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!
Centripetal force = M*V^2/R
= 191 Newtons
Solve for V, in units of m/s.
V^2 = 209.6 m^2/s^2
V = 14.5 m/s
Well, to find the maximum speed, you need to consider the tension in the string when the mass is at the bottom of the circle. We can use the formula:
Tension = Centripetal force = (mass x velocity^2) / radius
But because the string is at its breaking point, we know that the tension in the string is equal to 191.0 N. So we can rearrange the formula to solve for the maximum velocity:
Velocity^2 = (Tension x radius) / mass
Now you can just plug in the values and calculate the maximum velocity. However, I must warn you, if the mass starts to sing while spinning, it might break the sound barrier! Keep an ear out for that!
The formula you need is the centripetal force formula:
F = (mv²)/r
where:
- F is the centripetal force,
- m is the mass of the object,
- v is the velocity of the object, and
- r is the radius of the circle.
In this case, the centripetal force is equal to the force required to break the string (191.0 N), the mass (m) is 1.75 kg, and the radius (r) is 1.92 m.
Now, we can rearrange the formula to solve for the velocity (v):
v = √(Fr/m)
Substituting the given values:
v = √((191.0 N) * (1.92 m) / (1.75 kg))
Now you can calculate the maximum speed (v) by plugging in the values and solving for it.
To determine the maximum speed that the mass can be whirled without breaking the string, we can use centripetal force.
The formula for centripetal force is:
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, the centripetal force is equal to the breaking force required for the string, which is given as 191.0 N. The mass is 1.75 kg, and the radius is 1.92 m.
Now we can rearrange the formula and solve for the velocity (v):
v^2 = (F * r) / m
v = sqrt((F * r) / m)
Plugging in the values:
v = sqrt((191.0 N * 1.92 m) / 1.75 kg)
Solving this equation will give us the maximum speed at which the mass can be whirled without breaking the string.