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Quick physics question?

Posted by: lightningbob - Tue Jun 26, 2012 9:07 pm
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Quick physics question? 
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Post Quick physics question?   Posted on: Tue Jun 26, 2012 9:07 pm
A 10K ball swings through a 10M arch from 0 degrees to 180 degrees in 1 sec giving us a net force at the 90 degree angle of 10x. If the speed is changed to 10 sec is the net force now X? Assume no acceleration just a constant speed.
Thank you for you time and responces.


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Post Re: Quick physics question?   Posted on: Wed Jun 27, 2012 10:12 am
Sorry, you said a change in speed, as opposed to a change in velocity. What you want to do is split the vectors, and then figure out what the acceleration is (change in velocity) and then multiply that by the mass, do that for both instances, and subtract to get the difference.
Acceleration isn't just a change in the magnitude (the number amount) of speed, it can also be a change in direction. The ball has acceleration, even though the speed doesn't change - but it is counterintuitive because the change in speed is only in one direction - closer or farther to an imaginary line drawn through the center of the string holding the ball. You have to ignore all other movement, which doesn't change. Think of it this way - the ball is moving in a straight line, and something is pulling it out of it's path. That "pull" can be imagined as a force. You have to figure out how much it is moving, taking into account movement that stays the same.

The way you do this is by using vectors - or the amount that the ball is moving left to right (away from the center), and the amount that the ball is moving up and down (towards the center). Together, these will tell you where the ball will move to - but only one changes, and can be counted as acceleration - the change in up and down.

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Last edited by SuperShuki on Wed Jun 27, 2012 1:17 pm, edited 1 time in total.



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Post Re: Quick physics question?   Posted on: Wed Jun 27, 2012 1:08 pm
Is this homework for a physics class?

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Post Re: Quick physics question?   Posted on: Thu Jun 28, 2012 7:51 am
Considering how little sense it makes, I doubt it. Unless the teacher doesn't understand what they're teaching, or lightningbob transcribed it wrong.

Reading the problem, there are a few things unclear, and the units are messed up. Let's see if we can make some sense of it. This seems to be a mechanics problem, so first we'll assume that a "10K ball" is not a ball at 10 Kelvin, but that it's supposed to be a ball with a mass of 10 kg. Furthermore, let's assume that the "10M arch" is a circular arc (that seems to match the degrees further down) with a radius of 10 m (meters). The ball is said to run through 180 degrees of this arc in 1 second.

Next, there's a net force "at the 90 degree angle". According to Newton, F = m * a, so there any force requires an acceleration, but in the last line it is said that we are to assume a constant speed. The only way I can reconcile those two is if we are to assume a constant speed along the arc, with the centripetal force acting perpendicular to the arc and providing the acceleration necessary to keep the ball on the arc. So "at the 90 degree angle" would mean at a 90 degree angle to the arc.

This centripetal force equals F = mv^2 / r = m r w^2 = m r 4 pi^2 / T^2 = 10 kg * 10 m * 4 * pi^2 / 4 s^2 = 100 * pi^2 N (with T the time taken to traverse a full circle, so 2 seconds). If we have the ball take 10 seconds for a half circle, or 20 s for a full one, this becomes 10 kg * 10 m * 4 * pi^2 / 400 s^2 = pi^2 N. So, to make the ball travel 10 times as fast on its arc, you need a centripetal force 10^2 = 100 times as strong.

It's not a linear relationship, but a quadratic one. You can actually see that just by looking at the formula F = m v^2 / r, the v is squared. See also Centripetal force on Wikipedia.

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Post Re: Quick physics question?   Posted on: Thu Jun 28, 2012 8:48 am
Quote:
Next, there's a net force "at the 90 degree angle". According to Newton, F = m * a, so there any force requires an acceleration, but in the last line it is said that we are to assume a constant speed. The only way I can reconcile those two is if we are to assume a constant speed along the arc, with the centripetal force acting perpendicular to the arc and providing the acceleration necessary to keep the ball on the arc. So "at the 90 degree angle" would mean at a 90 degree angle to the arc.


I think he is confusing speed with velocity - he says that there is no change in speed, so he thinks that the acceleration is constant - even though the angle is changing.

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Post Re: Quick physics question?   Posted on: Thu Jun 28, 2012 2:05 pm
Right. The velocity is changing, but it's only the velocity's direction that's changing, its magnitude remains the same. So the speed along the curve is constant.

