Physics Question

[noparlpf]

As the Physics thread seems to have died again, I guess this will have to do.


A bucket of water with a mass of 20.0 kg is suspended by a rope wrapped around a windlass in the form of a solid cylinder 0.400 m in diameter, also with a mass of 20.0 kg. The cylinder is pivoted on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls 20.0 m to the water. Neglect the weight of the rope.
a) What is the tension in the rope while the bucket is falling?
b) With what speed does the bucket strike the water?
c) What is the time of the fall?
d) While the bucket is falling, what is the force exerted on the cylinder by the axle?

I haven't had Physics in quite a long time, so I'm not entirely sure where to start here. Is there any tension in the rope at all? I'm torn between "no" and "there might be due to having to turn the windlass as it unwinds." Presumably it can't just be "no", though. Any thoughts?

[the_druid_droid]

I haven't had Physics in quite a long time, so I'm not entirely sure where to start here. Is there any tension in the rope at all? I'm torn between "no" and "there might be due to having to turn the windlass as it unwinds." Presumably it can't just be "no", though. Any thoughts?

It's been a long time since Mechanics, but the one rule about tension I memorized is that there's always tension if both ends are connected to something, and the tension is the same in both directions (obviously, this is for ideal, completely homogeneous ropes). So yeah, being attached to the bucket and and the windlass means there should be tension, and it's that tension that's converting the bucket's downward momentum into an unwinding of the windlass.

[noparlpf]

So how about part (d)? I'm torn between whether or not the tension is added to the normal force as well as the weight of the windlass itself.

[the_druid_droid]

So how about part (d)? I'm torn between whether or not the tension is added to the normal force as well as the weight of the windlass itself.

The axle is frictionless isn't it? That would imply it's incapable of exerting any force (unless you count the force keeping it above the ground or off the wall, which might be what you mean by the normal force, and even that seems more implied than anything else in the problem).

[factotum]

The axle is frictionless isn't it? That would imply it's incapable of exerting any force (unless you count the force keeping it above the ground or off the wall, which might be what you mean by the normal force, and even that seems more implied than anything else in the problem).

It will still take effort to accelerate the cylinder due to inertia, though, even with a frictionless axle--that's presumably what the question is asking about.

[thubby]

oh god i hate these problems.
basically, the bucket is trying to create a moment in the cylinder which will:
create rotational acceleration in the cylinder
decrease the rotational acceleration in the bucket

the potential energy in the system to start is
mass(20kg)*gravity*height=3920joules
because the bucket is suspended

and by the end that energy is all going to be kinetic or:
1/2*M*V^2+1/2*I*w^2=3920
the bucket will be moving and the rod spinning

"I" is its moment about the axis of interest, it's a formula in your book and is *googles* 1/2*mass (of the cylinder)*radius^2

w is rotational velocity=linear velocity (same as bucket) divided by radius (given)

so our equation to solve for is 1/2*M(bucket)*V^2+1/2*1/2*M(cylinder)*R^2*V^2/R^2=3920
note the canceling R^2

both masses are given, the radii cancel so calculate V and you have your final velocity.
my results

V(final)=16.2


once you have that, you have V final and V initial which means you can calculate V average
8.08

V(avg)*time=distance
solving for time is
2.47 seconds

you now have a distance and time, which lets you calculate acceleration
6.56

the tension is going to result from the difference in acceleration between what the bucket wants to do (9.8) and what we just got.
so calculate force and subtract
196-131.2=64.8 newtons

the last part is your teacher being a jerk. in all this math they're hoping you forget that the reaction force is both the MASS OF THE CYLINDER and the FORCE OF TENSION
drawing free body diagrams can help
260.8newtons

I was lazy with truncating, so if your teacher is a stickler you should work it out to 4 decimals then round to sig figs (3, if you typed out the problem exactly) but it should be something like that.

note that you could work this the other direction using force and rotational acceleration, i did it this way because it incidentally snakes through the data we need and also basically reviews the entirety of physics 1

im heading to bed, but ill happily answer any questions when im not running on pure OCD

[noparlpf]

It's not actually for me; this is a friend's class. Her professor, by the way, is obviously crazy. Tangential:
It's a 100-level freshman Physics class, and they meet 12-15 hours a week (depending on when he lets them out), plus something like eight hours of lab a week, plus an obscene amount of out-of-class online lecture and homework. She has more class time and work for one 100-level class than I do for my two 300-level classes and a 200-level class this summer session.

