I have a story problem that i cant seem to get..
an object moves along a track in the direction of the positive x axis while being pulled by a cable that makes an angle of \(\displaystyle \theta\) from the positive x-axis.
If \(\displaystyle \theta = 25^0\) and you want a 10 pound force applied to the object in the direction of the positive x axis what must the tension of the cable be? Use vector projection.
This is what i have came up with.
\(\displaystyle v = cos 25^0 i + sin25^0 j\)
w1 = \(\displaystyle ( \frac {u . v}{ ||v||^2})v \) = \(\displaystyle (F . V ) V\)
projF = \(\displaystyle 10( sin 25^0) V\)
w1 = \(\displaystyle 4.2261 ( cos25^0 + sin 25^0)\)
\(\displaystyle w1 = 4.2261\)
w2 = F - w1 ?
\(\displaystyle 10 j + 4.2261( cos25^0 i + sin 25^0 j)\)
\(\displaystyle = 3.8301 i - 11.786 j \)
I dont even think i did this right?
Please help me. Im not getting this. =(
any help in simple terms would be very thankful!
an object moves along a track in the direction of the positive x axis while being pulled by a cable that makes an angle of \(\displaystyle \theta\) from the positive x-axis.
If \(\displaystyle \theta = 25^0\) and you want a 10 pound force applied to the object in the direction of the positive x axis what must the tension of the cable be? Use vector projection.
This is what i have came up with.
\(\displaystyle v = cos 25^0 i + sin25^0 j\)
w1 = \(\displaystyle ( \frac {u . v}{ ||v||^2})v \) = \(\displaystyle (F . V ) V\)
projF = \(\displaystyle 10( sin 25^0) V\)
w1 = \(\displaystyle 4.2261 ( cos25^0 + sin 25^0)\)
\(\displaystyle w1 = 4.2261\)
w2 = F - w1 ?
\(\displaystyle 10 j + 4.2261( cos25^0 i + sin 25^0 j)\)
\(\displaystyle = 3.8301 i - 11.786 j \)
I dont even think i did this right?
Please help me. Im not getting this. =(
any help in simple terms would be very thankful!
