1. Levers & the Law of Moments

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

3. 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.

4. 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

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

6. 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)

7. The Law of Moments This formula is called the law of moments.
The “l” can also be called the torque arm or moment arm.

8. 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

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

10. 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

11. 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

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

13. 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.

14. 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.

15. 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

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

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

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

19. 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.

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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

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

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