A string under a tension of 43 N is used to whirl a rock in a horizontal circle of radius 3.3 m at a speed of 26.46 m/s. The string is pulled in, and the speed of the rock increases. When the string is 0.635 m long and the speed of the rock is 80.5 m/s, the string breaks. What is the breaking strength of the string? Answer in units of N
Spring tension is T = M V^2/R.
They do not tell you the value of M after the string is pulled in, but you can calculate it from the initial conditions with the larger radius. The mass will not change.
M = T*R/V^2
To find the breaking strength of the string, we need to consider the centripetal force acting on the rock and the tension in the string.
First, let's calculate the centripetal force at the initial speed of 26.46 m/s. The formula for centripetal force is:
F = (mass x velocity^2) / radius
Since the mass of the rock is not given, we can simplify the equation. The mass cancels out:
F = velocity^2 / radius
F = (26.46 m/s)^2 / 3.3 m
F = 692.2816 N
So, at the initial speed, the centripetal force acting on the rock is 692.2816 N. This force is provided by the tension in the string.
Now, let's calculate the centripetal force at the final speed of 80.5 m/s, when the string breaks. Again, using the centripetal force formula:
F = velocity^2 / radius
F = (80.5 m/s)^2 / 0.635 m
F = 10,333.0255 N
Therefore, the breaking strength of the string is 10,333.0255 N.
Hence, the breaking strength of the string is approximately 10,333 N.