What is the minimum length for x to lift the bucket 9 meters in 4 seconds?

[Hello2]

http://imgur.com/NMu80
http://imgur.com/NMu80

Hello!
I have a problem to solve and I am not quite sure how to.
In the linked image i have the values of G, F and D given.
F stays constant and right angled towards the lever.

The bucket needs to go up 9 meters in 4 seconds.
What is the smallest x can be for this to happen?

I know how to find x if the system was standing still, or at constant speed.
But it needs to move the bucket up 9 meters in 4 seconds.
Since the only thing i can change is x i presume that the extra moment given by extra length of x, correlates to the speed it needs to have?
Or can i look at this as a constant speed problem by saying that from the start of the movement, there was an average speed of 2.25 m/s?
Which then would mean that the length of x is equal to what it would be if the system was standing still.
As in
G*(D/2)-F*x=0
if using the center of the disc as the moment point.

Im confused.
Can i solve this simply through equilibrium analyzes or do i have to involve angular momentum or something like that?

Sry if my english isn't the best. Its not my native language.

 

[gneill]

http://imgur.com/NMu80
http://imgur.com/NMu80

Hello!
I have a problem to solve and I am not quite sure how to.
In the linked image i have the values of G, F and D given.
F stays constant and right angled towards the lever.

The bucket needs to go up 9 meters in 4 seconds.
What is the smallest x can be for this to happen?

I know how to find x if the system was standing still, or at constant speed.
But it needs to move the bucket up 9 meters in 4 seconds.
Since the only thing i can change is x i presume that the extra moment given by extra length of x, correlates to the speed it needs to have?
Or can i look at this as a constant speed problem by saying that from the start of the movement, there was an average speed of 2.25 m/s?
Which then would mean that the length of x is equal to what it would be if the system was standing still.
As in
G*(D/2)-F*x=0
if using the center of the disc as the moment point.

Im confused.
Can i solve this simply through equilibrium analyzes or do i have to involve angular momentum or something like that?

Sry if my english isn't the best. Its not my native language.

Hello Hello2, Welcome to Physics Forums.

Presumably 'x' is the length of a lever arm which will rotate the pulley? Are there masses specified for the items shown? Is it assumed that the force F will always act perpendicularly to the lever arm?

 

[Hello2]

Thanks for the welcome =)

Yes, x is the length of the lever.
I have the value of G, F and D
D=200mm
G=150N
F=70N
F stays constant and perpendicular to the lever during the movement.

 

[gneill]

Okay, so suppose that the bucket ends up with a uniform acceleration (never mind how for the moment). What acceleration 'a' would be required to cover the specified distance in the given time?

 

[Hello2]

If the bucket has a uniform acceleration, then a=1.125 m/(s^2)

 

[gneill]

If the bucket has a uniform acceleration, then a=1.125 m/(s^2)

Yes, very good. So, what upward force 'u' on the bucket is required to accomplish this? Remember, you have the weight of the bucket (G) and therefore its mass.

 

[Hello2]

Hm, am i right in saying that u=167.2N? using g=9.82 m/(s^2)

 

[Hello2]

So wait.. do i need to multiply u with the radius then and equal that to F*x
So
u*(D/2)=F*x
and break out x from that?
And look at it as having to be in equilibrium, only using the new force needed for that acceleration?
Or am i just confusing things now?

 

[gneill]

Hm, am i right in saying that u=167.2N? using g=9.82 m/(s^2)

Sure, that looks fine.

So wait.. do i need to multiply u with the radius then and equal that to F*x
So
u*(D/2)=F*x
and break out x from that?
And look at it as having to be in equilibrium, only using the new force needed for that acceleration?
Or am i just confusing things now?

No, that's correct. The arm x and the radius of the pulley form a lever with a fulcrum about the pulley's pivot. So using the moments about the pivot to relate the forces is the right way to go.

 

[Hello2]

Yaay so then x=238.9 mm
Unfortunately i don't have access to the answer right now but doing the same thing on a problem i do have the answer for, were i needed to find the radius instead of the lever arm length, i got the right answer.

Its tempting to overcomplicate things (as in trying angular acceleration and such) when you havnt done these things too much yet.

Thanks a lot Gneill! You were awesome help!

 

[Hello2]

So, this problem wasnt really done yet.
I also need to find the reaction forces in the center of the disc.
Call that point A, and i need to find Amax and Amin reaction forces.
Would i be right in trying to find the answer using centripetal force? and combining that with G?

 

[gneill]

So, this problem wasnt really done yet.
I also need to find the reaction forces in the center of the disc.
Call that point A, and i need to find Amax and Amin reaction forces.
Would i be right in trying to find the answer using centripetal force? and combining that with G?

Hmm. I think you'll want to look at the external forces acting on the system and see what reaction force at the pivot would keep the system pinned in place there. The force from the tension of the bucket rope is constant and directed vertically. The force from the lever arm starts out vertically too, but then changes direction. Presumably there will be points along its position that correspond to maxima and minima total force.

 

[Hello2]

ok.
Do you mean something like in this picture?
http://imgur.com/A4pX5
http://imgur.com/A4pX5

I only did those two cases because that's what would give Amax and Amin, if its the right way to go.
But maybe i should use the force u, and not G like i wrote on there.
And the moment doesn't affect the resulting force in A right? since it can't stop the moment from turning?

 

[gneill]

The approach looks reasonable, but I would reconsider the total force applied by the rope with the bucket. It'll be accelerating, so the tension won't be just G.