How do we calculate and compare the advantages that machines give us? Watch this video to learn about mechanical advantage.
Lesson D6: Mechanical Advantage
Figure D.2.6.1 – The input force of a bicyclist is greater than the output force of the bicycle.
Figure D.2.6.2 – Class 3 levers have a mechanical advantage of less than 1.
Figure D.2.6.3 – Catapults and trebuchets fling projectiles from class 3 levers.
Reading and Materials
for This Lesson
Science in Action 8
Reading: Pages 280–286
Materials:
2 identical lightweight plastic or styrofoam cups, 45 identical coins (nickels or dimes), tape, ruler (30 cm), pencil, empty 4 L milk jug with a cap and handle, water, broom, tape measure, plastic rope (15 m length).
Mechanical Advantage Less Than 1
Some machines require more input force than they deliver in output force. Machines like this have a mechanical advantage of less than 1. Machines with a mechanical advantage of less than 1 are still useful, but not for multiplying force. Instead,
these machines make an object move a longer distance than the machine’s user could achieve on their own. Bicycles, catapults, and third class levers are
machines that have a mechanical advantage of less than 1. These machines all make an object move a longer distance at a faster speed.
Try It!
Figure D.2.6.4 – People loading heavy boxes into trucks may use inclined planes of different lengths and heights. Image courtesy Sunset Removals.
Calculating Mechanical Advantage and Speed Ratio
Try these practice calculations of mechanical advantage and speed ratio for a mover using different ramps (inclined planes).
Download:
DOWNLOAD this document. It provides a table for you to record
your calculations. It also provides space for you to do your math work, so it would be a good idea to print this document. It also provides space for you to answer the questions later in this activity.
Instructions:
A mover must place loads into a moving truck 1 m above the ground. The loads are very heavy; 500 N of force is required to lift each load straight up. The mover will therefore use a series of longer and longer ramps to make the task easier. Your
job is to calculate the mechanical advantage and speed ratio for the different ramps.
A mover must place loads into a moving truck 1 m above the ground. The loads are very heavy; 500 N of force is required to lift each load straight up. The mover will therefore use a series of longer and longer ramps to make the task easier. Your
job is to calculate the mechanical advantage and speed ratio for the different ramps.
Calculate and record the mechanical advantage for the 2 m ramp. Remember, mechanical advantage is equal to the output force (the force needed to lift the load straight up) divided by the input force (the force needed to move the load using the ramp).
Calculate and record speed ratio for the 2 m ramp. Remember, speed ratio is equal to the input distance (the distance moved along the ramp) divided by the output distance (the distance the load is actually moved upward).
Repeat steps 2 and 3 for the other ramps (3 m, 4 m, 5 m).
Observations:
Questions:
Think about the following questions very carefully. Then, type or write your answers. After you have your answers, click the questions for feedback.
Mechanical advantage and speed ratio are the same for all the ramps. This is a situation with an ideal mechanical advantage. There is no friction affecting the input force.
Most people would choose the 5-metre ramp, because the it requires the least amount of force input. But that might not always be the best choice under real-world conditions. To get the least amount of force input, the mover requires the longest
ramp, but it may not be convenient to place a 5-metre where the mover is working. Note that the speed ratio for the 5-metre ramp is 5, meaning that mover must move the load a distance of 5 units using the machine (in this case, a ramp) for
every 1 unit of distance that load actually moves upward. For many reasons, the mover may not want to do all that walking, and might choose a shorter ramp.
You would need to apply a greater input force to overcome friction on the ramp. When you divide the output force by a larger input force, you get a smaller mechanical advantage.
Try It!
Mechanical Advantage of Levers
Try this simple experiment to measure the mechanical advantage and speed ratio of different levers.
Materials:
2 identical lightweight plastic or styrofoam cups
45 identical coins (nickels or dimes)
Tape
Ruler (30 cm)
Pencil
Download:
DOWNLOAD this document. It provides a table for you to record
your calculations. It also provides space for you to do your math work, so it would be a good idea to print this document. It also provides space for you to answer the questions later in this activity.
