Simple centrifugal force problem

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  • #1
antonio glez
37
0
simple centrifugal force problem please help

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

theres 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
 
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  • #2
welcome to pf!

hi antonio! welcome to pf! :smile:

(have an omega: ω :wink:)

hint: d2r/dt2 = … ? :smile:
 
  • #3


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 :)
 
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  • #4
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  • #5


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 :)
 
  • #6
hi antonio! :smile:

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 :wink:),

= 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? :smile:
 
  • #7


antonio glez said:
i have a 2m long tube spinning around its center at w=1

theres 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?
 
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  • #8


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?
 
  • #9
antonio glez said:
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 :smile:
 
  • #10


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?
 

1. What is simple centrifugal force?

Simple centrifugal force is the inertial force that acts on an object moving in a circular path. It is directed away from the center of rotation and is caused by the object's tendency to continue moving in a straight line.

2. How is simple centrifugal force calculated?

The formula for calculating simple centrifugal force is Fc = (m * v^2) / r, where Fc is the centrifugal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.

3. How does simple centrifugal force differ from centripetal force?

Centripetal force is the force that keeps an object moving in a circular path, while simple centrifugal force is the equal and opposite force that acts on the object in the opposite direction. In other words, centripetal force pulls the object towards the center of rotation, while simple centrifugal force pushes it away.

4. What are some real-life examples of simple centrifugal force?

Simple centrifugal force can be observed in many everyday activities, such as swinging a bucket of water around in a circular motion or riding a roller coaster around a loop. It is also responsible for the curve in a baseball pitch and the movement of a car around a sharp turn.

5. How does simple centrifugal force affect the stability of a rotating object?

Simple centrifugal force can cause an object to become unstable, especially if the force is greater than other forces acting on the object. This can result in the object flying off its circular path or even breaking apart. Engineers must take into account simple centrifugal force when designing rotating objects to ensure their stability and safety.

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