Question

Question in attached picture

Answer 1

voila

Answer 2

First and foremost, free body diagram.
I guess we should probably work in a circular coordinate system, (r, \(\theta\))

Let's set up a summation of forces equation: \[\sum F_r = ma = T-mg \cos(\theta)\]\[\sum F_\theta = m \alpha = -mg \sin(\theta)\]

Solving both for \(a\) and \(\alpha\), respectively, yields:
\[a = {T \over m} - g \cos(\theta) \]\[\alpha = -g \sin(\theta)\]

Remember that the magnitude of two orthogonal vectors is\[|a| = \sqrt{a_x^2 + a_y^2}\]Here \(a\) and \(\alpha\) are orthogonal. Therefore, we get\[|a| = \sqrt{ \left [ \left (T \over m \right) - g \cos(\theta) \right]^2 + \left[g \sin(\theta) \right]^2 }\]

I'll let you tackle the expansion and simplification of this.

Answer 3

what are orthogonal vectors?

Answer 4

Orthogonal vectors are vectors perpendicular to each other.

Answer 5

ooh thank you!

Answer 6

Wlecome :)