# vectors

• Jul 31st 2006, 06:00 AM
cheesepie
vectors
1) The centrifugal force acting on an object of mass m kg , with position vector r from the origin, and rotating at a constant angular velocity w radians per second is given by -mw(wXr) Newtons. calculate the centrifugal force vector and its magnitude for an object with m = 3kg,r=-2i+5j+7k metres and w=j+2 radians per sec

2) An electric charge of q1 coulomb, at a position vector r and moving velocity v1 produces a magnetic induction B given B =
m vXr
__ q [_____]
4pi lrlsquare

where m is the constant of permeability . The magnetic force F exerted on a second charge of q2 coulombs and moving with velocity v2 is given f=q2v2XB Find the magnetic force F if v1=i+j-k,v2=-3i+j,r=2i-j+3k and q1=q2=1
• Jul 31st 2006, 08:08 AM
topsquark
Quote:

Originally Posted by cheesepie
1) The centrifugal force acting on an object of mass m kg , with position vector r from the origin, and rotating at a constant angular velocity w radians per second is given by -mw(wXr) Newtons. calculate the centrifugal force vector and its magnitude for an object with m = 3kg,r=-2i+5j+7k metres and w=j+2 radians per sec

First off, are you trying to talk about a "centripetal" force?

Second, when you give the formula F = -mw(wXr) what are you trying to say? I'm guessing: $\displaystyle \vec F = -m | \vec w | ( \vec w \times \vec r)$.

Finally you said $\displaystyle w = \hat j + 2$. What direction is the "2" in?

-Dan
• Jul 31st 2006, 08:25 AM
topsquark
Quote:

Originally Posted by cheesepie
2) An electric charge of q1 coulomb, at a position vector r and moving velocity v1 produces a magnetic induction B given B =
m vXr
__ q [_____]
4pi lrlsquare

where m is the constant of permeability . The magnetic force F exerted on a second charge of q2 coulombs and moving with velocity v2 is given f=q2v2XB Find the magnetic force F if v1=i+j-k,v2=-3i+j,r=2i-j+3k and q1=q2=1

Ummm...$\displaystyle \vec B = \frac{m}{4 \pi} \frac{q_1 \vec v_1 \times \vec r}{r^2}$, yes? Then $\displaystyle \vec F = q_2 \vec v_2 \times \vec B$.

So. I'll do the vector part. (Ignoring the fact that you haven't given units...)
$\displaystyle \vec v_1 = \hat i + \hat j - \hat k$
$\displaystyle \vec v_2 = -3 \hat i + \hat j$
$\displaystyle \vec r = 2 \hat i - \hat j + 3 \hat k$

$\displaystyle \vec v_1 \times \vec r = \begin{vmatrix} \hat i & \hat j & \hat k \\ 1 & 1 & -1 \\ 2 & -1 & 3 \end{vmatrix}$ $\displaystyle = 2 \hat i - 5 \hat j - 3 \hat k$

And, of course $\displaystyle r^2 = \left ( \sqrt{2^2 + (-1)^2 + 3^2} \right ) ^2 = 14$.

Thus
$\displaystyle \vec v_2 \times \vec B$ is proportional to
$\displaystyle \begin{vmatrix} \hat i & \hat j & \hat k \\ -3 & 1 & 0 \\ 2 & -5 & -3 \end{vmatrix}$ $\displaystyle = -3 \hat i - 9 \hat j + 13 \hat k$.

-Dan