Using Momentum Principle to Find Ratio of Speeds?

[Spooky123]

Homework Statement

Two different experiments are performed. In the first experiment, a constant force is applied to a hydrogen ion. In the second experiment, the same constant applied force is applied to an ion that has a mass 12 times the mass of hydrogen. In each experiment, the ion is at rest at location A. Note that this force is much larger than any possible gravitational force on the ions, so you can neglect gravity.

Relevant Equations

Derive an expression for the final y-velocity of an ion as a function of its mass, the time interval At, and the force on the ion F.

Pf = Pi + FnetT
Vavg = v1 + v2 / 2
Vavg = r/t

Given that the ions are initially at rest my initial velocity is 0. Therefore my Vavg is equal to vf/2
Using the formula Vavg = Change in positon/time, I can solve vf to be equal to 2r/t.

Using the momentum principle, I get an equation of 2r/t = FnetT/12m -> Given that the mass of the ion is 12x Hydrogen.

However, when I solve for FnetT/12m divided by FnetT/m I get a ration of 1/12. Which is incorrect...

This question should only use the momentum principle and velocity equations without having to involve acceleration.

 

[topsquark]

Homework Statement: Two different experiments are performed. In the first experiment, a constant force is applied to a hydrogen ion. In the second experiment, the same constant applied force is applied to an ion that has a mass 12 times the mass of hydrogen. In each experiment, the ion is at rest at location A. Note that this force is much larger than any possible gravitational force on the ions, so you can neglect gravity.
Relevant Equations: Derive an expression for the final y-velocity of an ion as a function of its mass, the time interval At, and the force on the ion F.

Pf = Pi + FnetT
Vavg = v1 + v2 / 2
Vavg = r/t

Given that the ions are initially at rest my initial velocity is 0. Therefore my Vavg is equal to vf/2
Using the formula Vavg = Change in positon/time, I can solve vf to be equal to 2r/t.

Using the momentum principle, I get an equation of 2r/t = FnetT/12m -> Given that the mass of the ion is 12x Hydrogen.

However, when I solve for FnetT/12m divided by FnetT/m I get a ration of 1/12. Which is incorrect...

This question should only use the momentum principle and velocity equations without having to involve acceleration.

If you are acting on both ions for the same amount of time, then
$v = v_0 + aT$

Assuming that $v_0 = 0$ m/s for both, then
$v = aT$.

Now, $F = ma$, so
$v = \dfrac{FT}{m}$

So, for Hydrogen:
$v = \dfrac{FT}{m}$

Let's call the other ion carbon. So for carbon:
$V = \dfrac{FT}{12m}$

The ratio of these will be

$\dfrac{V}{v} = \dfrac{1}{12}$

as you said above.

-Dan

 

[kuruman]

Pf = Pi + FnetT
This question should only use the momentum principle and velocity equations without having to involve acceleration.

You have all the ingredients above to do what you are asked. Remember that pi = 0. You don't need any velocity or acceleration equations.

 

[Spooky123]

The correct answer for this question is 0.2889. I guess it might be an error.

 

[kuruman]

The correct answer for this question is 0.2889. I guess it might be an error.

How can the correct answer be a number (with no units) when the task is to "Derive an expression for the final y-velocity of an ion as a function of its mass, the time interval At, and the force on the ion F"?