A string 1.0 m long breaks when it's tension is 100 N. What is the greatest speed at which it can be used to whirl a 1.0 kg stone? (neglect the gravitational pull of the earth on the stone)
Speed can be counted in many ways, depending on the values we know, so that we can calculate the speed. Here we have a known value for tension 100 N. We also have a weight of 1kg stone whose speed we want to calculate. In this case we will use the formula for tension T = mg + ma, where we will ignore mg the expression due to the fact that we reject the influence of earth's gravity, so that we get the expression T = ma. From this expression we will extract the acceleration value and move it to the left side of the formula:
a = T/m, a - acceleration (m/s²), T - tension (N, kgm/s²), m - weight (kg), the length of the string is one meter.
a = 100(kgm/s²) / 1(kg) = 100 m/s² and the velocity is v = √a = √100 = 10 m/s.