Lever Mechanical Advantage (M.A.)
Introduction:
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How does a lever make work easier? It multiplies your force! (That’s the mechanical advantage.)
The LONGER your side of the lever is, the easier it is to lift something!
Mechanical advantage has NO units! (Yay! You don’t need to label units if you’re calculating M.A.)
There are different equations for Mechanical Advantage. (Use whichever one you have data for.)
Mechanical Advantage explains HOW much the machine multiplies your force. (Ex: M.A. of 2 doubles your force!)
A lever has parts that are labeled below:
Effort
Arm
(Input arm)
Resistance Arm (Output arm)
Load (or Resistance Force)
Fulcrum
Lever Mechanical Advantage Equations:
MAlever = Fo(output force, resistance force)
Fi (input force, effort force)
Or you can use the ratio of the input arm length to the output arm length:
MAlever = Li (length of input arm, effort arm)
Lo (length of output arm, resistance arm)
Example 1: A construction worker uses a board as a lever to lift a heavy rock. If the input arm is 3
meters long and the output arm is 0.75 meters long, what is the mechanical advantage of the lever?
MA = 3 meters = 4
0.75 meter
Example 2: Sometimes levers are used to multiply distance. For a broom, your
upper hand is the fulcrum and your lower hand provides the input force:
Notice the input arm is shorter than the output arm.
The mechanical advantage of this broom is:
MA = 0.3 meter = 0.25
1.2 meters
Lever probs. YOU BETTER SHOW YOUR WORK (or else)!! Write each equation used!
1. A lever used to lift a heavy box has an effort arm of 4 meters and a resistance arm of 0.8 meters.
What is the mechanical advantage of the lever? (Use second equation b/c that’s what you have info for!)
2. What is the mechanical advantage of a lever that has an effort arm of 3 meters and a resistance
arm of 2 meters?
3. A lever with an effort arm of 2 meters has a mechanical advantage of 4. What is the resistance
arm’s length? (Don’t forget to include UNITS in this answer!)
4. You apply 40 Newtons of force (input force) to a lever that has a 120 Newton weight on the other
end (output force) and lift it! What is the mechanical advantage of the lever? (Use the 1st equation)
5. Your coach needs you to be able to lift 150 pounds (660 Newtons) but you can only lift 100 pounds
(440 Newtons). You tell your coach that you can lift that amount…using a machine. What is the
Mechanical Advantage of the lever you need to lift 150 pounds?
6. A lever with a resistance arm of 0.8 meter has a mechanical advantage of 6. What is the length of
the effort arm? (Include UNITS!)
7. A rake is held so that its effort arm is 0.4 meters and its resistance arm is 1.0 meters. What is the
mechanical advantage of the rake?
8. A broom with an effort arm length of 0.4 meters has a mechanical advantage of 0.5. What is the
length of the resistance arm? (UNITS!)
9. A child’s toy rake is held so that its resistance arm is 0.75 meters. If the mechanical advantage is
0.33, what is the effort arm length? (UNITS! Round to 2 decimal places.)
10. a. Your friend wants to lift your dad’s Porsche off the ground to look underneath it. Your friend
has a maximum input force of 100 Newtons (weakling) and the car weighs 4,000 pounds (17,000
Newtons). What is the mechanical advantage of the lever necessary for your friend to lift the car?
b. He gets a lever and a rock for a fulcrum. He puts the car 2 meters away from the fulcrum. Using
the mechanical advantage of the lever (calculated from part a), what is the length of the effort arm?
c. How long is the lever in total? (UNITS!)