# Momentum, Force, and Impulse: help with balance pan problem

• toboldlygo
In summary: So you'll need to double your calculated value of Δv.That's it. So you'll need to double your calculated value of Δv.In summary, to solve this problem, the velocity of the beads before and after hitting the pan must be taken into account, as well as the difference between the two. By doubling the calculated value of Δv, the correct answer for the mass needed in the other pan of the balance can be obtained.
toboldlygo

## Homework Statement

[/B]
A stream of elastic glass beads, each with a mass of 0.53 g, comes out of a horizontal tube at a rate of 99 per second. The beads fall a distance of 0.49 m to a balance pan and bounce back to their original height. How much mass must be placed in the other pan of the balance to keep the pointer at zero?

## Homework Equations

impulse = force * Δp ==> F = mΔv/Δt
conservation of energy: potential energy = kinetic energy ==> mgh = 0.5mv2

## The Attempt at a Solution

I think I'm supposed to find the velocity of the initial and final moments (when the beads exit the tube, and as they hit the pan, respectively), then use that to find the force (using the impulse equation), and then find mass from that.

So, I set mgh = 0.5mv2, and using the velocity that I obtained, I solved for F (I used 1/99 as Δt), and then I divided that number by 9.81 m/s/s to get my answer. I don't know where I'm going wrong, though. Any help would be much appreciated!

toboldlygo said:
So, I set mgh = 0.5mv2, and using the velocity that I obtained, I solved for F (I used 1/99 as Δt), and then I divided that number by 9.81 m/s/s to get my answer.
(I suspect you used the wrong value for Δv.)

haruspex said:
(I suspect you used the wrong value for Δv.)

Here's my work. I've attached it to the reply.

#### Attachments

• Doc - 11-11-15, 8-35 PM.pdf
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toboldlygo said:
Here's my work. I've attached it to the reply.
My suspicion is confirmed.
What happens to the bead after it hits the pan?

After it hits the pan, the beads bounce back up to their original height. But how does that factor into the velocity? The velocity of the bead is 3.1006 m/s before it hits the pan, and then zero when it does. Isn't that a change of 3.1006 m/s?

toboldlygo said:
After it hits the pan, the beads bounce back up to their original height. But how does that factor into the velocity? The velocity of the bead is 3.1006 m/s before it hits the pan, and then zero when it does. Isn't that a change of 3.1006 m/s?
If its velocity is zero after hitting the pan, how does it regain its original height?

haruspex said:
If its velocity is zero after hitting the pan, how does it regain its original height?

It couldn't, if its velocity were zero. Does that mean it hits the pan with twice the velocity? There can't be zero change in velocity, could there? I know what you're saying now, but I don't know how I would factor that into a solution.

toboldlygo said:
It couldn't, if its velocity were zero. Does that mean it hits the pan with twice the velocity? There can't be zero change in velocity, could there? I know what you're saying now, but I don't know how I would factor that into a solution.
Velocity and momentum are vectors; signs matter. If the velocity before impact is -x (up positive) what will it be after bouncing? What is the difference of the two?

toboldlygo
haruspex said:
Velocity and momentum are vectors; signs matter. If the velocity before impact is -x (up positive) what will it be after bouncing? What is the difference of the two?

Oh, that makes sense! So if I were to subtract initial from final, I'd get x-(-x), which is just 2x, right? Or did I completely miss the mark?

toboldlygo said:
Oh, that makes sense! So if I were to subtract initial from final, I'd get x-(-x), which is just 2x, right? Or did I completely miss the mark?
That's it.

toboldlygo

## What is momentum?

Momentum is a measure of an object's motion and is defined as the product of its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction.

## What is force?

Force is a push or pull that causes an object to accelerate or change its motion. It is also a vector quantity and is measured in Newtons (N).

## What is impulse?

Impulse is a change in momentum and is equal to the force applied to an object multiplied by the time it is applied. It is also a vector quantity and has the same direction as the force.

## What is the relationship between momentum, force, and impulse?

The relationship between momentum, force, and impulse is described by Newton's Second Law of Motion, which states that the net force acting on an object is equal to the rate of change of its momentum. In other words, the greater the force or the longer it is applied, the greater the change in momentum.

## How can I use the balance pan problem to understand momentum, force, and impulse?

The balance pan problem is a common physics demonstration that involves balancing two unequal masses on a lever. By adjusting the position of the masses, you can observe how changes in force and momentum affect the balance of the system. This can help you understand the relationship between these concepts and how they apply in real-world situations.

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