i'm not sure how to go from P to PP, how do i explain what i'm doing
i really don't understand the projection matrix thing
for (a) , i don't know how to solve it still, i just know that I am using the proj formula, and doing it twice, but why is that the same as proj^2 like you said, i don't...
okay so i understand the fact that we have the same thing, but how do i proceed from there?
drawing it on paper, i know that it is 0, but i cannot prove this algebraically still, i am still stuck in the same place
I'm going to use . as dot product
To Prove: proj u (proj u (v)) = proj u (v)
proj u ((u.v / u.u) u)
= proj u ((u.v / |u|^2) u)
= [u . (u.v/ |u|^2)u ]u / u.u
= [u . (u.v/ |u|^2)u ]u / |u|^2
and i'm stuck here
okay so for (b) i have expanded and collected the terms.
q(t) = v\bulletv + v\bullettw + tw\bulletv + tw\bullettw
q(t) = |v|^2 + 2(v\bullettw) + |tw|^2
so do i use the hint and say that in order for q(t) >= 0 it must satisfy a>0 and b^2-4ac <=0 which it does.
but what about to show...
(a)Let u be a nonzero vector in R^{n}. For all v\epsilonR^{n}, show that proj_{u}(proj_{u}(v)) = proj_{u}(v) and proj_{u}(v - proj_{u}(v)) = \vec{0}
(b) An alternate proof of the Cauchy-Schwarz inequality. For v,w \epsilonR^{n}, consider the function q: R -> R defined by q(t) =...
i dont really understand whats wrong with it
but here is the diagram, i guess i did miss this
http://img63.imageshack.us/img63/9140/phys27rv.jpg [Broken]
question:
find the location of the center of mass for the following disk of radius a. it has a three circular cut outs. one with a diameter of a and the other two have a diameter of b.
http://img479.imageshack.us/img479/2743/physics4ld.jpg [Broken]
solution:
Xc = m/m(Xo - a/2)
Xc = Xo -...
question:
three uniform disks of the same mass per unit area, and radii a, 2a, 3a are placed in contact with each other with their centers on a straight line. how far is the center of mass of the system from the center of the smallest disk?
solution:
m1=pi a^2
m2=4pi a^2
m3=9pi a^2
Xc...
actually i have a question, i used 2Ft in one of the equations, and im wondering if this is right.
for this step i used 2Ft :
for the mass 2 fbd, i got
Fg - 2Ft = ma2 (is it 2Ft???)
for (a) i found the Ff of m1 by:
Ff = ma
Ff = 4(5.2)
Ff = 20.8
mew (u) = Ff/Fn
u = 20.8/(4)(9.8)
u = 0.53
so for (b) the u k = 1/2 (0.53) = 0.265
am i right for (a)? and (b), i've no idea how to start
so, a2 = 0.30m/s / 0.80m = 0.375 m/s^2
and then sub it in to get Ff = 0.856 N
oops, thats not the acceleraton
hmm, u need kinematics??
is the veloctiy given v1 or v2
a = 9.8 m/s^2
d= 0.80
if velocity given is v2, so v1 = 0?
okay, this is what i got so far, i dont know if its right. correct me if i had a mistake
taking xaxis is // to side of funnel, and yais is perpendicular to side of funnel, i drew fbd and the forces i got are
x components : Fs, - mg cos theta
y components : Fn, - mg sin theta
so i hvae...
ohh.
okay, i did it like u said, but now im stuck
for the mass 1 fbd, i got
Ft - Ff = a1
for the mass 2 fbd, i got
Fg - 2Ft = ma2 (is it 2Ft???)
then isolate for a2
4.9 - 2Ft = 0.5a2
9.8 - 4Ft = a2
and the equaion from fbd #1:
Ft - Ff = ma1
since a1 = 2a2
Ft - Ff = 4a2 (1)
then i substituted...
The block with mass m2=0.50kg is found to have a speed of 0.30m/s after it has dropped 0.80m. how large a (kinetic) friction force retards the motion of the block with mass m1=2.0kg?
(side note from teacher)
To solve this problem, you can use a string constraint. the total length of the...
a block with mass m1=4.0kg is placed on top of a block with mass m2=12.0kg.
(a) if the acceleration of the lower block is a2=5.2m/s^2, calculate the minimum coefficient of static friction (u minimum, where u is mew), for the contact surface between 1 and 2, that will prevent block 1 from...
a very small cube of mass m is placed on the inside wall of a funnel. The wall of the funnel makes an angle theta with the vertical axis of rotation (dotted line). The center of the cube is a distance r from the axis of rotation. the cube is held by static friciton. The funnel is then rotated...