Hi,
It's been many years since my H.S. physics class, so I was wondering
if someone could be kind enough to re-educate me about how to do this
type of problem:

If a 75 kg object is moving perpendicular to the force of gravity at a
(constant) speed of 0.01 m/s, and it is on a surface that has a
coefficient of friction of 0.004, then how do I figure out how much
force is required to stop, reverse and accelerate this object back to
0.01 m/s?

I'd like it to compare the force required to reverse direction and
accelerate back to its original speed all within 5 milliseconds, 50
milliseconds, or 500 milliseconds.

If someone could be kind enough to describe how to set up the problem,
show the equation and how it is solved, then I can apply this to other
similar problems I have to solve...I'd be very appreciative.

Thanks!
Randy

Randy MacKenna wrote:
Hi,
It's been many years since my H.S. physics class, so I was
wondering
if someone could be kind enough to re-educate me about how to do this
type of problem:

If a 75 kg object is moving perpendicular to the force of gravity at
a
(constant) speed of 0.01 m/s, and it is on a surface that has a
coefficient of friction of 0.004,

If there is friction, the speed is not constant. The
object is slowing down.

then how do I figure out how much
force is required to stop, reverse and accelerate this object back to
0.01 m/s?

Depends on how long a time you want this to take.

The total change in velocity from +0.01 to -0.01
m/sec is 0.02 m/sec. The acceleration is 0.02/T where
T is the time in seconds, and the force is 75*(0.02/T) N.

That's the net force. The presence of friction complicates
things somewhat.

I'd like it to compare the force required to reverse direction and
accelerate back to its original speed all within 5 milliseconds, 50
milliseconds, or 500 milliseconds.

OK.

Without the friction, you would just use 75*(0.02/T) N
= 1.5/T. So that is 300 N, 30 N, and 3 N respectively
for your three cases.

As I said, friction complicates things slightly. Using
0.02/T as the acceleration assumes that the net force is
the same for both forward and reverse motion, but that's
probably not a good model. Instead, you probably apply
a constant external force F_e. While the object is moving
forward, F_e and friction F_f are acting in the same
direction, to slow things down. Once the object is reversed,
F_f and F_e are in opposite directions. So the problem
breaks down into two parts:

In both cases I'll use F = ma = m*(delta-v)/t, with T1
being the time to brake and T2 being the time to reverse,
now different because the forces are different.

Braking: (F_e + F_f) = m*0.01/T1 or
T1(F_e + F_f) = m*0.01

Reversing: (F_e - F_f) = m*0.01/T2 or
T2(F_e - F_f) = m*0.01

And T1 + T2 = T, required total time, so T2 = T-T1:

So I have three equations in three unknowns (T1, T2,
F_e) which can be solved with a fair amount of algebra.

If this is a practical problem, I'd probably do it
numerically, especially since your friction is so
small. There's a technique called fixed point iteration
which would work pretty well but I don't have time to
go into it right now. Roughly it would go like this:

1. Take the initial estimate of F_e that I gave you
above (friction-free estimate).

2. Plug it into T1(F_e + F_f) = m*0.01 and solve for
a new guess for T1.

3. Use that to get a new T2 = T - T1.

4. Use that T2 in T2(F_e - F_f) = m*0.01 to get a new
value for F_e.

5. Repeat steps 2-4 until the values stop changing
(they're self-consistent).

There's a chance this procedure won't converge, sometimes
you need to manipulate your equations a bit, but I think
you'd be OK in this case.

- Randy

Thanks!

For a 75Kg object on Earth, it is exerting a downward force of 735.5N,
so if I have a coefficient of friction of 0.004, then F_f is (roughly)
3N, so I don't think I need to even worry about it (for my application,
anyway).

So, if I'm dealing with a motor that can produce 2000N of force
(through a screw drive), I think I'm well within my design limits if I
want this object to reverse direction in under 5 milliseconds.

Thanks again for the explanation...

-Randy M.

"Randy MacKenna" wrote in message
oups.com...
Thanks!

For a 75Kg object on Earth, it is exerting a downward force of 735.5N,
so if I have a coefficient of friction of 0.004, then F_f is (roughly)
3N, so I don't think I need to even worry about it (for my application,
anyway).

So, if I'm dealing with a motor that can produce 2000N of force
(through a screw drive), I think I'm well within my design limits if I
want this object to reverse direction in under 5 milliseconds.

Split the problem into two parts. 1) the time to stop 2) the time to get
going again. Then it's a matter of making two sets of equations using:

a = (v-u)/t
and
f=ma
and
T=t1+t2

(u or v = zero depending on which phase)

If friction was significant you would just add it to the force available to
slow down the object (because it helps) then for the second part subtract it
from that available to accelerate it (because it hinders).

The rest is maths.

Randy MacKenna wrote:
Thanks!

For a 75Kg object on Earth, it is exerting a downward force of
735.5N,
so if I have a coefficient of friction of 0.004, then F_f is
(roughly)
3N, so I don't think I need to even worry about it (for my
application,
anyway).

So, if I'm dealing with a motor that can produce 2000N of force
(through a screw drive), I think I'm well within my design limits if
I
want this object to reverse direction in under 5 milliseconds.


Yes. But there are other effects the ideal analysis left
out as well. I'm wondering if reversing in 5 msec is not
going to introduce transients that will stress some of
your elements in ways you haven't anticipated. Also
whether you even CAN reverse in 5 msec because of
those transient vibrations (you apply a sudden
force to an object, it is going to ring).

The real world is so much more interesting than toy
physics problems.

- Randy

"Randy MacKenna" wrote in message
oups.com...
Thanks!

For a 75Kg object on Earth, it is exerting a downward force of 735.5N,
so if I have a coefficient of friction of 0.004, then F_f is (roughly)
3N, so I don't think I need to even worry about it (for my application,
anyway).

So, if I'm dealing with a motor that can produce 2000N of force
(through a screw drive), I think I'm well within my design limits if I
want this object to reverse direction in under 5 milliseconds.

Yes I made the force required to stop about an order of magnitude less than
what you have available.

However check how much backlash you have in the drive train. It might take
more than 5mS take up the backlash.

Thanks for all the help...I have design headroom around 5 milliseconds,
so I think I'm in pretty good shape. The drive system is very close to
zero backlash.

-Randy M