A light string can support a stationary hanging load of 26.4 kg before breaking. An object of mass m = 3.19 kg attached to the string rotates on a frictionless, horizontal table in a circle of radius r = 0.795 m, and the other end of the string is held fixed as in the figure below. What range of speeds can the object have before the string breaks?
0 to what?? please help!
Ac = omega^2 R
F = m Ac
26.4*9.81 = 3.19 (omega^2)(.795)
omega^2 = 102
omega = 10.1 radians/s maximum
v = omega R
so v </= 8.03 meters/ second
To determine the range of speeds before the string breaks, we need to find the maximum tension the string can withstand. The maximum tension occurs when the object is moving in a horizontal circle at its maximum speed. At this point, the tension must be equal to or less than the weight of the object.
The formula for the tension in the string is:
T = m * v^2 / r
Where:
T is the tension in the string,
m is the mass of the object,
v is the velocity (speed) of the object, and
r is the radius of the circle.
We can rearrange the formula to solve for the maximum speed:
v = sqrt(T * r / m)
Substituting the given values into the formula, we have:
v = sqrt(26.4 kg * 0.795 m / 3.19 kg)
v ≈ sqrt(6.573 m^2/s^2)
v ≈ 2.563 m/s
Therefore, the object can have a speed ranging from 0 m/s to approximately 2.563 m/s before the string breaks.