Using the work-energy theorem would be best in solving this problem. The net work on an object causes a change in the kinetic energy of the object, based from the work-energy theorem. For this, the formula for net work = change in kinetic energy = final kinetic energy - initial kinetic energy.
So, first sliding distance covered 3/4 with a net force 1-5/9 = 4/9 and w (w stands for weight of acrobat)
Therefore, work done = 4/9
* 3/4
In the next step, the distance to be covered is 1/4.
So, let the new frictional force required be X w
Therefore, net force upward = (X - 1) w
Thus, work to be done = (X - 1) * 1/4 w---------(2)
Equating X = 1 + 4/3 = 7/3
So, the frictional force that she must produce in the last
quarter has to be 7/3 times her weight.
