# TBR Physics Exam 1.2 #9 Change in momentum

#### Fruitjuice

2+ Year Member
As a hot-air balloon ascends upward at a constant speed, a package is dropped out of the balloon. At the instant the package is released, the momentum of the balloon:

A.) increases
B.) decreases
C.) is unaffected because the force does not change
D.) is unaffected because the decrease in mass is compensated by an increase in velocity

I couldn't choose an answer because: p=mv, so how do we know if the change in speed is large enough to offset the loss in mass? Or since the question says "instant", I can think of the mass decreasing the instant the package is dropped but it'll take some time for the velocity to increase enough to offset the loss of mass (although the the amount of mass loss is nowhere mentioned). Therefore, by that logic, the momentum should decrease (B).

#### walloobi

2+ Year Member
As a hot-air balloon ascends upward at a constant speed, a package is dropped out of the balloon. At the instant the package is released, the momentum of the balloon:

A.) increases
B.) decreases
C.) is unaffected because the force does not change
D.) is unaffected because the decrease in mass is compensated by an increase in velocity

I couldn't choose an answer because: p=mv, so how do we know if the change in speed is large enough to offset the loss in mass? Or since the question says "instant", I can think of the mass decreasing the instant the package is dropped but it'll take some time for the velocity to increase enough to offset the loss of mass (although the the amount of mass loss is nowhere mentioned). Therefore, by that logic, the momentum should decrease (B).
I don't think the mass of the package is included in the mass of the balloon, is it?

#### BerkReviewTeach

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The package-and-balloon system is rising at a constant speed (before release), so the net force is zero. In the absence of an external force, momentum is conserved. So if the balloon-and-package are moving at some set speed v prior to dropping the package, then because the package falls downward after letting go (the collision if you will), the balloon must offset that downward speed of the package by moving upward a little faster than it was moving before (how much depends on the relative mass of the package and the balloon system).

This is meant to be a simple concept in a setup that screws with your mind a little but. Take the simplest route to your answers.

#### gallons

2+ Year Member
Why are you guys covering momentum? It's no longer tested...

#### BerkReviewTeach

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10+ Year Member
Why are you guys covering momentum? It's no longer tested...
Because acceleration and fluids are covered.

This question is actually part of a fluids passage in the end-of-the-book practice test and it can be analyzed using relative densities before and after the package is dropped. Momentum is an alternative perspective fi you happen to prefer that way of reasoning. So while the word momentum appears in the question, this can be classified as a fluids question according to their guideline.