Water falling into bucket, Force question

[Leeoku]

Homework Statement

13. Water falls at the rate of 271 g/s from a height of 56.2 m into a 776g bucket on a scale (without splashing). If the bucket is originally empty, what does the scale read after 3.14 s?
Answer: 2.50e+01 N

Homework Equations

Density, estimate 1kg/m^3
F = ma (a = gravity)
1kg = 1L

The Attempt at a Solution

In 3 seconds, .271*3 = .851 L dropped->.851 KG
Add weight of bucket, .851+.776 = 1.63 kg
F =ma
= 15.9 N

 

[Doc Al]

You found the weight of the water + bucket. Good! But an additional force is required to stop the momentum of the flowing water.

 

[Leeoku]

i actually have no clue. what I am puzzled at is why they gave us distance. the first thing that comes to mind is work, but i don't think that helps..

 

[Doc Al]

i actually have no clue. what I am puzzled at is why they gave us distance. the first thing that comes to mind is work, but i don't think that helps..

They gave you the distance so you can figure out the speed of the water as it hits the bucket. Hint: Use that speed to find the rate of change of the momentum of the water as it hits the bucket.

 

[Leeoku]

ok using v=d/t, 56.2/3.14 = 17.9 m/s
Impulse = delta p = (sum F)delta T
Delta p = 15.9*3.14
= 50 N.s
Using 50 as momentum, p = mv
50 = 17.89 M
m = 2.8 kg

Weird part is answer is given in Newtons, so mass*g = 27.4 N. Still not right, close though..

 

[Doc Al]

ok using v=d/t, 56.2/3.14 = 17.9 m/s

Two problems:
(1) The 3.14 s time given is not the time it takes for the water to fall from the given height.
(2) The speed of the water is not constant as it falls.

To find the speed of the water as it hits the scale, treat it as a falling body (falling from rest through a height of 56.2 m).