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Uni Stuff => Science => Faculties => Physics => Topic started by: trinon on March 12, 2010, 12:04:54 am

Title: trinon's advanced physics question thread
Post by: trinon on March 12, 2010, 12:04:54 am: Hey guys. Now that I've began my advanced physics subject at melbourne uni, I expect that there will be many questions arising from tutorial sheets and whatnot. So in expectation of the near future, I'm creating this thread with some top notch questions to boot! Your help will be much appreciated.

Q: A wheel of radius 45cm rolls along a horizontal floor. A dot, P, is painted on the rim. Initially P is in contact with the floor. After the wheel has rotated half a revolution, P is at the top of the wheel. What is the displacement (magnitude and direction) of P from its initial position when it is at the top of the wheel?

To answer the question I found out first the x component (how far along the horizontal axis it traveled. To do this I found half the circumference of the wheel. The y component was obviously the diameter (90cm)

The direction of the displacement I got was $0.45\pi\mathbf{i} + 0.9\mathbf{j}$ and the magnitude was about 1.68 metres. Is this correct? The lecturer always said answer in SI units.. so was it correct of me to answer it in metres and not centimetres?
Title: Re: trinon's advanced physics question thread
Post by: trinon on March 12, 2010, 12:45:15 am: This one is giving me some strife.. I realise this is a simple question, I just can't get it.

Two objects are released at the same height 1.0 seconds apart, and fall freely from rest. How long after the first object begins to fall will the two objects be 10 m apart? (use $g = 9.8 m/s^2$ )
Title: Re: trinon's advanced physics question thread
Post by: moekamo on March 12, 2010, 08:45:36 am: Quote from: trinon on March 12, 2010, 12:04:54 am
Hey guys. Now that I've began my advanced physics subject at melbourne uni, I expect that there will be many questions arising from tutorial sheets and whatnot. So in expectation of the near future, I'm creating this thread with some top notch questions to boot! Your help will be much appreciated.

Q: A wheel of radius 45cm rolls along a horizontal floor. A dot, P, is painted on the rim. Initially P is in contact with the floor. After the wheel has rotated half a revolution, P is at the top of the wheel. What is the displacement (magnitude and direction) of P from its initial position when it is at the top of the wheel?

doesnt the point just go to the top of the wheel so its displacement is 0.90 m up?

Quote from: trinon on March 12, 2010, 12:45:15 am
This one is giving me some strife.. I realise this is a simple question, I just can't get it.

Two objects are released at the same height 1.0 seconds apart, and fall freely from rest. How long after the first object begins to fall will the two objects be 10 m apart? (use $g = 9.8 m/s^2$ )
The objects released first is object 1, the other is object 2
Object 1:
$u_1 = 0, a=-g, t_1 = t, x_1 = ?$

Object 2:
$u_2 = 0, a=-g, t_2 = t_1 -1 = t-1, x_2 = ?$

$x_1 = u_1t +\frac{1}{2} at^2 = -\frac{1}{2}gt^2$

$x_2 = u_2t + \frac{1}{2} a(t-1)^2 = -\frac{1}{2} g(t^2-2t+1)$

if at a certain time, $t$ the objects are 10m apart, then $x_2=x_1+10$
$\implies -\frac{1}{2} g(t^2-2t+1)=-\frac{1}{2} gt^2 +10$
$\implies -\frac{1}{2}gt^2 + gt -\frac{1}{2}g = -\frac{1}{2}gt^2 + 10$
$\implies gt = 10 + \frac{1}{2} g$
$\implies t= \frac{10}{g} + \frac{1}{2} \approx 1.52 \mbox{ secs}$
Title: Re: trinon's advanced physics question thread
Post by: kamil9876 on March 12, 2010, 04:43:12 pm: Quote
doesnt the point just go to the top of the wheel so its displacement is 0.90 m up?

But the point is directly above the centre, which is at $x=0.45\pi$ .

http://en.wikipedia.org/wiki/Cycloid
Title: Re: trinon's advanced physics question thread
Post by: QuantumJG on March 12, 2010, 04:45:10 pm: Quote from: moekamo on March 12, 2010, 08:45:36 am
Quote from: trinon on March 12, 2010, 12:04:54 am
Hey guys. Now that I've began my advanced physics subject at melbourne uni, I expect that there will be many questions arising from tutorial sheets and whatnot. So in expectation of the near future, I'm creating this thread with some top notch questions to boot! Your help will be much appreciated.

Q: A wheel of radius 45cm rolls along a horizontal floor. A dot, P, is painted on the rim. Initially P is in contact with the floor. After the wheel has rotated half a revolution, P is at the top of the wheel. What is the displacement (magnitude and direction) of P from its initial position when it is at the top of the wheel?

doesnt the point just go to the top of the wheel so its displacement is 0.90 m up?

No it's the displacement from where it started from. I remember doing this question last year.
Title: Re: trinon's advanced physics question thread
Post by: trinon on March 13, 2010, 02:17:55 pm: Alright, Tutorial Sheet 2:

Q3. For each of the following cases, determine whether a reference frame in which the given object is considered to be at rest is or is not an inertial frame. Explain your reasoning.
(a) a rocket is moving at a steady speed in free space.

There are four different scenarios, but I've provided just the one because I want to understand this reference frame stuff then try to apply it to the other three.

Thanks!