Anyway, thanks. I had managed to walk her through part (a) by solving for the linear acceleration using torque, and then she got (b) and (c). We were a bit confused with (d), but eventually decided that it would be the weight of the windlass plus the tension in the rope.

[Devils_Advocate]

Physics questions (http://www.smbc-comics.com/index.php?db=comics&id=2783#comic) often seem to be peculiarly different from other types of question (http://www.smbc-comics.com/index.php?db=comics&id=3003#comic) for some reason...

(Yeah, I probably could have contributed to this discussion more constructively, but pointing to someone else's wry observations was way easier. :P)

[Mollez]

Physics questions (http://www.smbc-comics.com/index.php?db=comics&id=2783#comic) often seem to be peculiarly different from other types of question (http://www.smbc-comics.com/index.php?db=comics&id=3003#comic) for some reason...

(Yeah, I probably could have contributed to this discussion more constructively, but pointing to someone else's wry observations was way easier. :P)

That's because every little thing affects the end result in some way, unless you're ignoring it. So: if you're learning about F=ma for the first time, you want a question like "Assuming there's no friction and there's a uniform cube of 1kg sitting on a perfectly level plane, how much force is required to accelerate it by 10 m/s^2?".

What you do not want is "There's a friction coefficient of .45 on a plane slanted at 30*, Earth gravity is in effect and there's a stiff breeze from the east, how much force does it take to accelerate a pyramid of 20 grams by 6.25 m/s^2?"

:smallwink:

[thubby]

What you do not want is "There's a friction coefficient of .45 on a plane slanted at 30*, Earth gravity is in effect and there's a stiff breeze from the east, how much force does it take to accelerate a pyramid of 20 grams by 6.25 m/s^2?"

:smallwink:

this actually isn't that terrible. even if the wind is a relevant force it works like a simple multiplier for low velocity newtonian applications like this.

[Mollez]

this actually isn't that terrible. even if the wind is a relevant force it works like a simple multiplier for low velocity newtonian applications like this.

It's still solvable, if you have the right equations. But you get to that stuff later. When you're just learning something, you simplify it as much as you can, even if it doesn't make strict rational sense.

F=ma is a simpler equation than Fa - μ(mg - Fy) = ma, that's all I'm saying.

[Devils_Advocate]

That's because every little thing affects the end result in some way, unless you're ignoring it.
Every little thing affects the end result whether you ignore it or not. Reality is that which, when you stop believing in it, doesn't go away.


What you do not want is "There's a friction coefficient of .45 on a plane slanted at 30*, Earth gravity is in effect and there's a stiff breeze from the east, how much force does it take to accelerate a pyramid of 20 grams by 6.25 m/s^2?"
No, I want questions like this one.

You don't know me.

[thubby]

Every little thing affects the end result whether you ignore it or not. Reality is that which, when you stop believing in it, doesn't go away.


No, I want questions like this one.

You don't know me.

in absolute terms, sure. in practice? meh.
there are a lot of things you can ignore and still get within 10^-5

[Rockphed]

in absolute terms, sure. in practice? meh.
there are a lot of things you can ignore and still get within 10^-5

This is the entire basis of engineering.

[Jimorian]

This is the entire basis of engineering.

"Assume a spherical cow."

[noparlpf]

"Assume a spherical cow."

My favorite line from Physics besides "If you push your physics teacher off of a cliff..."