Question

# 3 Points possible: 1. Total attempts: 6 A bucket that has a mass of 20 kg when filled with sand needs to be lifted to the top of a 15 meter tall building. You have a rope that has a mass of 0.4 kg/m that must be secured to the bucket. It takes I meter of rope to secure the bucket. Once the bucket reaches the top of the building it only has mass 12 kg because there was a hole in the bottom and sand was leaking out at a constant rate while it was being lifted to the top of the building. Find the work done lifting the bucket (sand and rope) to the top of the building. Joules

Answer 1

Work Done

cb F(r)dx a

If a object is moves from point a to b due to force F

Force = mass * acceleration

Total weight of the bucket = 20 kg

When it reaches top it has weight = 12 kg

So loss of 8 kg is due to leakage

So per meter weight loss = 8/15

as a function of height = 8/15 * x = 8x/15

==> 1 meter of rope need to secure the bucket when has a weight 0.4kg

So total weight of bucket becomes ==> 20 + 0.4 = 20.4 kg

==> Now total weight of rope = 15* 0.4 = 6 kg

and length of rope reduced as we pulled it up.So effective weight of rope = 6 - 0.4x = 6 - 2x/5

==>Total weight as a function of height = 20.4 + 6 - 2x/5 - 8x/15 = 26.4 - 14x/15

Work Done:

15 14r )9.8dx 15 W (26.4

15 14r -da 15 - 9.8 26.4 9.8 291 2851.8

W 2851.8 kgm/s