A string under a tension of 43.0 N is used to whirl a rock in a horizontal circle of radius 2.25 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 49.5 m/s, the string breaks. What is the breaking strength, in newtons, of the string?
Jack, meet Kevin (prev post)
To find the breaking strength of the string, we can use the concept of centripetal force.
The centripetal force is the force that keeps an object moving in a circular path and is given by the equation:
Fc = (mv^2) / r
where Fc is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circular path.
In this problem, the mass of the rock is not given, but we can still find the centripetal force by rearranging the formula as follows:
Fc = (mv^2) / r
mv^2 = Fc * r
mv^2 = Tension * r
We know that the tension in the string when it breaks is equal to the breaking strength of the string.
Therefore, we can write the equation as:
(m * 49.5^2) = Tension * 1.00
To find the breaking strength, we need to determine the mass of the rock. However, the mass of the rock is canceled when we rearrange the equation.
Tension = (m * 49.5^2) / 1.00
To find the breaking strength, we can substitute the given values and compute the equation:
Tension = (mass * 49.5^2) / 1.00
Since the mass of the rock is canceled, we only need to calculate:
Tension = 49.5^2 / 1.00
Tension = 2450.25 N
Therefore, the breaking strength of the string is 2450.25 N.