Levers the Law of Torques Lever A lever

Levers & the Law of Torques

Lever • A lever is a rigid bar that turns around a point. • The fixed point is called the pivot point or the fulcrum

Lever • Gravity exerts a downward force on a person on a seesaw. • However, the seesaw rotates around the fulcrum as the person descends. • So the lever moving about the fulcrum is a form of rotational motion.

Lever • If the weights and positions of people on a seesaw are balanced, the seesaw is said to be in a state of rotational equilibrium. weight A = weight B no acceleration weight A weight B

Lever • Anytime a force acts perpendicularly on a rotating lever, it produces a quantity called a torque or a moment.

The Law of Torques • When the seesaw is balanced, the torques are equal. • This law can be written as a formula: w 1 l 1 = w 2 l 2 weight (N) distance from fulcrum (m)

The Law of Torques • This formula is called the law of torques. • The “l” can also be called the torque arm.

Sample Problem 1 If a 600 N girl sits on one side of a seesaw (3 m from the fulcrum), where should a 450 N girl sit in order to balance the seesaw?

Sample Problem 1 If a 600 N girl sits on one side of a seesaw (3 m from the fulcrum), where should a 450 N girl sit in order to balance the seesaw? (600 N)(3 m) = (450 N)(l 2)

Sample Problem 1 If a 600 N girl sits on one side of a seesaw (3 m from the fulcrum), where should a 450 N girl sit in order to balance the seesaw? (600 N)(3 m) = (450 N)(l 2) 1800 N • m = (450 N)(l 2) 4 m=l 2

Sample Problem 2 What is the AMA of the seesaw?

Sample Problem 2 What is the AMA of the seesaw? resistance AMA = = effort =

Sample Problem 2 What is the AMA of the seesaw? resistance 600 N AMA = = = 1. 33 effort 450 N

Sample Problem 2 What is the AMA of the seesaw? resistance 600 N AMA = = =1 effort 450 N (1 SDs)

First-Class Levers • In a first-class lever the fulcrum is in the middle. • The push (effort) is at one end. weight • The weight (resistance) is fulcrum at the other end. push • Example: seesaw

First-Class Levers • The side on which the push occurs is called the effort arm. • The side on which the weight is found is called resistance weight the resistance arm. effort push

First-Class Levers • The law of moments allows us to solve problems involving levers. resistance effort

First-Class Levers • First-class levers can have an IMA of less than 1, 1, or greater than 1 depending on the lengths of the moment arms. • If the arm lengths are equal, the MA = 1. • If they are unequal, one side of the seesaw has an MA > 1 and the other side has an MA < 1.

Second-Class Levers • A second-class lever has the resistance in the middle. § Examples: wheelbarrow, door hinge • The MA will always be greater than 1 because the effort arm is longer.

Sample Problem 3 If a 500 N force sits in a wheelbarrow 0. 5 m from the fulcrum and a boy lifts the wheelbarrow 1. 2 m from the fulcrum, what is the MA?

Sample Problem 3 If a 500 N force sits in a wheelbarrow 0. 5 m from the fulcrum and a boy lifts the wheelbarrow 1. 2 m from the fulcrum, what is the MA? effort arm MA = = resist arm =

Sample Problem 3 If a 500 N force sits in a wheelbarrow 0. 5 m from the fulcrum and a boy lifts the wheelbarrow 1. 2 m from the fulcrum, what is the MA? effort arm 1. 2 m MA = = = 2. 4 resist arm 0. 5 m

Second-Class Levers • Second-class levers allow for a smaller effort by exerting that force over a longer distance.

Third-Class Levers • A third-class lever has the effort applied between the fulcrum and the resistance. effort resistance fulcrum

Third-Class Levers • Since this makes the effort arm shorter, the MA is always less than 1. effort resistance fulcrum

Third-Class Levers • MA that is less than 1 multiplies the amount of effort motion. • MA that is greater than 1 multiplies that effort force.

What two quantities are used in the law of moments? 1. 2. 3. 4. Force and work Force and time Work and distance Distance and force Ques tion

On a balanced seesaw, a 500 N girl sits 5 m from the fulcrum, on the other side a boy sits 4 m from the fulcrum, what is his weight? 1. 2. 3. 4. 2, 500 N 2, 496 N 625 N 10, 000 N Ques tion

On a balanced seesaw, a 500 N girl sits 5 m from the fulcrum, on the other side a boy sits 4 m from the fulcrum, what is his weight? w 1 l 1 = w 2 l 2 (500 N)(5 m) = w 2 (4 m) 2, 500 N = 4 • w 2 625 N = w 2

If you have to push down on a crowbar with 50 N of force to lift a 700 N object, what is the MA? 1. 2. 3. 4. 3, 500 14 650 750 Ques tion

If you have to push down on a crowbar with 50 N of force to lift a 700 N object, what is the MA? MA = resistance / effort MA = 700 N / 50 N MA = 14

If you lift a wheelbarrow 1. 0 m, which lifts the resistance 0. 4 m, what is the MA? 1. 2. 3. 4. 2. 5 0. 6 1. 4 0. 4 Ques tion

If you lift a wheelbarrow 1. 0 m, which lifts the resistance 0. 4 m, what is the MA? effort arm distance MA = resistance arm distance 1. 0 m MA = 0. 4 m MA = 2. 5

What class lever is a wheelbarrow? 1. 2. 3. 4. First Second Third Fourth Ques tion

What class lever is a pair of tweezers? 1. 2. 3. 4. First Second Third Fourth Ques tion

IDENTIFY THE FOLLOWING LEVERS

Crowbar

Body Parts

Nutcracker

Serving Tongs

Hitting a baseball

Shoveling snow

Rowing a canoe

Determine the IMA of this lever