Moment
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Helt
Trenger hjelp med følgende oppgave: A uniform solid sphere of mass M and radius R is free to rotate about a horizontal axis through its center. A string is wrapped around the sphere and is attached to an object of mass m. Assume that the string does not slip on the sphere. Find the acceleration of the object and the tension in the string.
Finner summen av alle dreiemoment
[tex]\Sigma \tau=TR=I\alpha[/tex]
Sett inn for treghetsmomentet.
[tex]TR=\frac{2}{5}MR^2\frac{a}{R}[/tex]
Summer kreftene som virker
[tex]\Sigma F=mg-T=ma\Rightarrow T=m(g-a)[/tex]
Substituer
[tex]a=\frac{g}{1+\frac{2M}{5m}}[/tex]
Sbustituer svaret du fant i sta
[tex]T=m(g-\frac{g}{1+\frac{2M}{5m}})=\frac{2mMg}{5m+2M}[/tex]
[tex]\Sigma \tau=TR=I\alpha[/tex]
Sett inn for treghetsmomentet.
[tex]TR=\frac{2}{5}MR^2\frac{a}{R}[/tex]
Summer kreftene som virker
[tex]\Sigma F=mg-T=ma\Rightarrow T=m(g-a)[/tex]
Substituer
[tex]a=\frac{g}{1+\frac{2M}{5m}}[/tex]
Sbustituer svaret du fant i sta
[tex]T=m(g-\frac{g}{1+\frac{2M}{5m}})=\frac{2mMg}{5m+2M}[/tex]