Simple centrifugal force problem

[antonio glez]

simple centrifugal force problem please help

i have a 2m long tube spinning around its center at w=1

there's a 1 kg projectile at 1 m distance from the axe inside the tube that is released at a certain moment

what speed does the projectile have when it leaves the tube?

please show me how you do the calculations

 

[tiny-tim]

welcome to pf!

hi antonio! welcome to pf!

(have an omega: ω )

hint: d²r/dt² = … ?

 

[antonio glez]

hi tiny tim

im trying to get hold in the concept of derivative

the problem is that in the physics I am studying derivative is only treated in theoretical cases and not at all in practice

i can only understand practice, theoretics is too abstract for me

thats why i thought of this problem

but I am new to derivative still I am lost

im thinking also to solve a rocket of varying mass problem

so could you explain this problem to me please taking into account i hardly know derivation

also could you please point me to other practical probelms where there's derivatives or antiderivatives

thanks in advance :)

 

[tiny-tim]

hi antonio!

ok, let's go back one step

to solve this, you need to use good ol' https://www.physicsforums.com/library.php?do=view_item&itemid=26" as usual (F = ma) …

do it in the radial direction …

you can use either an inertial frame, or the rotating frame

… what do you get? ​

 

[antonio glez]

i know the object moves radially by the formula of centrifugal force so force = m*w*w*r

and being the mass =1 and f=m*a i know that force equals aceleration

so aceleration= m*w*w*r

but the radius is variable so i know its a derivative but i don't know how to apply it

thanks for your time :)

 

[tiny-tim]

hi antonio!

that's right … acceleration = r

we can write that: dv/dt= r

to solve this, we use a trick: dv/dt = dv/dr dr/dt (that's the chain rule ),

= v dv/dr (because dr/dt = v)

= d(v²/2)/dr …

so now your original equation can be rewritten = d(v²/2)/dr = r …

does that help? ​

 

[gneill]

i have a 2m long tube spinning around its center at w=1

there's a 1 kg projectile at 1 m distance from the axe inside the tube that is released at a certain moment

what speed does the projectile have when it leaves the tube?

If the tube is 2m long and spinning about its center, and the projectile is 1m from the axis, doesn't that put the projectile right at the very end of the tube to begin with?

 

[antonio glez]

oh yes i meant a 4 m long tube

thanks tiny tim with your help i obtained the radial velocity

but i understand that the final velocity is the resultant to the components of radial velocity and the velocity perpendicular to the radius that when the projectile lives the tube is 1*2=2

is this correct?

 

[tiny-tim]

but i understand that the final velocity is the resultant to the components of radial velocity and the velocity perpendicular to the radius that when the projectile lives the tube is 1*2=2

is this correct?

yes, the total speed will be the combination of those two perpendicular components, and yes the tangential speed is ωr = 1*2 = 2

 

[antonio glez]

thanks I am on now solving a varying mass rocket problem , i don't have to do it but i like it :)

could you point me to more problems where i have to use derivative or antiderivatives please?