In a do‑nothing machine, two sliders are confined to perpendicular channels and are connected by a rod. the rod can be rotated, causing the sliders to move back and forth in their respective channels. suppose that the channels line up with the x‑ and y ‑directions and that the slider in the x ‑channel has velocity vx at some instant. let theta be the instantaneous angle of the connecting rod with respect to the x ‑direction. the length of the rod between the two sliders is l. find an expression for the instantaneous velocity vy of the slider in the y‑channel. express your answer in terms of vx, l, and theta.

Vy = -Vx * cotg(θ)

Explanation:

From the Pythagoras theorem:

X^2 + Y^2 = L^2

The first derivative respect of time is:

2*X*Vx + 2*Y*Vy = 0

X*Vx = -Y*Vy

Vy = -Vx * X/Y

From trigonometry:

X = L * cos(θ)

Y = L * sin(θ)

X/Y = (L *cos(θ)) / (L * sin(θ))

X/Y = cotg(θ)

Vy = -Vx * cotg(θ)

The speed does not depend on the length of the arm L.

it is given that trillions of microbes make up to 1% to 3% of the body mass.

let's take average of this percentage: 2%

consider the average mass of the human body as 70 kg.

then, trillions of microbes would have mass  

therefore, 100 trillion micro-organisms would weigh:

this is an approximate value and could change depending on the mass of the human body and percentage of the microbes present in it.

average mass per microorganism =