A 0.4 kg toy tied on a string can be whirled in a horizontal circle of of 1.2 m radius at a maximum of 3 rev/s before the string breaks. what is the force needed to break the string?

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To determine the force needed to break the string, we can use the concept of centripetal force. Centripetal force is the force required to keep an object moving in a circular path.

The formula for centripetal force is:

Fc = (m * v²) / r

Where:
- Fc is the centripetal force
- m is the mass of the object (0.4 kg)
- v is the velocity (in m/s)
- r is the radius of the circle (1.2 m)

Since the toy is whirled in a horizontal circle, the velocity can be calculated by multiplying the angular velocity (rev/s) by the circumference of the circle (2πr):

v = ω * 2πr

Where:
- v is the velocity
- ω is the angular velocity (in rad/s)
- r is the radius of the circle (1.2 m)

Given that the maximum angular velocity is 3 rev/s, we need to convert it to rad/s by multiplying it by 2π:

ω = 3 rev/s * 2π rad/rev

Now we can substitute the values into the formula for velocity:

v = (3 rev/s * 2π rad/rev) * 2πr

Next, substitute the calculated velocity and other values into the formula for centripetal force:

Fc = (m * v²) / r

Substituting the values for mass (m), velocity (v), and radius (r) will give you the force needed to break the string.