# The Lever. The law of conservation of energy applies to all machines!

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1 Simple Machines A machine is a device for multiplying forces or simply changing the direction of forces. Many machines can increase the speed with which work is done.

2 The Lever The law of conservation of energy applies to all machines! At the same time we do work on one end of the lever, the other end does work on the load.

3 The Lever We see that the direction of the force is changed. If we push down, the load is lifted up. More importantly, the small force we use has been multiplied into a much larger force.

4 The Lever In this example, the small force this person exerts on the car jack handle has been multiplied so much it can lift the weight of the car. The price you pay for this is that you have to exert your force over a much larger distance. When the handle moves down 25 cm, the car moves up only 0.25 cm.

5 Energy Conservation Input work = output work input force x input distance = output force x output distance F x d = F x d A machine can multiply force but never energy! NO WAY!

6 1 st class lever The first class lever places the pivot point (fulcrum) in the middle. F R F E Examples: the playground see-saw, the pry bar, scissors, and car jack

7 2 nd class lever The second class lever places the load (resistance force) in the middle. F E F R An example would be a wheelbarrow.

8 3 rd class lever In the third class lever, the input force (effort force) is in the middle. F R F E An example would be a tennis racket. What advantages and disadvantages can you identify for each class of lever?

9 Pulleys Another type of simple machine is the pulley. Like the lever, pulleys can also multiply force and change its direction. REMEMBER: No simple machine can multiply energy!

10 Pulleys Can you see that a pulley is just a lever in disguise? This is a single fixed pulley. It acts like a lever with equal arms. It changes only the direction of the input force. When the person pulls down on the rope, the load is lifted up.

11 The advantage here is that the load can be lifted with an input force that is only half of the load's true weight. Pulleys This is a single movable pulley. Why is the fulcrum pictured on the left?

12 Mechanical Advantage Many people say that simple machines make work seem easier to do. Physicists can actually quantify the term mechanical advantage. Ideal Mechanical Advantage (IMA) stands for the number of times your input force is multiplied under ideal conditions, i.e. no friction. Actual Mechanical Advantage (AMA) stands for the number of times your input force is multiplied under real world conditions. (friction is present)

13 Single Fixed Pulley In this case, the IMA = 1. This pulley does not multiply the input force. It does change the direction of the force from up to down, and for many people, that is an advantage. W in = W out F in d in = F out d out (100 N)(10 cm) = (100 N)(10 cm)

14 One Fixed, One Movable Pulley In this case, the IMA = 2. Not only does this pulley change the direction of the force, but it also multiplies it. The 50 newton input force is able to lift 100 N of load. W in = W out F in d in = F out d out (50 N)(20 cm) = (100 N)(10 cm)

15 Two Fixed, One Movable Pulley In this case, the IMA = 3. Again, this pulley change the direction of the force, and it also multiplies it. The 33 N input force is able to lift 100 N of load. W in = W out F in d in = F out d out (33 N)(30 cm) = (100 N)(10 cm)

16 Two Fixed, Two Movable Pulleys In this case, the IMA = 4. Again, this pulley change the direction of the force, and it also multiplies it. The 25 N input force is able to lift 100 N of load. W in = W out F in d in = F out d out (25 N)(40 cm) = (100 N)(10 cm)

17 Actual Mechanical Advantage The actual input force in this case would be a little greater than the ideal value of 25 N. It might be 30 newtons. (The extra 5 newtons is used to overcome friction). W in > W out F in d in > F out d out (30 N)(40 cm) > (100 N)(10 cm)

18 Actual Mechanical Advantage The actual mechanical advantage (AMA) would be the ratio of the output force to the input force. F E = 30 N AMA= F R F E = 100 N 30 N =3.33 The AMA will always be less than the IMA.

19 How Large is the IMA? There is an easy way to tell, just by looking at the picture. This method works even if there are no numerical values labeled on the diagram. Just count the number of strands of rope that directly support the load. In this case it is 4. Therefore, the IMA is 4.

20 Let's try another one! There's move than one way to wind the cord around two fixed and two movable pulleys. Again, to find the IMA, we count the number of strands that lead directly to the load. In this case, there are 5. Therefore, the IMA is 5. The effort force is only 20 N.

21 What's the IMA here? If you said 4, you were correct! Remember not to count the strand where the input force is applied when it doesn't lead directly to the load, as in this case.

22 Other Kinds of Simple Machines Besides the lever and pulley, there are four other simples machines. the screw the inclined plane the wedge

23 What Can Machines Do? All complex machines can be seen as combinations of simple machines. Machines can change the direction of forces. They can multiply forces or multiply distances. No machine can create energy; it can only transfer energy or transform it from one form to another.

24 Simple Machines A machine is a device for multiplying forces or simply changing the direction of forces. Many machines can increase the speed with which work is done. 1

25 The Lever The law of conservation of energy applies to all machines! At the same time we do work on one end of the lever, the other end does work on the load. 2

26 The Lever We see that the direction of the force is changed. If we push down, the load is lifted up. More importantly, the small force we use has been multiplied into a much larger force. 3

27 The Lever In this example, the small force this person exerts on the car jack handle has been multiplied so much it can lift the weight of the car. The price you pay for this is that you have to exert your force over a much larger distance. When the handle moves down 25 cm, the car moves up only 0.25 cm. 4

28 Energy Conservation Input work = output work input force x input distance = output force x output distance F x d = F x d A machine can multiply force but never energy! NO WAY! 5 input work = output work only when there is no friction. In the real world, input work is greater than output work. The difference is the energy dissipated away due to friction. Nevertheless, the input force is less than the output force and the advantage of using the machine is still there.

