Answer to Question #219581 in Mechanics | Relativity for Moyo

Question #219581
A stone of mass 0.5kg attached to a string of length 50cm will break when the tension exceed 20N. The stone is whirled in a vertical circle, the axis of rotation at height 100cm above the ground. At what position and angular speed is the break most likely to occur.
1
Expert's answer
2021-07-22T10:03:29-0400

T=Fc+Fg\vec T = \vec F_{c}+\vec F_{g}

where:\text{where:}

Fccentrifugal force\vec{F}_{c}-\text{centrifugal force}

Fc=ma=mω2r\vec{F}_{c}= m\vec a= m\omega^2r

Fggravity force\vec{F_g}- \text{gravity force}

Fg=mg\vec F_{g}= mg

The break will happen when:\text{The break will happen when:}

Fc+Fgmaximum \vec F_c+\vec F_g - \text{maximum }

The maximum occurs when the forces are equally directed,\text{The maximum occurs when the forces are equally directed,}

that is, at the lowest point of the trajectory.\text{that is, at the lowest point of the trajectory.}

We take into account the fact that gravity is directed\text{We take into account the fact that gravity is directed}

 vertically downward\text{ vertically downward}

Lowest point of trajectory:\text {Lowest point of trajectory:}

100cmr=100cm50cm=0.5m100cm - r = 100cm-50cm = 0.5m

Fc+Fg=20\vec F_c+\vec F_g = 20

mω2r+mg=20m\omega^2r +mg = 20

0.5ω20.5+0.59.8=200.5*\omega^2*0.5+0.5*9.8 = 20

ω=204.90.25=7.77rads\omega=\sqrt\frac{20-4.9}{0.25}=7.77\frac{rad}{s}


Answer: h=0.5m over the ground\text{Answer: }h = 0.5m\text{ over the ground}

ω=7.77rads\omega=7.77\frac{rad}{s}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment