# ME 203 Homework

## Spring 2008

A compilation of Spring 2008 posts
...and it begins. The first homework is now available on the website. Download...view...work...enjoy...and post any questions or comments here.
So I had the following question via email:
i am getting tripped up when its asking to write “i” and “j” in terms of e1 and e2... is there any quick advice you can give over an email

yes...lots of advice. Actually, I think the simplest thing to do is to redraw the (i,j), and (e1,e2) basis so that (e1,e2) is horizontal and vertical, while (i,j) is rotated clockwise from there by an angle theta. This would be equivalent to tilting your head counter-clockwise . Then, all should be clear(er)...
• hint* you should get the same answer for problem 2 parts a and b if you did the redefinition of e1 and e2 (or i and j) correctly. if you didn’t, then you know you haven’t got the hang of the thing yet.

Homework 02 is up and ready...go...
I am having some trouble working through Problem 3. I am trying to use the
y(x) that we defined in class on monday, and solve for Va, but I am getting too small of an answer. Is there a better way to work through this problem?
Thanks,
Jenn
Hi Jenn,

The answer should be something on the order of 100 ft/s. My advice is to check all of your variables. For example, notice that the hose is pointed down by 20 degrees, so this implies that theta = -20. Likewise the point A is below the fireman so y(final) = -30. Also, don’t forget that your units are given in terms of ft, so g = 32.2 ft/s^2. If this does not work out, you can also go back to the equations for x(t) and y(t), using them directly (instead of y(x)).

Good luck...
• hint* what i did was define the (a) and (b) dimensions in terms of sines and cosines (kinda like how we did the projectile ex from monday’s class). if you solve for one value - either the initial velocity value or the time - in one eqn, you can substitute it into the other eqn.... this *should* work (because the *exact same* procedure can be used to solve #4 correctly) HOWEVER i am still getting the wrong answer in 3... according to the back of the book. i can’t seem to find my error (it’s def calculation error tho).
I have a pretty simple question about 6b... The instructions say to assume that the nozzle is at ground level. Does that mean assume that theta = 0 or just that we’re supposed to neglect the vertical distance between the ground and the nozzle?
Hi Angela,

The latter, neglect the distance between the ground and the nozzle. The problem simplifies if you assume that the initial height of the water is y=0 and once it travels through the air (some unknown distance x) it again lands at zero height (y=0).
im probably skipping over something but on problem 6b dont we need to know either the angle of theta or at what time the water particle leaves the nozzle...
Greg, you can solve for the range of the water as a function of theta, much like we did in class...
any tips on Q4? i can figure out the conditions at y=-100, but don’t quite know how to find the end part (the sloping ground)
> any tips on Q4? i can figure out the conditions at y=-100, but don’t quite know how to find the end part (the sloping ground)

try setting y=100 + d*sin(5.7) where 5.7 is the degree of the slope and letting the down direction being positive
You need to look at the sloping ground like a right triangle. Because they gave you the slope of the ground, you should be able to find the other two sides of the triangle in terms of d.
I got the y side to equal 1/(101
.5) times d.
I got the x side to equal 10/(101
.5) times d.
• Use sine or cosine if you find that easier.

Now your total change in the y direction should be -100-(1/(101
.5))d
and in the x direction should be (10/(101
.5))d

These represent your final x and final y which you should be able to use in the equations to solve for the final velocity. (I had to solve for d and t before I could find the final velocity.)
Wow that didnt show up right. I was trying to represent the square root of 101. I hope you can read it.

Problem 1:

I have gotten equations for x and y values then i solved the x equation for dt and tried to plug it into the y function. Once there i am not able to solve for dt. Any hints?
Basically the motion of each ball is similar, with a different initial angle for the velocity. In addition, the balls must pass through the same point in space so that they collide. So I would work backwards. For each ball to be at the same point right now, how long ago must each of them have been thrown? How’s that?
I don’t really understand how to do these rotation problems... at all. I am coming up with equations and stuff, but I have no idea if they’re right. I don’t really feel confident with my answers. Does anyone have any suggestions of examples to look at or anything? Maybe an approach method?
Well, you can go through the solutions to the last homework. In general, you want to describe the kinematics in terms of some (unknown) coordinates like theta(t) and r(t). Then identify what information is given in the problem statement, what you can determine, and what quantities you need to find. This is a pretty vague answer, but if you can identify a specific problem and/or example, then maybe I can work from there...
I think i got it except i don’t know how to find phi dot (derivative of angle btw horizontal and BP). it seems it would be zero but then the answer doesn’t make sense.
Hi Christina,

Sorry I missed you today. The presentation ran longer than I expected...

