Force and the Power Tower

The power tower is a large pulley system that lifts a large bucket of water into the air when a swimmer swims. As the swimmer swims, she has to pull the weight of the bucket, the water inside the bucket, and her own weight to reach the other end of the pool as quickly as she can.

http://www.aquavolo.com/journal/article/2011/03/dragsox™-vs-power-tower

We will calculate the amount of force needed to move the bucket, water, and the swimmer.

As stated in Newton's second law,

$$Force = mass * acceleration

so for this problem we would need to figure out

$$Force = (mass of bucket + mass of water + mass of swimmer)(acceleration)

to find the acceleration we must use the equation bellow

$$x = (xo) + (vo)t + 0.5at^2

The final position of an object is equal to the initial position plus the initial velocity multiplied by time plus half the acceleration multiplied by time squared

using this equation and plugging in what we know, we get the equation

22.86m = 0m/s(t) + 0.5at^2
or
22.86m = 0.5at^2

using the time of 13.88s we get

$$22.86m = 0.5a(18.04s)^2 = 0.141m/s^2

substituting this into our force equation we get that

$$Force = 0.141m/s^2(71.44kg) = 10.07 N

It takes 10.07 N of force to reach the other end of a swimming pool while pulling about 26lbs of extra weight.