Ideal Mechincal Advantage Sample Problems

First of all, be sure you have written down the formulas from the last page.

If you haven't done so, <click here to go get them>  Now we are ready to continue.

If you want to go directly to a certain problem, click on the link below:
Sample Problems:   Solving for IMA of a lever
Solving for IMA of a wheel and axle
Solving for IMA of an Inclined Plane
Using the IMA for predict output from a machine
Problem number one (solving for IMA of a lever):

When watching a circus act, you notice the tumblers using a first class lever and wonder how if one of them jumps, it can propel two of them into the air.  When the tumbling lever is measured, it shows the effort arm (which they jump on) is 8 meters long, the resistance arm (where their tumbler is being propelled from) is 2 meters long.  What is the mechanical advantage of this lever?

In order to solve this we have to do some different steps.  First we write the formula as we intend to use it.  Second, we place the numbers into the formula where they go (called the set-up) and lastly we do the mathematical calculations to attain the answer.

Step One: Write the formula as we need to use it.  In this question, we are using a lever, so we need the formula for ideal mechanical advantage of the lever.

Formula:  IMA = effort arm / resistance arm

Step Two: Now we have to figure out what value goes for each:  the effort  and the resistance.  In this problem, it tells us the effort measures is 8 meters, and the resistance is only 2 meters.  So put them in the formula.

IMA = 8m / 2m

 

Step Three: Now the last and easiest part, do the math.  The units will cancel out, so you are left with just a single number, no units.

IMA = 4*

<back to top> *This means when the tumblers jump on the beam, it multiplies their force by 4.
Problem number two (solving for IMA of a Wheel and Axle ):

When you made your mousetrap cars, wheels were very important, some had larger wheels than others.  One of the cars has the following measurements for their wheels:  the radius axle (the small wheel) measured only 1 cm.  The radius of the larger wheel (the one that touched the pavement) measured a whopping 10cm.  What was the mechanical advantage of these large wheels? 

In order to solve this we have to do some different steps.  First we write the formula as we intend to use it.  Second, we place the numbers into the formula where they go (called the set-up) and lastly we do the mathematical calculations to attain the answer.

Step One: Write the formula as we need to use it.  In this question, we are using a wheel and axle, so we need the formula for ideal mechanical advantage of the wheel and axle. Formula:  IMA = Radius(wheel) / Radius (axle)
Step Two: Now we have to figure out what value goes for each variable.  This problem tells us the radius of the axle was 1 cm and the radius of the wheel was 10cm.  So put them in the formula. IMA = 10cm / 1cm
Step Three: Now the last and easiest part, do the math.  The units will cancel out, so you are left with just a single number, no units. IMA = 10*
<back to top> *This means with each turn of the axle, you get 10 times the distance.  Those big wheels really help!
Problem number three (solving for IMA of an Inclined Plane):

You got roped into helping your parents' friend move.  You are loading some pretty heavy boxes, but luckily they have a ramp on the back of the truck. The truck is 1.5 meters of the ground and the ramp is 6 meters long.  What is the IMA of this ramp?

In order to solve this we have to do some different steps.  First we write the formula as we intend to use it.  Second, we place the numbers into the formula where they go (called the set-up) and lastly we do the mathematical calculations to attain the answer.

Step One: Write the formula as we need to use it.  In this question, we are using an inclined plane, so we need the formula for ideal mechanical advantage of the inclined plane. Formula:  IMA = length of slope / height of slope
Step Two: Now we have to figure out what value goes for each letter.  In this problem, it tells us the truck is 1.5 meters high (the height of the slope) and the ramp is 6 meters long (the length of the slope).  Just put them in the formula. IMA = 6m / 1.5m
Step Three: Now the last and easiest part, do the math.  The units will cancel out, so you are left with just a single number, no units. IMA= 4
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Problem number four (using IMA to predict the output of a machine):

You are getting ready to build your mousetrap car, the best one possible.  If you set up your wheels such that they have a mechanical advantage of 5, and you get your axle to turn a total of 5 meters, how many meters will the car move?

In order to solve this we have to do some different steps.  First we write the formula as we intend to use it.  Second, we place the numbers into the formula where they go (called the set-up) and lastly we do the mathematical calculations to attain the answer.

Step One: Write the formula as we need to use it.  In this question, they are asking for output.  Output = Input x IMA
Step Two: Now we have to figure out what value goes for each letter. These problems are very easy.  It tells us the IMA, and it tells how the distance which is put in.  (This problem could also give us the work put it and we would do the same thing.) Output = 5m x 5(IMA)
Step Three: Now the last and easiest part, do the math.  Notice the units stay the same since all I did was multiply what was put in by the IMA (a simple number.) Output= 25m 
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