Understanding Levers: A Guide to Mechanical Advantage and Force Distribution

  • Thread starter scientist
  • Start date
  • Tags
    Lever
In summary, a 2-meter long lever is being used to lift a load of 1000 Newtons with a mechanical advantage of 4. The lever can be classified as a class 1, 2, or 3 lever depending on the ratio of the lever arms. To determine the reaction force at the fulcrum, a balance of vertical forces can be done where the load is equal to the sum of the applied force and the reaction force.
  • #1
scientist
28
0
A lever 2 meters long is used to lift up a load of 1000 Newtons. The lever gives a mechanical advantage of 4. Sketch the lever and show the forces at each end of the lever and at the pivot point.

Steer me in the right direction. What class of lever are we talking about?
 
Physics news on Phys.org
  • #2
You're talking about a straight bar. With a load of 1000N at one end. And a force of P Newtons, say, at the other end which you have to work out, The lever/bar will have a fulcrum, or pivot point, at some point along it to give the MA of 4. You should also mark on the reaction at the fulcrum.
 
  • #3
It's the one kind Archimedes was referring to when he said 'Give me a rod long enough and I shall lift the earth.'

I believe that the mention of Mechanical Advantage imediately tells you what kind of lever we're talking about...
 
  • #4
As for which class lever... it could be anyone of the three. Just get the ratio of lever arms correct for whichever you pick.
 
  • #5
Chi Meson said:
As for which class lever... it could be anyone of the three. Just get the ratio of lever arms correct for whichever you pick.


Not quite true. With a class 3 lever, the mechanical advantage is always less than 1.

The basic concept for a lever is "conservation of energy" together with "work = force times distance". To have a mechanical advantage of 4, the load must be 4 times as great as the force applied. Set up your equation with "force applied*applied lever arm= (4*force applied)*load lever arm" to determine the relation between the two lever arms.
 
  • #6
Fermat said:
You're talking about a straight bar. With a load of 1000N at one end. And a force of P Newtons, say, at the other end which you have to work out, The lever/bar will have a fulcrum, or pivot point, at some point along it to give the MA of 4. You should also mark on the reaction at the fulcrum.
--------------------------------------------------------------------------

A force of P Newtons equals

1000 Newtons
------------
4

= 250 Newtons

So what we have so far is a load of 1000 Newtons on one end and a force of 250 Newtons on the other.
 
  • #7
Since this has been here for a while now, with a class 1 lever (you have the fulcrum between the applied force and the load), the mechanical advantage is the length of the "application arm" (the distance between the application point and the fulcrum) and the length of the "load arm" (the distance between the load and the fulcrum). Here that must be 4. Draw a picture. label the length between the application and the fulcrum "4" and the length between the fulcrum and the load "1". What is the length of the entire lever?
 
  • #8
HallsofIvy said:
Not quite true. With a class 3 lever, the mechanical advantage is always less than 1.
I knew that. Don't you think I knew that? I knew that. Of course I knew that. I did. :grumpy:
 
  • #9
HallsofIvy said:
Since this has been here for a while now, with a class 1 lever (you have the fulcrum between the applied force and the load), the mechanical advantage is the length of the "application arm" (the distance between the application point and the fulcrum) and the length of the "load arm" (the distance between the load and the fulcrum). Here that must be 4. Draw a picture. label the length between the application and the fulcrum "4" and the length between the fulcrum and the load "1". What is the length of the entire lever?
-----------------------------------------------------
The length of the entire lever is 4m.
The ma=4 x 1
 
  • #10
scientist said:
The length of the entire lever is 4m.
Then why does the problem state "A lever 2 meters long..."
 
  • #11
scientist said:
The length of the entire lever is 4m.
The ma=4 x 1

i'd say, by logics, that the fulcrum is at 1/5th of the length, starting at the end which lifts, am i right?
 
  • #12
formula

Fermat said:
You're talking about a straight bar. With a load of 1000N at one end. And a force of P Newtons, say, at the other end which you have to work out, The lever/bar will have a fulcrum, or pivot point, at some point along it to give the MA of 4. You should also mark on the reaction at the fulcrum.
-------------------------------------------------------------

Is there a formula I use to calculate the reaction at the fulcrum?
 
  • #13
All the forces - load, effort and reaction (at the fulcrum) are considered to be in the same direction. Assuming they are all vertical, do a balance of Vertical Forces.
 
  • #14
Fermat said:
All the forces - load, effort and reaction (at the fulcrum) are considered to be in the same direction. Assuming they are all vertical, do a balance of Vertical Forces.
------------------------------------------------------------
Ok then,
the load = 1000 Newtons + force of 250 Newtons = 1250 Newtons, reaction force at the fulcrum.
the effort = load
------
MA

= 1000N
-----
4

= 250 Newtons

---------------------------------------------

Taking moments about the fulcrum:
Would clockwise moments = anticlockwise moments apply in this question?
This is what my book says.

Please post your reply and correct my answer.
scientist
 
  • #15
This is what you mean to post, yes?

scientist said:
------------------------------------------------------------
Ok then,
the load = 1000 Newtons + force of 250 Newtons = 1250 Newtons, reaction force at the fulcrum.
Code:
the effort =    load
                ------
                 MA
             
               = 1000N
                 -----
                  4
              
               = 250 Newtons

---------------------------------------------

Taking moments about the fulcrum:
Would clockwise moments = anticlockwise moments apply in this question?
This is what my book says.

