Help needed on statics, and also to check my answers

[Danny_c]

I have this assignment to hand in and I've been having problems remembering how to do these problems. I am not sure if my answers are correct. I have no idea how to do the third one if anyone can walk me through the solution.

My answers are:
#1: -59.8
#2: Tension=14715N Mechanical Advantage=4, 3678.74
#3: I have no idea how to solve
#4: Tension on C= 1.84Kips Tension on B= 1.74kips

If i have any of these wrong could you please should me the way. I am sorry for giving so many problems. I am thankful for any help or direction that you can give.

The problems are on the link below
[img=http://img303.imageshack.us/img303/7843/problems9hm.th.png]

 

[Cyrus]

Too small give me a bigger image! YIKES

 

[Danny_c]

sorry, i just noticed and fixed it. lol

 

[Cyrus]

ahhhhhhhh my eyes! thanks

 

[Cyrus]

For Tension in number two i get 3,678.75, Just cut the ropes, then there is 4T going up and 1500*9.81 going down, and solve for t, very simple.
The mechanical advantage you provide is 3,678.75 to lift up 1500*9.81 or 14715/3678.75 = 4 times. But I am not sure how that is defined, so i may be wrong. A mechanical advantage of 4k just doesn't make sense to me, sorry. Ah, I read what you wrote, you have good numbers but assigned them wrong. 14,715 is the weight of the block no the tension, that 3k value is the tension, and 4 is right for the advantage.

 

[Danny_c]

For Tension in number two i get 3,678.75, Just cut the ropes, then there is 4T going up and 1500*9.81 going down, and solve for t, very simple.
The mechanical advantage is you provie 3,678.75 to lift up 1500*9.81 or 14715/3678.75 = 4 times. But I am not sure how that is defined, so i may be wrong. A mechanical advantage of 4k just doesn't make sense to me, sorry.

Sorry I am slow lol. I did T=1500*9.81 and i got 14715.00N. What did you do to get 3678.75. Thanks

 

[Cyrus]

Number 3 is simple as well. For a square, the force acts at the center along the x axis, so the total force is F= 5kn/m * 3m = 15kN acting at x=1.5 m.

Now for the triangle, the force acts 1/3 from the height of the trangle, or 2/3 of x from the other direciton. so the total force is again the area, so its F = (5kn/m* 3m )/2
(the area of that triangle). and it acts a distance 2/3 rds away, (BUT add in the distance for the rectangle too!) so its [(2/3) *3 ] +3, the +3 is because of the distance due to the rectangle! Now you have two forces at two distances, and you have to add them, and find the resultant distance this force acts, by summing the moments about the pin. (But first find the reaction of the smooth roller!) I Hope that helps you. I won't do it for you though.

 

[Cyrus]

Sorry I am slow lol. I did T=1500*9.81 and i got 14715.00N. What did you do to get 3678.75. Thanks

NO! Weight = 1500*9.81, thatsthe WEIGHT of the block. The tension is what holds it up. Look, just cut the ropes so that its 4 ropes magically pointing up. Do you see what i mean?
...T...T...T...T
.../\... /\.../\... /\
__|_____|_____|_____|
|....W ...|
|.....|...|
|....\/...|
------------------------

So 4T acts UP, and the Weight W, acts DOWN.

Now find what T is, its 1/4 the total weight, obviously.

 

[Cyrus]

do you get what I am saying?

 

[Danny_c]

Thanks alot, its slowly coming back to me. I hate the summer time it always ruins my memory. Thanks again for your help

 

[Cyrus]

Yeah, but do you understand what I am trying to show you? If its not clear let me know.

 

[Danny_c]

Only thing I am trying to figure out is where you got the 2/3s from the triangle one. How do i decide the point?

 

[Cyrus]

You have to go back and read about centroids of various areas. This is the location that works when you find the centrioid, or geometric center of a shape based on a mathematical definition. If you have a right triangle, the centroid is ALWAYS 1/3 away form the base so graphically:
......./..|
......./...|
....../...|
......./ ...|
...... /... |
....../... |
....../....|
....../.....|
...... /...|
....../ -----------|
...../\
...... |<-1/3->|

So that distance of the centroid is 1/3 from the side with the |'s, or 2/3s away from the side with the /, get it?

 

[Danny_c]

Thank you, now i understand