air resistance, then they would hit the ground at the same time? (That's very unrealistic I know.) Why is the acceleration independent of mass?
The simple answer is that the larger mass needs a larger force to accelerate it downwards (F=ma) but the larger mass has more weight. It's the weight that causes it to accelerate.
Double the mass and you need double the force to accelerate a mass downwards. Double the mass and you get double the force because you double the weight. So all masses have the same initial acceleration due to gravity.
It's the effect of air resistance that stops them hitting the ground at the same time. The smaller the mass, the more the air resistance begins to dominate.
'If it is already moving it continues to move at the same velocity.'
But the force that started it moving in the first place has met a resistive force which has balanced it, how can it still be moving?
Why should it not be moving? It it is already moving, to stop it you need to apply a resultant breaking force. If the air resistance balances the weight then there is no resultant force. So no acceleration or deceleration. It just continues with uniform velocity.
You need to go through Newtons 1st and 2nd Laws again, as this is basic theory for this sort of question.

'Using trig you can find the angles'
Okay, I see how you would do that, so do you think I was supposed to use trig to find the angle between the first cable and the weight, then draw the triangle, then use Pythagoras to find the tension in the second cable? I was just a bit confused because in the example triangle on the mark scheme there was no labelled angle about from the right angle, and no mention of trig?
Mark schemes are not model answers, they are just notes for examiners. They often cause confusion for students.
5. (Original post by Stonebridge)
The simple answer is that the larger mass needs a larger force to accelerate it downwards (F=ma) but the larger mass has more weight. It's the weight that causes it to accelerate.
Double the mass and you need double the force to accelerate a mass downwards. Double the mass and you get double the force because you double the weight. So all masses have the same initial acceleration due to gravity.
It's the effect of air resistance that stops them hitting the ground at the same time. The smaller the mass, the more the air resistance begins to dominate.

Why should it not be moving? It it is already moving, to stop it you need to apply a resultant breaking force. If the air resistance balances the weight then there is no resultant force. So no acceleration or deceleration. It just continues with uniform velocity.
You need to go through Newtons 1st and 2nd Laws again, as this is basic theory for this sort of question.

Mark schemes are not model answers, they are just notes for examiners. They often cause confusion for students.
Oh my god, thankyou! You explain things so well aha this all seems really obvious now. Thanks so much for the help. Also, your icon is brilliant, I can't stop staring at it.

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