Once you get your velocity equation, you should have two unknowns (probably phidot and xdot) and the vector equation can be broken up into two directions, giving you two equations. Then, you can solve for both phidot and xdot simultaneously...
what direction is Vb or Vb/c in?
This one is pretty similar to question 06, except the velocity of the slider is in a different direction. However, just looking at the first link AB, we know that the velocity of B is perpendicular to this ink.

You got questions? We got answers...

It’s up...and please use this thread for any comments. You can only get something out of all this if you put some effort in.
I have a question for number one. I have started the problem but have hit a wall when finding the angular velocity. I set three coordinate systems and then wrote an equation for velocity of point c by using the common velocity equation. Than i solved for the angular velocity of c. Does this sound like the right procedure or do i need to take a diffrent path. The answer i get does not seem right due to the fact it has an i and j coordinate component in it.
Do you actually mean the velocity of point B? The velocity of C is zero, as this point is fixed in the corner. As I discussed in class, you should express the velocity of point B in terms of link BC as well as in terms of link AB. The contact point is fixed relative to link BC while link AB does not rotate (zero angular velocity) but the contact point moves relative to this link.

In general, there is no problem with having i and j components in your velocity equation, but the angular velocity should only be in the k direction. Have you checked that your cross-product has be taken correctly?
I’m stuck on problem one, too. I defined 3 coordinate systems, but I solved for the velocity of P instead of C. My answer is really close to what is in the back of the book, but I’m messing up somewhere with the sines and cosines. The only thing that I wasn’t really sure of when I was working through it was the velocity of P that I found with respect to the bar AB. I defined coordinates fixed in the bar and said that the velocity of P is the same in magnitude as the translating velocity of the entire bar, but in a different direction. I don’t know if that makes sense, but if it does, is that a bad assumption?
That is it...the speed of the contact point is not simply the speed of the translating bar (they call the contact point B in the text but I called it P yesterday in class...I’ll stick with B here so everyone can follow). If you apply the velocity equation for link AB, keeping in mind that this link has zero angular velocity because its not rotating, you should be able to find the correct velocity of B.
Is there any hint or direction you can direct me in on question 2? The pulleys seem to be giving me trouble. Is this like a pulley problem from last week?
Since the angular velocity and acceleration of the bar is given, you can find the velocity and acceleration at B. Then, this becomes very similar to problem 3 (12-195 in the text) from last week, with the velocity of B known (but not simply in the vertical direction as in the previous problem.
Doesn’t seem like we are given much information for prob 4, i hate these problems that dont have numerical values... have no clue where to start??????? Also any suggestions on problems that have no “Givens”?
Since the wheel does not slip at point B the instantaneous velocity of this point must be zero, since the ground has zero velocity. The you can use the velocity equation to find the velocity of A, as both of these points are fixed in the disk.

If it helps, assume some numbers for the radii and angular speed of the disk. Then once you are comfortable with your approach, go back and use the original variables.
I have a beginning question for 2. When it says that the cord is 6m long does that mean the length of Sa or Sa + section DB.

Also on question 6 what is the path of the velocity of the person with respect to the body?
The length of the rope between the end of the bar, the pulley, and the mass is constant, its S_a + DB.

In question 6, the path of the girl in part a is straight across the disk (straight line relative to the disk). For part b, she moves along a path with constant radius in the disk.
Dr. Quinn,

I am struggling with the relative motion equations for problem six, especially with relating the girls horizontal velocity to the angular velocity/acceleration of the disk. I know that the acceleration is equal to the cross product of the angular acceleration and radius plus the cross product of the angular velocity and the cross of the angular velocity and the radius, but i’m not sure how to figure the girls velocity in
Ryan (and everybody else),

The acceleration (with respect to the ground) is not just the two terms that you describe below, but contains the acceleration of the girl with respect to the disk, the Coriolis acceleration (2 omega cross v), and the acceleration of the center of the disk, which vanishes in this problem. So the motion of the girl relative to the disk (drawn in the horizontal direction but in general rotating with the disk) enters into both of these terms.

So I’m having trouble relating the acceleration in the truck to the acceleration at B.... any ideas?
Also, this is a question about the homework in general. When
we’re doing our homework, do you want us to leave our answers in terms of variables? The homework problems posted online a lot of times don’t have the actual values written in the problems, but then the problems in the book do.
I have the same question.
Hi all,

In general I like to work out problem solutions in terms of variables. I find that I can often simplify the expressions when I work in terms of variables. However, I also substitute in the given variables in the homework solutions.

I don’t really mind if you don’t work in terms of variables. Ultimately for problems in which the numeric values are given, the numerical answer is what is evaluated.
Hey Dr. Quinn,

on problem 2 of the homework, i have my equations for the safe and boy complete, but i cant figure out how to determine the actual value for acceleration, thru the pulley equation i did figure out that 2Vs+Vb=0, so this corresponds to acceleration, such that 2As+Ab=0, but what do i do now? they don’t give us the acceleration the boy or the safe? any help would be sweet
...I’m not Dr. Quinn but I can tell you what I did...

