Levers & the Law of Moments

Lever A lever is a rigid bar that turns around a point. The fixed point is called the pivot point or the fulcrum. 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 weight A weight B no acceleration

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

distance from fulcrum (m) The Law of Moments When the seesaw is balanced, the torques are equal. This law can be written as a formula: w1l1 = w2l2 distance from fulcrum (m) weight (N)

The Law of Moments This formula is called the law of moments. The “l” can also be called the torque arm or moment 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? (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? resistance 600 N AMA = = 1 effort 450 N (1 SD)

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

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 the resistance arm. resistance weight 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 wheel-barrow 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. resistance effort fulcrum

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

https://www.youtube.com/watch?v=OdM2jWg2uEE https://www.youtube.com/watch?v=sLcz_92Gbh0

Question What two quantities are used in the law of moments? Force and work Force and time Work and distance Distance and force Question

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? 2,500 N 2,496 N 625 N 10,000 N Question

w1l1 = w2l2 (500 N)(5 m) = w2 (4 m) 2,500 N = 4 • w2 625 N = w2 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? w1l1 = w2l2 (500 N)(5 m) = w2 (4 m) 2,500 N = 4 • w2 625 N = w2

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

MA = resistance / effort MA = 700 N / 50 N MA = 14 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 If you lift a wheelbarrow 1.0 m, which lifts the resistance 0.4 m, what is the MA? 2.5 0.6 1.4 0.4 Question

If you lift a wheelbarrow 1. 0 m, which lifts the resistance 0 If you lift a wheelbarrow 1.0 m, which lifts the resistance 0.4 m, what is the MA? MA = effort arm distance resistance arm distance MA = 1.0 m 0.4 m MA = 2.5

What class lever is a wheelbarrow? First Second Third Fourth Question

Question What class lever is a pair of tweezers? First Second Third Fourth Question