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On the International Space Station an object with mass m = 280 g is attached to a massless string L = 0.97 m. The string can handle a tension of T = 7.7 N before breaking. The object undergoes uniform circular motion, being spun around by the string horizontally. What is the maximum speed v the mass can have before the string breaks? Give your answer in units of m/s.

Respuesta :

skyluke89

Answer:

5.16 m/s

Explanation:

The tension in the string provides the centripetal force that keeps the object spinning in circular motion, therefore we can write:

[tex]T=m\frac{v^2}{r}[/tex]

where

T is the tension

m is the mass of the object

v is the speed

r is the radius of the circle

Here we have:

m = 280 g = 0.280 kg

r = L = 0.97 m (the radius of the circle is the length of the string)

The maximum tension allowed is

T = 7.7 N

Therefore, by solving for v, we find the maximum speed allowed before the string breaks:

[tex]v=\sqrt{\frac{Tr}{m}}=\sqrt{\frac{(7.7)(0.97)}{.280}}=5.16 m/s[/tex]

hamzaahmeds

This question involves the concept of centripetal force and tension.

The maximum speed, the mass can have before the string breaks, is "5.16 m/s".

The centripetal force in the string acts as the tension in this scenario. Hence, the maximum possible speed can be found using the formula of the centripetal force.

[tex]Tension=Centripetal\ Force\\\\T = \frac{mv^2}{r}[/tex]

where,

T = Maximum Allowable Tension = 7.7 N

m = mass = 280 g = 0.28 kg

v = maximum speed = ?

r = radius of circle = length of string = 0.97 m

Therefor,

[tex]7.7\ N = \frac{(0.28\ kg)v^2}{0.97\ m}\\\\v = \sqrt{\frac{(7.7\ N)(0.97\ m)}{0.28\ kg}}\\\\[/tex]

v = 5.16 m/s

Learn more about centripetal force here:

https://brainly.com/question/11324711?referrer=searchResults

The attached picture shows the centripetal force.

Ver imagen hamzaahmeds

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