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The maximum mass the can be hung vertically from a string without breaking the string is 10kg. A length of this string that is 2m long is used to rotate a 0.5kg object in a circle on a frictionless table with the string horizontal. The maximum speed that the mass can attain under these conditions without the string breaking is most nearly:

Answer is 20 m/s
Please show me how I can get the answer. Thank you.

Answer :

Answer:

Explanation:

Think about circular motion when answering this question. First determine the maximum force that can be applied on the string. F = mg so F = (10)(10) = 100 N. Then determine the centripetal acceleration of the .5 kg mass, a = F/m so a = 100/.5 = 200 m/s².  On the equation sheet, use equation a(centripetal acceleration) = v²/r so 200 = v²/2 therefore v = 20 m/s. Hope this helps!

Cricetus

The maximum speed will be "20 m/s".

Given:

Radius of circle,

  • r = 2 m

Mass attached,

  • m = 0.5 kg

→ [tex]T_{max} = Maximum \ tension \ possible \ in \ the \ rope[/tex]

            [tex]= Weight \ of \ 10 \ kg \ mass[/tex]

            [tex]= 10\times 9.8[/tex]

            [tex]= 98 \ N[/tex]

hence,

→ [tex]T_{max} = \frac{mv^2}{r}[/tex]

By substituting the values, we get

→     [tex]98= \frac{(0.5)v^2}{2}[/tex]

→       [tex]v = 20 \ m/s[/tex]

Thus the above answer is right.

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