# Finding normal force with momentum

1. Oct 29, 2006

### vu10758

Water falls without splashing at a X kg/s from a height H into a bucket of mass M. The bucket sits on a sacle. Determine the reading of the sacle as a function of time.

I know the the sum of all forces is equal to the derivative of momentum with respect to time.

Mg is the force at time = 0.

The correct answer is mg + xtg + x*SQRT(2gH)

I know

F = dp / dt
dp = F dt

but I don't know what to do.

2. Oct 29, 2006

### Noein

Since p = mv, the expression F = dp/dt can be expanded for situations involving changing masses: F = m dv/dt + v dm/dt.

3. Oct 29, 2006

### Andrew Mason

The scale is going to measure the downward force. There are two things that contribute the downard force. What are they?

AM

4. Oct 29, 2006

### vu10758

The total force measured by the bucket is the weight of the bucket + weight of water + force of collision.

So, I understand mg + xtg which gives me force. But where did the x * SQRT(2gH) come from. SQRT(2gH) is equivalent to time, meaing that x * SQRT(2gH) is a mass. Why is a mass included in an equation for force?

Last edited: Oct 29, 2006
5. Oct 29, 2006

### Andrew Mason

The rate of change of momentum is the rate of mass flow x the speed of the water when it hits the bucket.

$$dp/dt = vdm/dt$$

In order to determine the speed, use the fact that potential energy is converted to kinetic energy. So, for an element of mass, $\Delta m$:

$$\Delta mgh = xtgh = \frac{1}{2}\Delta mv^2 = \frac{1}{2}xtv^2$$

AM