Question

Help please with acceleration vector problem. Question Below:

Answer 1

Are you familiar with centripetal acceleration?

Answer 2

I meant as in components. My answer was initially the vector sum of the centripetal, tangential, and vertical accelerations, but this brings up the issue of what happens when the man reaches the pole.

Answer 3

In term of i,j, and k?

Answer 4

it would be the components added together.

Answer 5

yes, but how would i find the magnitude? would it be the square root of the sum of their squares?

Answer 6

\[a_{tot}=a_c+a_{\tan}+a_{vertical}\]
also is this the correct vector sum?

Answer 7

That looks right to me. I am thinking.

Answer 8

I believe it would be sum of the squares because lets look at 2D. If we look at the tangential and centripetal acceleration we have this...

Answer 9

You agree?

Answer 10

yes that looks right

Answer 11

the resultant of tangential and centripetal vectors is the square root of the sum of the squares, and since the vertical acceleration vector is perpendicular to that resultant, then we have another iteration of the pythagorean theorem, meaning that \[\left| a_{tot} \right|=\sqrt{\left| a_{centripetal} \right|^2+\left| a_{tangential} \right|^2+\left| a_{vertical} \right|^2}\]

Answer 12

great, thanks