Instructions:
Tape one cup to either side of the ruler.
Build a first class lever with the ruler as the lever and the pencil as the fulcrum. Place the fulcrum exactly in the middle of the ruler at the 15 cm mark. Tape the pencil to the ruler to hold it in place. The input and output distances are both
15 cm for this lever (see figure D.2.6.5).
Put 20 identical coins into the cup closest to the 0 cm mark on the ruler. These coins are the “output force”.
Add coins one at a time to the other cup. Add coins until the lever just tips to lift the “output force” cup. On the observations table, record the number of coins you added to the second cup as the “input force”.
Calculate and record the mechanical advantage for this lever. Mechanical advantage is equal to the output force divided by the input force.
Calculate and record the speed ratio for this lever. Speed ratio is equal to the input distance divided by the output distance.
Repeat steps 2-6, but change the fulcrum of the lever. Place and tape the fulcrum at the 10 cm mark on the ruler. The new output distance is 10 cm and the new input distance is 20 cm (see figure D.2.6.6).
Repeat steps 2-6, but change the fulcrum of the lever. Place and tape the fulcrum at the 5 cm mark on the ruler. The new output distance is 5 cm and the new input distance is 25 cm (see figure D.2.6.7).
Figure D.2.6.5 – Pencil at 15 cm mark on ruler.
Figure D.2.6.6 – Pencil at 10 cm mark on ruler.
Figure D.2.6.7 – Pencil at 5 cm mark on ruler.
Observations:
Force and Distance to Lift 20 Coins
Questions:
Think about the following questions very carefully. Then, type or write your answers. After you have your answers, click the questions for feedback.
In your experiment, the mechanical advantage and speed ratio for the lever are exactly the same or close to the same. There was not much friction to reduce the input force on this lever.
You can increase the mechanical advantage of a first class lever by moving the fulcrum closer to the output force on the lever.
Try It!
Broomstick Pulleys
Try
this experiment to measure the speed ratio of a pulley system. You will need two other people to help you with this experiment.
Figure D.2.6.8 – A single loop of rope over the broom handle
Figure D.2.6.9 – Two loops of rope over the broom handle.
Figure D.2.6.10 – Three loops of rope over the broom handle.
Materials:
Empty 4 L milk jug with a cap and handle
Water
Broom
Tape measure
Plastic rope (15 m length)
Download:
DOWNLOAD this document. It provides a table for you to record
your calculations. It also provides space for you to do your math work, so it would be a good idea to print this document. It also provides space for you to answer the questions later in this activity.
Instructions:
Fill the empty milk jug half full with water and close it tightly.
Have your two helpers hold the broom horizontally, approximately 1 meter high off the floor.
Loop the rope around the broom handle and tie it together with a knot.
Place the milk jug on the floor, centered with the broom. Thread the loose end of the rope through the milk jug handle.
Loop the loose end of the rope back up and over the broom handle. The loose end of the rope should now be hanging loosely on the floor (see figure D.2.6.8).
Using the tape measure, adjust the broom handle and the rope so that the broom handle is held 100 cm above the point where the rope is attached to the jug. Have your helpers hold the broom handle at exactly this height. The rope looped around
the jug and broom handle should be tight, without lifting the jug off the floor.
Place a piece of tape at the spot on the rope where it makes its final loop around the broom.
Pull on the loose end of the rope and lift the jug until the jug handle reaches the height of the broom handle.
Place a second piece of tape at the new spot on the rope where it makes its final loop around the broom.
Release the jug.
Use the tape measure to measure the distance in centimetres between the two pieces of tape on the rope. Record this measurement as the input distance in the observations table.
Repeat steps 2-11, but during step 5, loop the rope through the jug handle and back around the broom a second time (see figure D.2.6.9).
