OK, have bunch of problems, but two of them I don’t know where to start.
First, I have to “Find the sum of the following four vectors in unit vector notation. ( m ) i + ( m ) j” I’ve looked on the internet about finding sum of vectors, and none of them mention degrees counterclockwise/clockwise.
P: 12.0 m, at 25.0° counterclockwise from +x
Q: 12.0 m, at 12.0° counterclockwise from +y
R: 4.00 m, at 20.0° clockwise from -y
S: 9.00 m, at 40.0° counterclockwise from -y
If someone could help explain this to me or just point me to a website that explains how to do it, I would appreciate it.
The second is “A sphere of mass 3.2 10-4 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes an angle of 36° with the vertical when at rest.”
Thanks a bunch.
Can someone give me an equation(s) to find the answer, as I don’t have any that mention tension.
Use the right hand rule. CCW is positive, CW is negative.
Draw a free body diagram, use a little trig. Tension is the force along the cord in the direction of the mass.
It sounds like you had a little problem with terminology and I’m willing to help you with that. You’ll have to do the rest of your homework on your own.
So 90degrees from y+ would be a 102 degrees? OK, I’ve drawn what all of that looks like, do I just find the area? I know it can’t just be adding up the magnitudes, because then there would be no point of having the angles in the first place.
The clockwise/counter-clockwise thing makes more sense if you draw out the x and y axes. +x is to the right and -x is to the left. +y is up and -y is down. So, to use R as an example, 20[sup]o[/sup] clockwise from -y means to take a vector pointing in the -y direction (down) and then rotate it 20 degrees in the clockwise direction. It’ll end up pointing down and to the left, making a 20 angle with the y-axis.
To add the vectors, convert them to x and y coordinates and add all those together. The components of the vector R is given by:
You’ll notice that I have written sin(theta) for v[sub]x[/sub], rather than cos(theta) as you’ll usually see in textbooks. The general rule is to put the cos with the same component whose axis defines the angle. An easy way to remember this is that cos(0) is 1, so if the angle was zero (i.e. flat against the y axis) vy would equal |v|, i.e. the vector would be completely in the y direction. Alternatively, you can convert all the angles so that they are with respect to the x-axis and use the traditional form.
Lastly, you can make sure the signs are right by just looking at the direction of the total vector. Down and to the left means both v[sub]x[/sub] and v[sub]y[/sub] should be negative.
Make sure you fully and completely understand this problem. If you truly get vectors, you’ll have a much easier time with physics.
Whoops, I meant to finish typing out the values for the vector R, as an example:
v[sub]x[/sub] = -4cos(20) or 4cos(180+20) or 4sin(360-110)
v[sub]y[/sub] = -4sin(20) or 4sin(200) or 4cos(250)
I’ve written three equivalent ways of calculating the value. The first just uses the angle with the negative y-axis and puts in the signs by hand. The second uses the angle with the positive y-axis. The third uses the angle with the positive x-axis. (Hopefully I didn’t make a mistake.)
Trigonometery is a bitch. Instead of following the examples of the other dopers, I’ll tell you what helped me most in my statics class.
i, j, and k are all relative measurements that are better dealt with in three dimensions. Remember your traditional 2-dimensional laws:
sin= opposite/ hyp or y-comp
cos= adjacent/ hyp or x-comp
tan= opposite/ adjacent for (hypotenuse)
in this case:
F(sub)x = magnitude * (cos (of curious angle)) = Force/length of inquired vector with respect to the x-axis
(duh)
resultant vectors follow a law similar to pathagoras’.
R= sqrt (x^2 + y^2 + z^2)
laws of cos and sin (brief internet research will help if you’re not familiar) will help you greatly in 2-dimensional situations.
don’t be afraid to rotate axis to simplify the problem.
The last bit of wisdom that I can grant you in my drunken state is to follow a pattern. For me, it’s make a pictoral representation, label all known and unknown info, then move on to info from past classes which may help you (i.e. derivitives, 3-4-5 triangles, trig ID’s, etc.), then calculate. It’s not the answer that is important, it’s how you got there.
In classes such as these, it is wiser to look for ways to change your methods of thinking rather than look for solutions. Solutions are temporary, while a method to the madness will last you a lifetime.