Someone swints a 3.0 kg mass at the end of a 2.3 m string in a horizontal circle. If the string can withstand a tension of 80 N, at what speed can they swing the mass before they risk a lawsuit?
To calculate the maximum speed at which the mass can be swung without risking a lawsuit, we need to consider the tension in the string.
When an object moves in a circular path, it experiences a centripetal force that keeps it moving in a circle. This force is provided by the tension in the string in this case.
The centripetal force is given by the equation:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the object
v is the velocity/speed of the object
r is the radius of the circular path
In this case, the maximum tension the string can withstand is 80 N. So, the maximum centripetal force the string can provide is 80 N.
We can rearrange the equation to solve for the velocity (v):
v = sqrt((F * r) / m)
Substituting the given values:
m = 3.0 kg
r = 2.3 m
F = 80 N
v = sqrt((80 * 2.3) / 3.0)
Calculating this, we get:
v ≈ 8.08 m/s
Therefore, the person can swing the mass at a maximum speed of approximately 8.08 m/s without risking a lawsuit.