I solved for As in terms of Ab, and I used Newton’s second law to come up with an equation for the force the boy exerts on the rope in terms of his weight and his acceleration... Then you find that the tension applied to the safe is equal to the force the boy applies since the pullies are massless. So when you use F=ma on the safe, you can substitute those so that the only unknown is the acceleration of the boy.

I can’t guarantee that this is the right way to do it, but I got the right answer
I’m am also getting stuck on how to the acceleration of block “b” in problem #5. Do you use trig to find it or is it another way i am not thinking of??
> I’m am also getting stuck on how to the acceleration of block “b” in problem #5. Do you use trig to find it or is it another way i am not thinking of??

I had the same question about problem 5, so i went and talked to Dr. Quinn, what i found out was that if you use the kinematics equations for velocity and acceleration with respect to the pulley you can find the velocity and acceleration of a point on the rope, now i haven’t actually finished the problem yet, so i can’t say i got it to work, but hopefully we can both figure it out with this lil tip he gave me.

The homework, which was originally due on Friday March 14, will now be due after the break...
Dr. Quinn,

I am having trouble getting started on problems 6 & 7. I have defined coordinates systems and labeled the forces. Can you give me some advice?
1. once you have defined an appropriate set of coordinates, identify what the acceleration is in terms of these. I would probably use polar coordinates for each problem. Then,
2. try to identify the forces acting on the particle using a free body diagram, and
3. put it all together, with the sum of the forces equaling the mass times acceleration.
If you have done the first two steps correctly, then everything should already be there. Finally, you need to express momentum balance in terms of a single set of directions, and I would go with the directions used with the polar coordinates.
Dr. Quinn,

On the first problem is there a normal force at the pully A. I think there isn’t becuase we are assuming the pullies are massless but if there isn’t a normal force then the freebody diagram for the pully at A doesn’t make sense.

P.S. What date will the HW be due?

Thanks,
The pulley at A has two forces that can be easily identified, as well as one moment. The moment is applied by the motor and balances out the force that arises from the cable. The second force serves to anchor the pulley to the wall. I assume that it is this latter force that you are referring to as the normal force...so it certainly exists.

A good thing to remember: momentum balance must always hold on every part of the system. If it has no mass then the sum of the forces vanishes, but this still satisfies momentum balance.

Having said all of this, you should be able to work through this problem without really considering what happens at A. The kinematics is given directly in terms of the fuel assembly, instead of the motion of the motor. So knowing the acceleration of the assembly, we should be able to find the tension in the cable.

The homework is due March 24...

Where is the force supposed to be applied to the system at?
I’m having trouble with this problem.
What is the mass of block A?
How do I relate the force F to the veritcal motion of Block B?

I’m running out of clever things to say...just go download the homework.

Find enough clever things to say, and you’re a Prime Minister; write them down and you’re a Shakespeare.
George Bernard Shaw

Yep...its that time again...

If life was fair, Elvis would be alive and all the impersonators would be dead. - Johnny Carson

For problem 7, any ideas on how to find the acceleration of the mass center of the spool?
I was wondering if you had any suggested problems out of the book for chapters 18 and 19 since we did not have any homework over that material. If you could, preferably problems that relate to the final or that are similar.
> I just posted a number of suggested problems from the last chapters to help in your preparation for the exam. Cheers...
>
> p.s. Here’s a link to the Tacoma Narrows bridge collapse...
>
> Oh, this is cool...

Will the questions on the final be more geared towards the last chapters we did or a mix of everything?
The exam tomorrow will be comprehensive, although it will be geared more toward the material in Chapters 17, 18, and 19...
Dr. Quinn, I’m having trouble on 17-103, basically my problem is relating the acceleration’s of the system. If you could possibly do a video solution of this problem that would be great, thanks.
I generated the solution for 17-103, and it should be posted by 2:30pm...
Hey, wondering if the video solutions are working for everyone else? For me they all play for like 15 seconds and then just freeze up...
> Hey, wondering if the video solutions are working for everyone else? For me they all play for like 15 seconds and then just freeze up...

Yes, Im having that issue as well. This is bad timing.
> Hey, wondering if the video solutions are working for everyone else? For me they all play for like 15 seconds and then just freeze up...

yep same thing happening for me too
> Hey, wondering if the video solutions are working for everyone else? For me they all play for like 15 seconds and then just freeze up...

Yeah same thing for me too and I’m using Mozilla.
It is 8:45pm and they seem to be working fine for me. Is anyone else still having this problem?
> It is 8:45pm and they seem to be working fine for me. Is anyone else still having this problem?

not working for me
> the videos still arent working, i tried on firefox and explorer..