Lecture 3: Forces and Levers Flashcards
What is a lever?
rigid object that can pivot (rotate) around an axis
What can levers amplify?
force or distance
What is mechanical (force) advantage (MA)?
amplification (or reduction) in force due to relative lengths of the effort and load arm
MA = FL/FE = dE/dL
What is distance (or speed) advantage (DA)?
amplification (or reduction) in distance moved (and the speed) due to relative lengths of the effort and load arm
DA = FE/FL = dL/dE
Are distance advantage and speed advantage the same?
yes – if the distance from the fulcrum to A is 4x greater than the distance from the fulcrum to B, A moves 4x the distance of B, and at 4x the speed
How is MA and DA related?
they are the reciprocal of one another – levers conserve work (ie. lifting a 1 kg mass 10 m requires the same amount of energy as lifting a 10 kg mass 1 m)
How are the 3 types of levers defined?
by where the effort, load, and fulcrum are positioned along the lever
What is the effort moment arm?
force in – with a length of dE
What is the load moment arm?
force out – with a length of dL
What is the fulcrum?
pivot point or axis of rotation
What is a 1st class lever?
- fulcrum is between the effort and load
- dL > or < or = dE
ie. crowbar, scissors
What is a 2nd class lever?
- fulcrum is one side of both the effort and load – load is closer
- dL < dE
- MA > 1
ie. wheelbarrow, bottle opener
What is a 3rd class lever?
- fulcrum is one side of both the effort and load – effort is closer
- dL > dE
- MA < 1
ie. most levers in musculoskeletal system
What does MA > 1 mean?
force is amplified by the lever
What does MA < 1 mean?
force is reduced by the lever
What does DA > 1 mean?
distance/speed is amplified by the lever
What does DA < 1 mean?
distance/speed is reduced by the lever
What is torque (moment of force)?
force that causes an object to rotate about an axis
units: Nm
What is the moment arm?
distance between the axis of rotation and the applied force?
What direction is positive torque?
counter-clockwise
What direction is negative torque?
clockwise
What is the centre of gravity?
point where the entire mass of an object may be assumed to be concentrated – this is the point where you can consider the line of force acting
What do you need to know to solve this problem:
How much torque is acting on an elbow with the arm held horizontally?
(SEE SLIDES)
- force acting on the forearm
- length of the moment arm (dL) – ie. distance from the elbow to the centre of gravity of the arm
What do you need to know to solve this problem:
How much force must the bicep be producing to hold this position against gravity?
(SEE SLIDES)
- if the arm isn’t moving, then sum of all torques/forces must equal zero (balanced)
- muscle must produce an equal (but clockwise – negative) torque to the arm – ie. if the torque the muscle must counteract is 3.5 nm, the muscle needs to produce a torque of -3.53 Nm
- need to know the length of the moment arm for the muscle – distance between muscle insertion point and elbow (this is where the force exerted by the muscle will act
What is the length of the moment arm (dE)?
perpendicular distance from the axis of rotation (fulcrum) to the line of action of the force
How much of the effort force is contributing to the torque about the axis if the line of action and the moment are perpendicular (90º)?
all of the effort force (FE) is contributing to the torque about that axis
torque = FE x dE
How much of the effort force is contributing to the torque about the axis if the line of action and the moment are not perpendicular, at any other angle?
(SEE SLIDES)
some component of the force is not contributing to the torque around the axis of rotation – must calculate the amount
- calculate the component of the applied effort force (FE) that is perpendicular to the moment arm L using cos(θ), where L = dE for the perpendicular component of FEperp (torque = FEperp x L)
- calculate the length of the moment arm (dE), which is perpendicular to the line of action, and therefore FE
What is the length of dE compared to L?
dE is always shorter than L when θ ≠ 90º
What happens to the relationship between θ and dE if the muscle’s force is directed inward vs. outward relative to the lever?
relationship between θ and dE is the same
- calculate length of dE being acted on by FE
- use FE and calculated dE in any calculations of torque, DA, or MA
What happens to the relationship between θ and FEperp if the muscle’s force is directed inward vs. outward relative to the lever?
relationship between θ and FE perp is the same
- calculate the component of FE acting perpendicular to L
- use L = dE and cos(θ)FE to calculate torque BUT do not use L to calculate MA or DA
How does MA and DA change with a change in the angle?
(DON’T KNOW IF THIS IS RIGHT)
smaller angle → lower MA, higher DA
as close to 90º to maximize
What do forelegs of burrowing animals require?
digging requires high force at the end of the limb – slow, high force limbs
What do forelegs of running animals require?
running requires high speed at the end of the limb – fast, low force limbs
- very low MA
- very high DA (both distance and speed)
