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On the International Space Station an object with mass m = 250 g is attached to a massless string L = 0.87 m. The string can handle a tension of T = 8.7 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 :

Answer:

v = 5.5 m / s

Explanation:

For this exercise let's use Newton's second law, where the acceleration is centripetal

        F = ma

        a = v² / r

Before starting we reduce the mass to the SI system

        m = 250 g (1 kg / 1000g)

        m = 0.250 kg

Let's calculate the velocity for when the forces equal to T = 8.7N

        T = m v² / r

       v² = T r / m

       v = √ T r / m

       v = √ (8.7 0.87 /0.250)

       v = 5.5 m / s

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