Please post your reply and correct my answer.
scientist
You haven't actually said that the force at the fulcrum = 1250N but, if so, then that is correct. Your downward forces (load plus effort) = 1250N, so your single upward force (fulcrum reaction) is also 1250N.
Since the lever is assumed to be in static equilibrium, then
Σ Fv = 0
Σ Fh = 0
Σ T = 0
where Σ Fv is the sum of Vertical forces, Σ Fh is the sum of Horizontal forces, and Σ T is the sum of the Torques.
There are no horizontal forces and you have dealt with the vertical forces when finding the reaction at the fulcrum.
scientist said:
------------------------------------------------------------
...

Taking moments about the fulcrum:
Would clockwise moments = anticlockwise moments apply in this question?

...
They could, yes.
Now you can do Σ T = 0, as one way of evaluating the position of the fulcrum
Take moments about the fulcrum. Call the distance from the fulcrum to the load as x. So what is the distance fornt the fulcrum to the effort?
Then the moment of the Load about the fulcrum is equal to the moment of the Effort about the fulcrum. Solve for x.
 
  • #16
x solved

Fermat said:
This is what you mean to post, yes?


You haven't actually said that the force at the fulcrum = 1250N but, if so, then that is correct. Your downward forces (load plus effort) = 1250N, so your single upward force (fulcrum reaction) is also 1250N.
Since the lever is assumed to be in static equilibrium, then
Σ Fv = 0
Σ Fh = 0
Σ T = 0
where Σ Fv is the sum of Vertical forces, Σ Fh is the sum of Horizontal forces, and Σ T is the sum of the Torques.
There are no horizontal forces and you have dealt with the vertical forces when finding the reaction at the fulcrum.

They could, yes.
Now you can do Σ T = 0, as one way of evaluating the position of the fulcrum
Take moments about the fulcrum. Call the distance from the fulcrum to the load as x. So what is the distance fornt the fulcrum to the effort?
Then the moment of the Load about the fulcrum is equal to the moment of the Effort about the fulcrum. Solve for x.
----------------------------------------------------------------
Yes, I mentioned at the beginning of my post that the reaction force at the fulcrum is 1250 Newtons.
The length between the application and the fulcrum is 4 meters. The length between the fulcrum and the load is 1 meter.
This is taken from the MA =4:1.
I added the 4 + 1 = 5 meters
The total lever length is 2 meters as stated in the question.
I divided the lever length of 2 meters by 5 meters.
2/5=0.4 meters.

X = 0.4 meters as the final answer.
So the pivot point is 0.4 meters from the load arm of the lever.
This is a first class lever.
The lever is said to be in a static equilibrium because the lever has no movement and the lever is balanced. So in other words the lever is perfectly straight across and there are no outside forces acting upon this lever.

Please post a reply.
 
  • #17
scientist said:
The length between the application and the fulcrum is 4 meters. The length between the fulcrum and the load is 1 meter.
This is taken from the MA =4:1.
Careful. The ratio of the lengths is 4 to 1; this does not mean that the lengths are 4 meters and 1 meter! (Since the total length is only 2 meters, you know that can't make sense.)
I added the 4 + 1 = 5 meters
The total lever length is 2 meters as stated in the question.
I divided the lever length of 2 meters by 5 meters.
2/5=0.4 meters.
If you call the load-fulcrum distance X, then the two distances are X and 4X. Their sum must equal 2 meters, so X + 4X = 5X = 2 meters. Thus X = 2/5 meters.
 
  • #18
Yes, and 2/5= 0.4 meters as he said.
 
  • #19
Correct

Neohaven said:
i'd say, by logics, that the fulcrum is at 1/5th of the length, starting at the end which lifts, am i right?
-------------------------------------------
You are correct! Because the total length of 2 meters divide by
the MA of 4:1 equals 0.4 meters.

2 meters
-------
4+1=5

=0.4 meters
 
  • #20
From scientist

I would like to thank all my physics tutors for the outstanding information I received during this lengthly post! I have learned a lot! I will study and learn these principles.
 

1. What is a lever?

A lever is a simple machine that consists of a rigid bar or beam that pivots on a fixed point, called a fulcrum. It is used to lift or move objects by applying force at one end of the lever, which causes the other end to move in the opposite direction.

2. What are the three types of levers?

The three types of levers are first-class, second-class, and third-class levers. First-class levers have the fulcrum between the effort force and the load. Second-class levers have the load between the fulcrum and the effort force. Third-class levers have the effort force between the fulcrum and the load.

3. How does a lever provide mechanical advantage?

A lever provides mechanical advantage by increasing the force that can be applied to an object. This is achieved by positioning the load closer to the fulcrum and the effort force further away from the fulcrum, which creates a longer lever arm and amplifies the force applied.

4. What is the equation for calculating mechanical advantage of a lever?

The equation for calculating the mechanical advantage of a lever is MA = length of effort arm / length of load arm. This means that the mechanical advantage is equal to the ratio of the length of the effort arm to the length of the load arm.

5. How does a lever distribute force?

A lever distributes force by transferring the input force (effort force) to the output force (load) through the lever arm. The distance of the input force from the fulcrum determines the amount of force that can be applied to the load. As the input force increases, the output force also increases, resulting in a more efficient distribution of force.

Similar threads

Replies
4
Views
543
  • Introductory Physics Homework Help
Replies
26
Views
7K
Replies
8
Views
1K
Replies
28
Views
765
  • Introductory Physics Homework Help
Replies
6
Views
1K
Replies
17
Views
7K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Back
Top