A string under a tension of 59.0 N is used to whirl a rock in a horizontal circle of radius 2.55 m at a speed of 20.0 m/s on a frictionless surface as shown in the figure below. As the string is pulled in, the speed of the rock increases. When the string on the table is 1.00 m long and the speed of the rock is 52.5 m/s, the string breaks. What is the breaking strength, in newtons, of the string?
Ft = Fc = (mv²)/r
59 = [m(20²)]/2.55
59(2.55) = 400m
150.45 = 400m
m = 0.376125 kg
Ft = Fc = (mv²)/r
Ft = [(0.376125)(52.5²)]/2.55
Ft = 406.546875 N
To find the breaking strength of the string, we need to calculate the centripetal force acting on the rock.
In this scenario, the rock is moving in a horizontal circle, and the tension in the string provides the centripetal force required to keep the rock moving in a circular path.
We can start by calculating the centripetal force at the moment the string breaks. The centripetal force is given by the equation:
Centripetal Force = (mass × speed²) / radius
Since the mass of the rock is not given in the problem, we can cancel it out by dividing the equation through by mass:
Centripetal Force / mass = speed² / radius
Now, we can plug in the given values to calculate the centripetal force/mass ratio at the moment the string breaks:
Centripetal Force / mass = (52.5 m/s)² / (1.00 m)
Simplifying the equation, we get:
Centripetal Force / mass = 2756.25 N/m
Since the string breaks at this point, the tension in the string must be equal to or greater than this force. Therefore, the breaking strength of the string is 2756.25 N or greater.