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

Again I just need the formula!

To find the maximum speed at which the mass can be whirled without breaking the string, we can use the concept of centripetal force.

The formula for centripetal force is given by:

F = (m * v^2) / r

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

In this case, we want to find the maximum velocity (v) without breaking the string, where the force (F) is equal to the breaking force of the string (191.0 N).

By rearranging the formula, we can solve for v:

v = sqrt((F * r) / m)

Substituting the known values into the equation:

v = sqrt((191.0 N * 1.92 m) / 1.75 kg)

Now we can calculate the value of v.

To calculate the maximum speed at which the mass can be whirled without breaking the string, you can use the formula for the tension in a vertical circle, which is:

Tension = (mass × radial acceleration) + weight

The radial acceleration can be calculated using the centripetal acceleration formula:

radial acceleration = (velocity^2) / radius

To find the maximum velocity, rearrange the formula for tension:

Tension - weight = (mass × radial acceleration)
(mass × radial acceleration) = (Tension - weight)

Substituting the formula for radial acceleration:

mass × (velocity^2) / radius = (Tension - weight)

Finally, solve for the maximum velocity (velocity_max):

velocity_max = sqrt((radius × (Tension - weight)) / mass)

Note: The weight of an object can be calculated using the formula:

weight = mass × acceleration due to gravity

Now you have the formula to calculate the maximum speed that the mass can be whirled without breaking the string.