1. Journal 2/24/16 Where do we see simple machines in the Bible? Objective Tonight’s Homework To learn about mechanical advantage and efficiency p 323: 2 p 334: review 5, 6, 7, 11

2. Mechanical Advantage and Efficiency On the posters you looked at last week was something called “mechanical advantage”. This is a measurement of how much we multiply our “force in” to get the “force out”. Most simple machines are designed to simply let you trade distance for force. You can use less force to do something hard if you’re willing to move more distance. Ex: The long-handled wrench lets you tighten things with tons of fore, but you have to move your arm a lot.

3. Mechanical Advantage and Efficiency Example: We have a lever that we’ve wedged under a rock. We make the handle 10 times longer on our side than on the side with the rock. So if I push down on my end, 1 have to move my hand 10 feet for every foot the rock moves up. What’s my mechanical advantage?

4. Mechanical Advantage and Efficiency Example: We have a lever that we’ve wedged under a rock. We make the handle 10 times longer on our side than on the side with the rock. So if I push down on my end, 1 have to move my hand 10 feet for every foot the rock moves up. What’s my mechanical advantage? We’re being told that the person has to push things 10 times farther. This means they’re only using 1/10 as much force. So according to the posters we did: MA = resistance / effort MA = 1 / (1/10) MA = 10

5. Mechanical Advantage and Efficiency For levers, we can get these numbers more easily using the Law of Moments. This was also something you wrote down from the posters. Let’s take a look at how this works as well.

6. Mechanical Advantage and Efficiency Example: If everything is in balance, the force*distance from box A to the fulcrum is equal to the force*distance from box B to the fulcrum. Or, written all mathy… F A d A = F B d B AB

7. Mechanical Advantage and Efficiency Example: A man is trying to wedge a crowbar into a box to pry it open. If he sets it up as shown below and pushes down with 200 N of force, how much force will pry on the other end of the crowbar? 60 cm 10 cm 200 N

8. Mechanical Advantage and Efficiency Example: A man is trying to wedge a crowbar into a box to pry it open. If he sets it up as shown below and pushes down with 200 N of force, how much force will pry on the other end of the crowbar? F A d A = F B d B (200 N)(60 cm) = F B (10 cm) F B = (200 N)(60 cm) / (10 cm) F B = 1200 N 60 cm 10 cm 200 N

9. Mechanical Advantage and Efficiency Efficiency is a measure of how much energy our machine wastes. This waste is usually due to friction causing things to rub against each other. For example: A car engine takes gasoline, makes it explode, and turns the energy it makes into motion. However, all the moving parts in the engine waste a lot of energy. For every 100 J of energy that goes into the car, only 25 J help move the car forward. What is the car’s efficiency?

10. Mechanical Advantage and Efficiency Efficiency is a measure of how much energy our machine wastes. This waste is usually due to friction causing things to rub against each other. For example: A car engine takes gasoline, makes it explode, and turns the energy it makes into motion. However, all the moving parts in the engine waste a lot of energy. For every 100 J of energy that goes into the car, only 25 J help move the car forward. What is the car’s efficiency? Efficiency = Useful Energy Out / Total Energy In Efficiency = 25 J / 100 JEfficiency = 25%

11. Practice 1. Jenna applied 20N of force to turn an ice cream freezer crank. The crank’s resistance was 60 N. What was the mechanical advantage of the crank? 2. Suppose you need to remove a nail from a board by using a claw hammer. If the handle is is 11.0 cm long and the nail moves 2.0 cm, how much force is being put on the nail if you apply 250 N? 3. A pulley is used to raise a heavy crate. The pulley is such that an input force of 223 N is needed to provide an output force of 1784 N. What is the mechanical advantage of this pulley? 4. A mover uses a ramp to load a crate of nails onto a truck. The crate, which must be lifted 1.4 m from the street to the bed of the truck, is pushed along the length of the ramp. If the ramp is 4.6 m long, what is the mechanical advantage of the ramp?

12. Machines in the Bible You have another assignment due on Friday as well. Your job is to find an example of each of the 6 simple machines in the Bible. We have a little time left in class, so you can start on this now if you wish.

13. Exit Question Can you ever have a mechanical advantage of less than 1? Yes No