A 2.15 kg disc is attached to the end of a string whose length is 0.410 m. The disc slides without friction on a horizontal surface. If the string can withstand a maximum tension of 131.1 N, what is the maximum tangential speed the disc can have before the cord breaks?
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To find the maximum tangential speed of the disc before the cord breaks, we need to consider the forces acting on the disc.
First, we know that the tension in the string provides the centripetal force required to keep the disc moving in a circular path. The tension force is equal to the product of the mass of the disc and the centripetal acceleration:
Tension = mass * centripetal acceleration
In this case, the centripetal acceleration is given by the equation:
centripetal acceleration = (tangential speed)^2 / radius
The radius is half of the length of the string, so it is equal to 0.410 m / 2 = 0.205 m.
Rearranging the equation, we can express the tangential speed as:
(tangential speed)^2 = centripetal acceleration * radius
Plugging in the values we know, the equation becomes:
(tangential speed)^2 = (Tension / mass) * radius
Substituting the given values, we have:
(tangential speed)^2 = (131.1 N) / (2.15 kg) * 0.205 m
Simplifying further, we get:
(tangential speed)^2 = 120.93023 m^2/s^2
Taking the square root of both sides of the equation, we find:
tangential speed = sqrt(120.93023 m^2/s^2)
Evaluating that expression, the maximum tangential speed the disc can have before the cord breaks is approximately 10.991 m/s.