Repeat steps 2-12, but after you complete step 5, loop the rope through the jug handle and around the broom handle a third time (see figure D.2.6.10).
Observations:
Questions:
Think about the following questions very carefully. Then, type or write your answers. After you have your answers, click the questions for feedback.
We did not measure force with a spring scale in this experiment. In order to calculate mechanical advantage, you need to measure input and output force. We measured input and output distance in this experiment, which are used to calculate
speed ratio.
The MA would be slightly lower than the SR for each pulley system. Friction between the rope, the broomstick, and the jug would increase the input force on the rope, reducing the MA of the system.
Make sure you have understood everything in this lesson. Use the Self-Check below, and the Self-Check & Lesson Review Tips to guide your learning.
Unit D Lesson 6 Self-Check
Instructions
Complete the following 6 steps.
Don't skip steps – if you do them in order, you will confirm your
understanding of this lesson and create a study bank for the future.
ANSWER all the questions on the downloaded quiz in the spaces provided. Think carefully before typing your answers. Review this lesson if you need to. Save your quiz when you are done.
COMPARE your answers with the suggested "Self-Check Quiz Answers" below. WAIT! You didn't skip step 2, did you? It's very important to carefully write out your own answers before checking the suggested answers.
REVISE your quiz answers if you need to. If you answered all the questions correctly, you can skip this step. Revise means to change, fix, and add extra notes if you need to. This quiz is NOT FOR MARKS, so it is perfectly OK to correct
any mistakes you made. This will make your self-check quiz an excellent study tool you can use later.
SAVE your quiz to a folder on your computer, or to your Private Files. That way you will know where it is for later studying.
CHECK with your teacher if you need to. If after completing all these steps you are still not sure about the questions or your answers, you should ask for more feedback from your teacher. To do this, post in the Course Questions Forum,
or send your teacher an email. In either case, attach your completed quiz and ask; "Can you look at this quiz and give me some feedback please?" They will be happy to help you!
Be a Self-Check
Superhero!
Self-Check Quiz Answers
Click each of the suggested answers below, and carefully compare your answers to the suggested answers.
If you have not done the quiz yet – STOP – and go back to step 1 above. Do not look at the answers without first trying the questions.
The output force required to move the box is 1000 N. The input force that the wagon exerts on the box is 400 N. Mechanical advantage equals the output force divided by the input force, so 1000/400 = 2.5. The wagon has a MA of 2.5.
There is another way to think of mechanical advantage that might be helpful here. Consider that most machines are created to make our lives easier... they make jobs feel easier than they actually are. The easier a machine makes the job, the greater the mechanical advantage. So when calculating mechanical advantage, you can also think of it this way: How much force would be needed to do the task if there was NO machine? In the case of this wagon example, it would take 1000 N to push the box (this would be the output force). Now compare that to how much force is needed when you use the machine. In the case of the wagon, using the wagon takes only 400 N (this would be the input force). Again, 1000 divided by 400 = 2.5, so using the wagon provides a mechanical advantage of 2.5.
Mechanical advantage and speed ratio would be exactly the same in an ideal situation where there is no friction to decrease the input force of the system.
The man’s input force is 1000 N, and the output force required for the machine to lift the rock is 1500 N. Mechanical advantage equals the output force divided by the input force, so 1500/1000 = 1.5. The lever has a MA of 1.5.
Multiplying force is not the only advantage of using a machine. A machine can also change the direction of a force. A pulley with a mechanical advantage of 1 does not reduce the force required to lift an object, but it can still change the direction
of the force. This allows you to lift an object by pulling downward instead of lifting upward.
Mechanical advantage equals the output force divided by the input force, so 210/300 = 0.7. The tennis racket has a MA of 0.7. This MA is less than 1, so it does not multiply force. However, you can use the tennis racket to make a ball move a
great distance than your hand moves, this makes the ball move much faster than your hand.
Reading and Materials
for This Lesson
