Why is the pressure used in flow work the pressure of the fluid? If the fluid was say at 10kPa and the external pressure was at 0Pa, why don't we use the 0Pa in our calculations for flow work, since it's the external pressure that's the resistance? Or is it not possible to have this difference...
Ohhh, after trying to piece together what everyone said and thinking about it some more, I remember the relationships now. I forgot it when I thought of the situation in my question!
Thanks for everyone's help!
How do I set up the equations without knowing the direction of the centripetal acceleration (except that it's some direction normal to the velocity)?
I tried writing it using parametric notation for a vector/point on a plane:
Σ ⃗Fz = (Fn) - (Fg)cos(θ) = m*(P + s*[z component of some vector N...
Hmm... so I decided to try writing down equations using this coordinate system:
(The x-axis is positive into the page.)
Σ ⃗Fz = (Fn) - (Fg)cos(θ) = m(v2/r)
Σ ⃗Fy = (Fg)sin(θ) + (y component of friction if there is any) = m*(ay)
Σ ⃗Fx = (x component of friction if there is any) = m*(ax)
Is...
I'm afraid I don't see why the forces cannot be equal in magnitude (except by proof by contradiction). Is it just one of those facts of the universe, or do I have a poor understanding of the situation?
If the two forces were instead replaced by strings in tension (maybe the wheel is lying down...
If a wheel is freely rolling on the ground (not torque driven, but by a force acting on its center of gravity) towards the right, the friction force on the bottom of the wheel would be acting towards the left.
What if the friction force was equal to the force acting on the wheel's COG? Then the...
Is this what you mean?
Where the X is the velocity into the page (or out, depending on which way the particle is going around the funnel) as well as the the acceleration component that's in the same direction as the velocity. Also, I think the velocity could be in any direction into the page...
Fg = mg
Σ ⃗Fy = -Fg + (Fn)*cos(θ) where θ is the angle of the funnel slope and y is the axis perpendicular to the ground
Σ ⃗Fx = -(Fn)*sin(θ) where x is the axis parallel to the ground
If Σ ⃗Fx ≠ -m*(v2/r) then I think the orbit radius will adjust until they are equal... but I don't know...
Homework Statement
A ball of mass m is given an initial velocity ⃗v and entered into a funnel. Model the acceleration of the ball over a period of time.
Note: I don't have a full problem statement because this isn't really a homework question (but I figured it was homework-like enough to post...