Finding normal force with momentum

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Homework Help Overview

The discussion revolves around a physics problem involving the dynamics of a falling water stream into a bucket, focusing on the calculation of the normal force as measured by a scale under varying conditions. The subject area includes concepts of momentum, forces, and energy conservation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between force and momentum, questioning how to apply the equation F = dp/dt in the context of changing mass due to water flow. They discuss the contributions to the total force measured by the scale, including the weight of the bucket, the weight of the water, and the force of collision. Some participants express confusion regarding the inclusion of terms like x * SQRT(2gH) in the force equation.

Discussion Status

The discussion is active, with participants raising questions about the derivation of specific terms in the force equation and exploring the implications of energy conservation principles. There is a focus on clarifying the relationships between mass flow, speed, and force, indicating a productive exchange of ideas without reaching a consensus on the final interpretation.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information available for solving the problem. There is an emphasis on understanding the underlying physics rather than deriving a complete solution.

vu10758
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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.
 
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Since p = mv, the expression F = dp/dt can be expanded for situations involving changing masses: F = m dv/dt + v dm/dt.
 
vu10758 said:
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.
The scale is going to measure the downward force. There are two things that contribute the downard force. What are they?

AM
 
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:
vu10758 said:
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?
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
 

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