Find Mass of Object in Kings Dominion's Drop Zone Ride | Formula & Solution

[suwarna07]

Homework Statement

Its the drop zone in kings dominion

d = 82.9 m
initial velocity = 0
final velocity (before the brakes are applied) = 32.19 m/s
i know there is gravity downward and airresistance upward.
I need to find the mass of the object.

Homework Equations

First i found the acceleration using

v₁²= v₀² + at

a = 6.25 m/s²

And i am confused since air resistance is directly proportional to objects velocity. Is the acceleration i found is the final acceleration before the brakes are applied or is it the average acceleration.

The Attempt at a Solution

I need to find the mass but i can't think of any way to start.

Any help is appreciated

 

[cepheid]

At first, I had NO idea what you were talking about (because I don't live in Virginia). You need to communicate a little better. Anyway...

Homework Equations

First i found the acceleration using

v₁²= v₀² + at

Well, this equation is totally wrong, but I'm assuming that you meant to write:

v₁²= v₀² + 2ad

because based on the number you got for the acceleration, this seems to be the equation that you used.

And i am confused since air resistance is directly proportional to objects velocity. Is the acceleration i found is the final acceleration before the brakes are applied or is it the average acceleration.

It might be neither -- it might just be completely wrong. Here is the problem: the equation I wrote above is valid ONLY for motion with CONSTANT acceleration. If you are going to model the drag as being proportional to velocity, then the object's acceleration will NOT be constant, because the force acting on it will not be constant. There is a way to solve this problem and figure out the object's motion. However it requires solving a differential equation (something from calculus). Do you know how to do this?

 

[suwarna07]

At first, I had NO idea what you were talking about (because I don't live in Virginia). You need to communicate a little better. Anyway...



Well, this equation is totally wrong, but I'm assuming that you meant to write:

v₁²= v₀² + 2ad

yea i put the wrong equation. sorry about that. and i thought everyone knows drop zone so didnt try to be too specific.

Anyway, i haven't learned calculus based physics
So, what i did is completely wrong?
Or if there is any other way to find the objects mass then it would be helpful too

 

[HallsofIvy]

"King's Dominion" is an amusement park roughly half way between Washington, D. C. and Richmond, Virginia (not the most informative title for the thread). "The drop zone" is a ride in which people are literaly dropped a fair distance.

Suwarna07, none of the formulas you suggest depend upon mass so you could not possibly "solve" them for mass. It might be the case that the "drag" force was dependent upon both velocity and mass but you would have to propose a formula for such a force before you could use it.

 

[cupid.callin]

The air resistance depends on the size of object ... (not mass but volume occupied!) that is,,, if two spheres of same volume but masses m and 2m are in free fall, force due to air is same for both.

So you can take it a constant F(air) for your calculation,
just take F(earth) downward and F(air) upward and equate it to mass times net acceleration!

also ... F(air) don't depend on weight of object but you can still write F(air) = m x a(air)

But yes this will only help you find acc due to air, mass gets canclelled.

I'll think of something else and get back on this

 

[cepheid]

cupid.callin,

I agree that the drag force depends on the physical size of the object. Unfortunately, this is not all that it depends on. As the original poster, HallsofIvy, and I have all alluded to, the drag force also depends on the velocity of the object. Common models that I have seen are like:

F_air = C*v

OR

F_air = C*v²

where C is some constant that depends upon the radius of the object, the drag coefficient, etc. In other words, the drag force increases with increasing velocity (until the terminal velocity is reached, assuming there is time for that to happen). So, the drag force is NOT constant, which makes this problem mathematically harder to solve.

 

[cupid.callin]

which level question is this?
then at least we can know what things we have to keep in mind before solving the problem

 

[suwarna07]

which level question is this?
then at least we can know what things we have to keep in mind before solving the problem

its high school non-calculus based physics

 

[cupid.callin]

so cepheid this question must not be involving any calculus(as suwarna07 said) or dealing with variable acceleration ...
there must be a little something we all are missing ...