29 1 st class lever The first class lever places the pivot point (fulcrum) in the middle. F R F E Examples: the playground see-saw, the pry bar, scissors, and car jack 6

30 2 nd class lever The second class lever places the load (resistance force) in the middle. F E F R An example would be a wheelbarrow. 7 The advantage of this arrangement is that the input force (effort force) is much farther from the fulcrum than the resistance force. That means that the effort force is multiplied by how many times it is farther from the fulcrum than the resistance force.

31 3 rd class lever In the third class lever, the input force (effort force) is in the middle. F R F E An example would be a tennis racket. What advantages and disadvantages can you identify for each class of lever? 8

32 Pulleys Another type of simple machine is the pulley. Like the lever, pulleys can also multiply force and change its direction. REMEMBER: No simple machine can multiply energy! 9

33 Pulleys Can you see that a pulley is just a lever in disguise? This is a single fixed pulley. It acts like a lever with equal arms. It changes only the direction of the input force. When the person pulls down on the rope, the load is lifted up. 10

34 The advantage here is that the load can be lifted with an input force that is only half of the load's true weight. Pulleys This is a single movable pulley. Why is the fulcrum pictured on the left? 11

35 Mechanical Advantage Many people say that simple machines make work seem easier to do. Physicists can actually quantify the term mechanical advantage. Ideal Mechanical Advantage (IMA) stands for the number of times your input force is multiplied under ideal conditions, i.e. no friction. Actual Mechanical Advantage (AMA) stands for the number of times your input force is multiplied under real world conditions. (friction is present) 12

36 Single Fixed Pulley In this case, the IMA = 1. This pulley does not multiply the input force. It does change the direction of the force from up to down, and for many people, that is an advantage. W in = W out F in d in = F out d out (100 N)(10 cm) = (100 N)(10 cm) 13

37 One Fixed, One Movable Pulley In this case, the IMA = 2. Not only does this pulley change the direction of the force, but it also multiplies it. The 50 newton input force is able to lift 100 N of load. W in = W out F in d in = F out d out (50 N)(20 cm) = (100 N)(10 cm) 14 Notice here that you have traded off distance for force. You have to pull down 20 cm of rope for every 10 cm you wish the load to rise up in the air.

38 Two Fixed, One Movable Pulley In this case, the IMA = 3. Again, this pulley change the direction of the force, and it also multiplies it. The 33 N input force is able to lift 100 N of load. W in = W out F in d in = F out d out (33 N)(30 cm) = (100 N)(10 cm) 15 Notice here that you have traded off distance for force. You have to pull down 20 cm of rope for every 10 cm you wish the load to rise up in the air.

39 Two Fixed, Two Movable Pulleys In this case, the IMA = 4. Again, this pulley change the direction of the force, and it also multiplies it. The 25 N input force is able to lift 100 N of load. W in = W out F in d in = F out d out (25 N)(40 cm) = (100 N)(10 cm) 16 Notice here that you have traded off distance for force. You have to pull down 20 cm of rope for every 10 cm you wish the load to rise up in the air.

40 Actual Mechanical Advantage The actual input force in this case would be a little greater than the ideal value of 25 N. It might be 30 newtons. (The extra 5 newtons is used to overcome friction). W in > W out F in d in > F out d out (30 N)(40 cm) > (100 N)(10 cm) 17 Notice here that you have traded off distance for force. You have to pull down 20 cm of rope for every 10 cm you wish the load to rise up in the air.

41 Actual Mechanical Advantage The actual mechanical advantage (AMA) would be the ratio of the output force to the input force. AMA= F R F E = 100 N 30 N =3.33 F E = 30 N The AMA will always be less than the IMA. 18 Notice that the effort distance is still 4 times longer than the distance the load moves up. The ratio of the distance is always equal to the IMA, even when a lot of friction is present.

42 How Large is the IMA? There is an easy way to tell, just by looking at the picture. This method works even if there are no numerical values labeled on the diagram. Just count the number of strands of rope that directly support the load. In this case it is 4. Therefore, the IMA is 4. 19

43 Let's try another one! There's move than one way to wind the cord around two fixed and two movable pulleys. Again, to find the IMA, we count the number of strands that lead directly to the load. In this case, there are 5. Therefore, the IMA is 5. The effort force is only 20 N. 20

44 What's the IMA here? If you said 4, you were correct! Remember not to count the strand where the input force is applied when it doesn't lead directly to the load, as in this case. 21

45 Other Kinds of Simple Machines Besides the lever and pulley, there are four other simples machines. the screw the inclined plane the wedge 22

46 What Can Machines Do? All complex machines can be seen as combinations of simple machines. Machines can change the direction of forces. They can multiply forces or multiply distances. No machine can create energy; it can only transfer energy or transform it from one form to another. 23

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