Transcript Mechanical advantage: Levers

Mechanical advantage: Levers
Look at the lever system on the right. A load of 30N is
supported by a 10N effort. What is its mechanical
advantage?
Mechanical advantage is 3
Stephen pushes down with a force of 60N to just lift the
load off the ground. What is the mechanical advantage
of the lever?
Mechanical advantage is 5
Stephen pushes down with a force of 300N to just lift the
load off the ground. What is the mechanical advantage of
the lever?
Mechanical advantage is 10
Distance from the fulcrum (moment)
moment = force X distance
You may have noticed when using a first order lever that little effort is needed to
move the load if you are further away from the fulcrum than the load. In fact the
further you are the less effort is needed. A famous philosopher once said "Give me a
lever long enough and I will move the world". You may have played on the see-saw
and tried to lift, using your hands, a person on the other side. It is very difficult. If the
person comes and sits closer to the fulcrum your work is made easy.
The mechanical advantage gained by a lever can be explained by the principle of
moments. A moment is the turning effect generated when a force(effort) is
applied to a lever to rotate it about the fulcrum.
The moment depends upon the size of the force and its distance from the fulcrum
Levers : Moment
When a lever is in equilibrium the two opposing forces just balance
each other. The moments on both sides of the fulcrum are equal.
Take the case on the right. The 30N force 10m away from the
fulcrum is just balanced by the 10N force 30m from the fulcrum.
The moments are equal according to the expression below
30N X 10m = 10N X 30m
What is the minimum force that is required to lift the load with a
force acting on it of 300N?
Firstly the moments must be equal on both sides of the fulcrum at
the point where the load force just balances the effort force.
2m X 300N = 10m X effort
effort = 60N.
So the minimum force required to just lift the load is 60N.
What is the maximum force that can be lifted with a force of 300N if
the lever on the right is used?
Firstly the moments must be equal on both sides of the fulcrum at the
point where the load force just balances the effort force.
6m X load = 18m X 300N
load = 900N.
So the maximum force that can be opposed with a force of 300N is
900N.
Moment exercises
What is the force that must be applied to just lift the rock
pushing down with a force of 500N?
Solution
500N X 2m = 8m X effort
125N = effort
What is the maximum force that can be opposed if the
person can apply a force of 300N ?
Solution
Load X 8m = 2m X 300N
Load = 75N
What distance must a person be from the fulcrum to apply a
force of 60N in order to lift a 300N load.
Solution
The moments on either side of the fulcrum should be equal. If
the force applied is 60N then the relationship below is true
300N X 8m = 60N X "X"
40m = X
Look at the lever on the right. The effort(piston) moves up 10cms while
the end of the lever moves 30cms over the same time period.
The velocity ratio is 1/3.
You may have observed that the closer the effort is to the
fulcrum the greater the distance the load moves through.
Notice how little the lever is lifted by the piston on the right.
One advantage, however, is the further away the effort is
from the fulcrum the greater the load that can be lifted.
The velocity ratio in this case is 1.
Using levers to multiply the velocity of the load was used to
great effect in medieval siege weapons.
Huge boulders were hurled at castles with devastating effect.
How far away from the fulcrum must the red 5kg mass be in order to
just lift the 10kg mass 10 metres away from the fulcrum?
The 10kg load will be lifted by the 5kg effort when the 5kg mass
is 20m away from the fulcrum
How far away from the fulcrum must the red 5kg mass be in order
to just lift the 10kg mass 30 metres away from the fulcrum?
The 10kg load will be lifted by the 5kg effort when the 5kg mass is 60m
away from the fulcrum.