Question

A stone with a mass of 0.600 kg is attached to one end of a string 0.800 m long. The string will break if its tension exceeds 55.0 N. The stone is whirled in a horizontal circle on a frictionless tabletop; the other end of the string remains fixed. Find the maximum speed the stone can attain without breaking the string.

Answer 1

To find the maximum speed the stone can attain without breaking the string, we need to determine the maximum tension the string can withstand.

We know that the tension in the string is equal to the centripetal force required to keep the stone moving in a circular path:

Tension = centripetal force = (mass x velocity^2) / radius

where the radius is the length of the string, 0.800 m.

If we rearrange the equation to solve for velocity, we get:

velocity = sqrt((Tension x radius) / mass)

Now we can substitute the given values:

Tension = 55.0 N (the maximum tension the string can withstand)
radius = 0.800 m
mass = 0.600 kg

Plugging these values into the equation, we get:

velocity = sqrt((55.0 N x 0.800 m) / 0.600 kg)
velocity = 3.31 m/s

Therefore, the maximum speed the stone can attain without breaking the string is 3.31 m/s.