A stopper tied to the end of a string is swung in a horizontal circle. If the mass of the stopper is 13.0 g, and the string is 93.0 cm, and the stopper revolves at a constant speed 10 times in 11.8s?

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they want the angular velocity

To find the tension in the string, we can use the formula for centripetal force:

F = (m * v^2) / r

Where:
F is the centripetal force
m is the mass of the stopper
v is the velocity of the stopper
r is the radius of the circle

First, let's calculate the velocity of the stopper. Since it revolves 10 times in 11.8s, we can divide the number of revolutions by the time to get the angular velocity:

Angular velocity = (10 revolutions) / (11.8s)

Next, we need to convert the angular velocity to linear velocity. The linear velocity is the distance traveled by the stopper in one revolution. In this case, the circumference of the circle (2πr) is equal to the distance traveled in one revolution. So:

Linear velocity = (circumference) / (time for one revolution)
= (2π * r) / (time for one revolution)

Now, we can substitute the linear velocity and the given mass and radius into the centripetal force formula:

F = (m * v^2) / r

Plug in the values:
F = (0.013 kg) * (linear velocity)^2 / (0.93 m)

We can calculate the linear velocity using the formula (2π * r) / (time for one revolution). Substituting the values we get:

Linear velocity = (2π * 0.93 m) / (10 revolutions / 11.8 s)

Simplify:
Linear velocity = (2π * 0.93 m) * (11.8 s / 10 revolutions)

Finally, we can substitute the linear velocity back into the centripetal force formula to find the tension in the string:

F = (0.013 kg) * (linear velocity)^2 / (0.93 m)

Solving this equation will give us the tension in the string.