Finding normal force with momentum

In summary, the scale reading as a function of time for water falling without splashing into a bucket on a scale can be determined by understanding the sum of all forces, which is equal to the derivative of momentum with respect to time. Initially, the force is Mg. The correct answer is mg + xtg + x*SQRT(2gH). This includes the contributions of the weight of the bucket, weight of water, and force of collision. The x*SQRT(2gH) term comes from the fact that potential energy is converted to kinetic energy and can be expressed as force = rate of mass flow x speed of the water when it hits the bucket.
  • #1
vu10758
96
0
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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  • #2
Since p = mv, the expression F = dp/dt can be expanded for situations involving changing masses: F = m dv/dt + v dm/dt.
 
  • #3
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
 
  • #4
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:
  • #5
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.

[tex]dp/dt = vdm/dt[/tex]

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

[tex]\Delta mgh = xtgh = \frac{1}{2}\Delta mv^2 = \frac{1}{2}xtv^2[/tex]

AM
 

Related to Finding normal force with momentum

1. What is normal force?

The normal force is the force that a surface exerts on an object that is in contact with it. It is always perpendicular to the surface and acts in the opposite direction of the force exerted by the object on the surface.

2. How is normal force related to momentum?

Normal force is not directly related to momentum. Momentum is a measure of an object's mass and velocity, while normal force is a measure of the force exerted by a surface on an object. However, normal force can affect an object's momentum if it changes the object's velocity or direction of motion.

3. How can I calculate normal force using momentum?

To calculate normal force using momentum, you need to know the mass and velocity of the object. The formula is Fn = mv2/r, where Fn is the normal force, m is the mass, v is the velocity, and r is the radius of curvature.

4. Can normal force be negative?

Yes, normal force can be negative. This occurs when the surface is angled or curved and the force exerted by the object is greater than the normal force exerted by the surface. In this case, the normal force is directed in the opposite direction of the object's force.

5. How does normal force affect an object's motion?

Normal force can affect an object's motion by changing its velocity or direction of motion. For example, if an object is on an inclined plane, the normal force will act perpendicular to the plane and will balance out the force of gravity, causing the object to move at a constant speed. If the surface is curved, the normal force can change the object's direction of motion as it moves along the curve.

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