Lightningbob, if that doesn't make sense to you: the difference between speed and velocity is that velocity is a vector while speed is a scalar. Velocity has a direction (i.e. the direction you're moving in) and a magnitude (how fast you're moving). This magnitude is referred to as speed. As a simple example, imagine you're at a baseball game, in the stands next to the home stretch. The pitcher throws the ball to the batter at 90 mph. This means that the ball's speed is 90 mph, and it's moving left-to-right, which we'll call the positive direction. So, the velocity of the ball is +90 mph. Now the batter hits a line drive right back to the pitcher, say also at 90 mph. The speed of the ball is still 90 mph, but it's now heading right-to-left, so the velocity is -90 mph.

Any change in velocity requires an accelerating force. If that force is always perpendicular to the velocity, then the acceleration will only change the direction of the velocity, not its magnitude, so the speed remains constant. However, the velocity does change, so there is still an acceleration, and a force acting on the object.

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Post Re: Quick physics question?   Posted on: Thu Jun 28, 2012 5:36 pm
Wooohooo!!! I don't think I could have worded this more poorly.

Yes the velocity is constant!!! I guess the answer I was looking for was related to centrifical force. I thought maybe a velocity change of 10X (i.e. 10 times as fast) would change the inertial force by 10.

Thank you for your responces and interpretations of my non-physics worded question.

Oh and it's not for a class I was just wondering.


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Post Re: Quick physics question?   Posted on: Fri Jun 29, 2012 1:46 pm
lightningbob wrote:
Wooohooo!!! I don't think I could have worded this more poorly.

Yes the velocity is constant!!! I guess the answer I was looking for was related to centrifical force. I thought maybe a velocity change of 10X (i.e. 10 times as fast) would change the inertial force by 10.

Thank you for your responces and interpretations of my non-physics worded question.

Oh and it's not for a class I was just wondering.


I think I get what you are saying.

The answer is that no - it doesn't matter if you have a constant velocity that is very high, or a constant velocity that is very low - since the definition of acceleration is change in velocity, and the definition of force is mass times acceleration (or change in velocity), if there is no change in velocity, i.e., acceleration is zero, then you can plug that into the equation f=ma = f=m(0) = f=0.

So it makes no difference (at least according to Newton's laws of physics - in quantum physics things get weird) how fast or slow an object is moving, or in which direction - if the speed and direction is constant, the force is zero.

This is the basis of Newton's first law of motion - something will keep moving at the same speed, and in the same direction, unless this thing that we call a "force" acts on it. Now, a force doesn't necessarily mean that you pick up your hand and hit the ball - gravity is a force, magnetism is a force, and there are other forces in the universe.

Now, there are some interesting things that happen when an object goes faster or slower, or is more or less massive, that were not taken into account by Newton, things that Einstein took into account, but you can only really see these effects when objects are either really massive (like a star, or a black hole) or going really fast, close to the speed of light. That's why physicists are so interested in the cosmos - because that's the only area where they can see things that are so big, and moving so fast, that these effects are noticeable.

All of that is about things that move in a straight line. When things move in a circle, it is because some pull or push that we call a "force" is making it move in a circle. Now, when we are talking about the pull that objects have to each other, we call that force gravity. However, gravity is directly dependent on the mass of the two objects involved, and their distance from each other, and nothing else - and it doesn't matter how fast an object is moving (again, without taking into account the effects that we can only perceive at really big masses and really big velocities). So if the mass of the object stays the same, and the distance between the two objects is the same, the force holding those two objects together will stay exactly the same, no matter what the velocity. Now, if the velocity increases, the force will no longer be enough to keep the same distance between the objects. You can see this for yourself - twirl a ball on a string in a circle, and then increase the speed of the twirling to a faster, constant speed. The ball will pull the string to a farther "orbit", and will stay in that "orbit" as long as you keep the same speed. The change in speeds is called "acceleration", and it results from a "force" which moves the ball farther away from you. The "force" comes from "energy" - the energy needed to twirl the string a little faster.

The reason that the ball keeps spinning in a circle is that the string is exerting a "force" in it - the second you let go of the string, the ball will fly off in a straight line. The farther out the ball is, the longer it has to travel to get around the circle, and therefore the faster it has to travel. To travel faster, to "change the velocity", or in other words, to "accelerate", takes what we call "energy".

All these words - "force", "energy", "acceleration", "mass", etc. are very specific scientific terms, and have very specific meanings. If there is no change in velocity (acceleration), and no change in mass, the force is zero - by definition.

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Last edited by SuperShuki on Fri Jun 29, 2012 2:18 pm, edited 3 times in total.



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Post Re: Quick physics question?   Posted on: Fri Jun 29, 2012 2:02 pm
By the way, don't be afraid to ask - speaking for myself, at least, I like showing off how smart I am. :lol:

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