FVCC Physics Laboratory 2009
Simple Machines
Objective:
Learn how to find the mechanical advantage in nearly any simple machine. Build or use 3
simple machines and measure the mechanical advantage in the machine. Calculate the efficiency of
these machines in the cases where forces can be directly measured.
Background:
Hopefully you have begun to experience in your homework how conservation of
energy can make many problems easier to solve than using Newton’s second law. In short conservation
of energy means that the total mechanical energy stays constant while the amount of kinetic and
potential energy can change. Equation 1 states this and is at the heart of conservation of energy.
𝐾𝐸𝑖 + 𝑃𝐸𝑖 = 𝐾𝐸𝑓 + 𝑃𝐸𝑓
When the total mechanical energy after motion is less than the total mechanical energy before motion,
then a non-conservative force has been at work. Friction is an example of a non-conservative force.
Where did the excess energy go? Generally into heat which quickly dissipates the energy and is usually
lost forever. From the work energy theorem, we know that calculating the work done by a force is
equal to the energy delivered by that force. So, using 𝑊 = 𝐹𝑑 = 𝑃𝐸 we get
𝐹𝑖𝑛 𝑑𝑖𝑛 = 𝐹𝑜𝑢𝑡 𝑑𝑜𝑢𝑡
when energy is conserved. But, Fin and Fout do not have to be equal nor do the distances din and dout. In
fact, in simple machines they are not equal. Only the products are equal. Suppose we multiply Fin by a
mechanical advantage constant MA. In order keep the same numeric value, if I multiple Fin by MA, I
must divide din by MA.
(𝑀𝐴)𝐹𝑖𝑛 (
1
) 𝑑 = 𝐹𝑜𝑢𝑡 𝑑𝑜𝑢𝑡
𝑀𝐴 𝑖𝑛
So, if I multiply the input force by an advantage of say MA=2, then must divide the input distance by 2.
Mechanical advantage can then be pulled from the above equation.
𝑀𝐴 =
𝐹𝑜𝑢𝑡
𝐹𝑖𝑛
𝑀𝐴 =
𝑑𝑖𝑛
𝑑𝑜𝑢𝑡
This suggests that we could measure the mechanical advantage MA of a simple machine either by
comparing input and output forces or distances. But in the real world not all forces are conservative and
some of the energy we input is lost to heat. So the mechanical advantage is further refined by defining
Ideal Mechanical Advantage IMA, and Actual Mechanical Advantage AMA. When the forces are
FVCC Physics Laboratory 2009
conservative, than MA is equal to IMA. If the forces are both non-conservative and conservative, then
we have AMA. Since it is in the force that this distinction shows up, we have a method of determining
IMA vs. AMA.
𝐼𝑀𝐴 =
𝑑𝑖𝑛
𝑑𝑜𝑢𝑡
𝐴𝑀𝐴 =
𝐹𝑜𝑢𝑡
𝐹𝑖𝑛
So the efficiency of the simple machine is simple the ratio of these factors.
𝐸𝑓𝑓 =
𝐴𝑀𝐴
100
𝐼𝑀𝐴
In this lab we will always be able to measure the input distance 𝑑𝑖𝑛 and output distance 𝑑𝑜𝑢𝑡 for various
machines. Doing this will give us a direct measure of the MA of a simple machine. In two cases we will
also be able to measure the input force 𝐹𝑖𝑛 and output force 𝐹𝑜𝑢𝑡 thereby getting an AMA estimate.
So what is a simple machine? It is a mechanical aid which allows us to magnify the force we need to
move something by increasing the distance we apply our input force to. Examples of simple machines
are many including the following list:
1.
2.
3.
4.
5.
Ramp
Scissors Screw jack
Lever arm
Pulley system
Hydraulic jack
6.
7.
8.
9.
Bicycle gears
Pump
Ratchet
Etc.
Equipment:
Pulley machine





Pulley Frame
2-100lb scales
1 double pulley
2 single pulleys
¼ inch rope
Ramp machine






