A student creates interest in a visualization by contrasting the amount of light and dark. What color element is used?Grayscale
A constant velocity implies the two forces must be equal and opposite.
Friction acts horizontal to the ground, therefore we must find the force applied to the sled rope that acts horizontal to the ground.
Do this by resolving:
Force = 80cos53
The force opposing this is equal, and so also = 80cos53 = 48 N (2 sig. fig.)
Stable isotopes, radioisotopes, oxygen
The work done by
along the given path <em>C</em> from <em>A</em> to <em>B</em> is given by the line integral,
![\displaystyle \int_C \mathbf F\cdot\mathrm d\mathbf r](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_C%20%5Cmathbf%20F%5Ccdot%5Cmathrm%20d%5Cmathbf%20r)
I assume the path itself is a line segment, which can be parameterized by
![\vec r(t) = (1-t)(-2\,\vec\imath + 5\,\vec\jmath) + t(4\,\vec\imath+7\,\vec\jmath) \\\\ \vec r(t) = (6t-2)\,\vec\imath+(2t+5)\,\vec\jmath \\\\ \vec r(t) = x(t)\,\vec\imath + y(t)\,\vec\jmath](https://tex.z-dn.net/?f=%5Cvec%20r%28t%29%20%3D%20%281-t%29%28-2%5C%2C%5Cvec%5Cimath%20%2B%205%5C%2C%5Cvec%5Cjmath%29%20%2B%20t%284%5C%2C%5Cvec%5Cimath%2B7%5C%2C%5Cvec%5Cjmath%29%20%5C%5C%5C%5C%20%5Cvec%20r%28t%29%20%3D%20%286t-2%29%5C%2C%5Cvec%5Cimath%2B%282t%2B5%29%5C%2C%5Cvec%5Cjmath%20%5C%5C%5C%5C%20%5Cvec%20r%28t%29%20%3D%20x%28t%29%5C%2C%5Cvec%5Cimath%20%2B%20y%28t%29%5C%2C%5Cvec%5Cjmath)
with 0 ≤ <em>t</em> ≤ 1. Then the work performed by <em>F</em> along <em>C</em> is
![\displaystyle \int_0^1 \left(6x(t)^3\,\vec\imath-4y(t)\,\vec\jmath\right)\cdot\frac{\mathrm d}{\mathrm dt}\left[x(t)\,\vec\imath + y(t)\,\vec\jmath\right]\,\mathrm dt \\\\ = \int_0^1 (288(3t-1)^3-8(2t+5)) \,\mathrm dt = \boxed{312}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E1%20%5Cleft%286x%28t%29%5E3%5C%2C%5Cvec%5Cimath-4y%28t%29%5C%2C%5Cvec%5Cjmath%5Cright%29%5Ccdot%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5Bx%28t%29%5C%2C%5Cvec%5Cimath%20%2B%20y%28t%29%5C%2C%5Cvec%5Cjmath%5Cright%5D%5C%2C%5Cmathrm%20dt%20%5C%5C%5C%5C%20%3D%20%5Cint_0%5E1%20%28288%283t-1%29%5E3-8%282t%2B5%29%29%20%5C%2C%5Cmathrm%20dt%20%3D%20%5Cboxed%7B312%7D)
Answer: Rn :)))) no explanation needed