A string requires a 191.0 N force in order to break. A 1.75 kg mass is tied to this string and whirled in a vertical circle with a radius of 1.92 m. The maximum speed that this mass can be whirled without breaking the string is
To determine the maximum speed at which the mass can be whirled without breaking the string, we can analyze the forces acting on the mass.
In this scenario, the centripetal force required to keep the mass moving in a circular path is provided by the tension in the string. At the maximum speed, when the tension in the string reaches its breaking point, it will be equal to the force required to break the string.
The centripetal force, which is equal to the tension in the string, can be calculated using the following formula:
F = (m * v^2) / r
where:
F = centripetal force (tension in the string)
m = mass of the object
v = velocity
r = radius of the circular path
In this case, we know that the force required to break the string is 191.0 N, the mass is 1.75 kg, and the radius is 1.92 m.
Rearranging the formula, we can solve for the maximum velocity:
v = √((F * r) / m)
Substituting the given values:
v = √((191.0 N * 1.92 m) / 1.75 kg)
Calculating this expression will give us the maximum speed at which the mass can be whirled without breaking the string.