Pasco track
End pulley for track
String
Weight hanger
3-beam balance
Weight set


Lab support for track
Rolling cart
Hydraulic jack machine



Hydraulic jack
Ruler
Tape measure
FVCC Physics Laboratory 2009
Procedure: In this lab we will investigate 3 simple machines. For two of these machines
(ramp and pulley) we can measure the efficiency of the machine.
A) The ramp…..
B) The hydraulic jack…..
C) The pulley system….
measure IMA and AMA, calculate efficiency
measure IMA
measure IMA and AMA, calculate efficiency
A) The Ramp. Lifting a heavy object can be made a lot easier if you use a ramp. Test this simple
concept by finding the mass needed to “lift” one of the frictionless carts up an incline. The setup is shown in Figure 1.
Figure 1. The Ramp simple machine.
1.
2.
3.
4.
Weigh the cart
Attach the cart to the hanging weights with a string routing it over the pulley as shown.
Add weights to the weight hanger until the cart barely moves up the plane.
Take the ratio of the masses to find AMA
𝑔𝑚𝑐𝑎𝑟𝑡
𝑚𝑐𝑎𝑟𝑡
𝐴𝑀𝐴 =
=
𝑔𝑚𝐻𝑎𝑛𝑔𝑒𝑟 𝑚𝐻𝑎𝑛𝑔𝑒𝑟
5. Measure the distance the hanging weights had to fall to lift the cart to the top of the ramp. (i.e.
measure dout and din)
6. Calculate the IMA and this simple machines efficiency.
7. Estimate the error in your result for efficiency. See the lab guide on errors.
FVCC Physics Laboratory 2009
B) The Hydraulic jack. Hydraulic jacks can lift an amazing amount of weight. To get an idea of the
mechanical advantage, measure how far you move your hand while pumping the jack handle
compared to the distance the jack actually rises. Estimate your error. Is this IMA or AMA?
C) The pulley. The pulleys used in this lab came from the
hardware section at the local Lowe’s home
improvement store. You can easily use these
inexpensive pulleys for many applications. In this lab
we will hook up the three arrangements shown in
Figure 2 and measure the AMA. Reading the figure left
to right, the first figure (a) is simply done to ensure that
the scales are measuring the same values. The second
figure (b) is using one pulley to multiply the force and
the third figure (c) uses a double pulley. In the two case
where pulleys are used as simple machines, (the second
two figures) measure AMA. To measure IMA you need
to measure the distance the rope moves. Since the
rope with significantly stretch in from the load, we
cannot get an accurate distance in. So, we will not measure IMA.
D) As an extra if you have time, remove the pulleys and simple use the rope through the eyebolts.
There is more friction in this case (Use figure b) but it is surprisingly good. Measure IMA and
AMA for this case.
Figure 2. Diagrams of the pulley configurations.
FVCC Physics Laboratory 2009
What’s in your report:
Here is a check list of items to address in your laboratory report.
1) Measured AMA and IMA for the ramp.
2) Calculated efficiency for the ramp.
3) Estimated error for the data and subsequent calculations such as AMA and IMA. Use the
propagation of errors outlined in the lab webpage.
4) Measured AMA for the two pulley systems
Rope Stretch data
Note that the rope used with the pulley stretches significantly under stress. If you measure the input
distance on the pulley sections, you need to estimate the rope for stretch. Here is some data from the
rope estimating stretch.
Position
48.9
CM
Load
0 initial
delta
48
47.5
47.2
46.9
46.5
46
45.9
stretch per cm
0 L=
KG
0.9
1.4
1.7
2
2.4
2.9
3
1
2
3
4
6
8
13
0.9
1.4
1.7
2
2.4
2.9
3
Stretch/length
0.01125
0.0175
0.02125
0.025
0.03
0.03625
0.0375
80
2 pulley
4 pulley
expected expected
stretch
stretch
2.7
4.5
4.2
7
5.1
8.5
6
10
7.2
12
8.7
14.5
9
15
cm
cm
cm
cm
cm
cm
cm