Lecture 3: Forces and Levers

Question 1

What is a lever?

Answer 1

rigid object that can pivot (rotate) around an axis

Question 2

What can levers amplify?

Answer 2

force or distance

Question 3

What is mechanical (force) advantage (MA)?

Answer 3

amplification (or reduction) in force due to relative lengths of the effort and load arm

MA = FL/FE = dE/dL

Question 4

What is distance (or speed) advantage (DA)?

Answer 4

amplification (or reduction) in distance moved (and the speed) due to relative lengths of the effort and load arm

DA = FE/FL = dL/dE

Question 5

Are distance advantage and speed advantage the same?

Answer 5

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

Question 6

How is MA and DA related?

Answer 6

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)

Question 7

How are the 3 types of levers defined?

Answer 7

by where the effort, load, and fulcrum are positioned along the lever

Question 8

What is the effort moment arm?

Answer 8

force in – with a length of dE

Question 9

What is the load moment arm?

Answer 9

force out – with a length of dL

Question 10

What is the fulcrum?

Answer 10

pivot point or axis of rotation

Question 11

What is a 1st class lever?

Answer 11

• fulcrum is between the effort and load
• dL > or < or = dE

ie. crowbar, scissors

Question 12

What is a 2nd class lever?

Answer 12

• fulcrum is one side of both the effort and load – load is closer
• dL < dE
• MA > 1

ie. wheelbarrow, bottle opener

Question 12

What is a 3rd class lever?

Answer 12

• fulcrum is one side of both the effort and load – effort is closer
• dL > dE
• MA < 1

ie. most levers in musculoskeletal system

Question 13

What does MA > 1 mean?

Answer 13

force is amplified by the lever

Question 14

What does MA < 1 mean?

Answer 14

force is reduced by the lever

Question 15

What does DA > 1 mean?

Answer 15

distance/speed is amplified by the lever

Question 16

What does DA < 1 mean?

Answer 16

distance/speed is reduced by the lever

Question 17

What is torque (moment of force)?

Answer 17

force that causes an object to rotate about an axis

units: Nm

Question 18

What is the moment arm?

Answer 18

distance between the axis of rotation and the applied force?

Question 19

What direction is positive torque?

Answer 19

counter-clockwise

Question 20

What direction is negative torque?

Answer 20

clockwise

Question 21

What is the centre of gravity?

Answer 21

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

Question 22

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)

Answer 22

• force acting on the forearm
• length of the moment arm (dL) – ie. distance from the elbow to the centre of gravity of the arm

Question 23

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)

Answer 23

• 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

Question 24

What is the length of the moment arm (dE)?

Answer 24

perpendicular distance from the axis of rotation (fulcrum) to the line of action of the force

Question 25

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)?

Answer 25

all of the effort force (FE) is contributing to the torque about that axis

torque = FE x dE

Question 26

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)

Answer 26

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

Question 27

What is the length of dE compared to L?

Answer 27

dE is always shorter than L when θ ≠ 90º

Question 28

What happens to the relationship between θ and dE if the muscle’s force is directed inward vs. outward relative to the lever?

Answer 28

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

Question 29

What happens to the relationship between θ and FEperp if the muscle’s force is directed inward vs. outward relative to the lever?

Answer 29

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

Question 30

How does MA and DA change with a change in the angle?

(DON’T KNOW IF THIS IS RIGHT)

Answer 30

smaller angle → lower MA, higher DA

as close to 90º to maximize

Question 31

What do forelegs of burrowing animals require?

Answer 31

digging requires high force at the end of the limb – slow, high force limbs

Question 32

What do forelegs of running animals require?

Answer 32

running requires high speed at the end of the limb – fast, low force limbs

• very low MA
• very high DA (both distance and speed)