Date __________
Partners ___________________________________________________
APHY101 – Lab #3 – Simple Machines
Introduction
The work done on an object is defined as the product of the force applied to an object and
the distance the object moved while under the influence of the force. Simple machines such as
the inclined plane decrease the force necessary to complete a certain task. However, the distance
the force must act through increases.
In order to compare different machines, we use the concepts of mechanical advantage and
efficiency. When studying an inclined plane, the theoretical mechanical advantage (TMA) is the
ratio of the distance the cart moves along the incline to the vertical distance the cart moves:
TMA =
length of incline L

height of incline h
Note that the TMA has no units.
force
L
weight
h2
h1

The actual mechanical advantage (AMA) is the ratio of the weight of the object being moved to
the force moving the object:
AMA =
mcart g
weight

force
mhanger masses g
Note that the AMA has no units. The efficiency of a machine is defined as the ratio of the work
output to the work input:
Efficiency =
work output
work input
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From the figure, we can define the work output as weight times height or mcartgh the work input
as force times length or mhanger+massesgL. Note that the efficiency also has no units and is usually
written as a percentage.
Equipment
Inclined plane w/pulley, dowel, metal cart, ring stand, clamp, weight hanger, slotted masses,
string, protractor, meter stick, equilibrium clamps, hooked masses.
Procedure
1. Record the mass of the cart mcart =
kg and the hanger mhanger =
kg .
Assemble the inclined plane at  = 55 as shown in the figure. The string should be long
enough so that when the cart is at the bottom of the incline, the hanger is just below the
pulley. With the hanger at its highest position, measure and record L.
2. With the hanger at its highest position, measure h1, the initial height of the cart's front axle
above the table. Now add enough mass to the hanger so that a light tap on the cart causes it
to move up the incline at a constant speed. With the hanger on the table, measure h2, the final
height of the cart's front axle above the table.
3. Record the weight of the cart and the total mass of the hanger and masses (mhanger+masses).
4. Calculate the TMA, AMA and Efficiency to 3 decimal places. If the efficiency of your
system is greater than 1, repeat the procedure.
5. Repeat steps 2-4 for  = 45 and 35.
 ()
55
45
35
L (m)
 ()
55
45
35
 ()
55
45
35
h1 (m)
weight (N)
h2 (m)
mhanger+masses (kg)
Work output (J)
force (N)
Work input (J)
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h = h2 - h1 (m)
TMA
AMA
Efficiency
6. A lever is a rigid bar which can rotate about a fixed point called the fulcrum. Any forces
acting on the bar will produce rotation in opposite directions. This rotation is due to a torque
which is the product of a force and a lever arm distance. When the net torque equals zero, the
lever is in equilibrium.
fulcrum
weight
force
The weight and force will be hooked masses. The lever arm distance of the weight (Lweight) and
force (Lforce) are measured from the fulcrum. Position the weight near one end of the meter stick
and find the location of the force so that the system is balanced. Repeat for two different
locations of the weight. The TMA of a lever is Lforce / Lweight and the AMA is weight / force.
mweight (kg)
0.2
weight (N)
Lweight (m)
mforce (kg)
0.5
force (N)
Lforce (m)
TMA
AMA
7. The next lever is similar to a wheelbarrow. Determine the force, using a spring scale,
necessary to make the lever horizontal and complete the table.
force
fulcrum
weight
mweight (kg)
1
weight (N)
Lweight (m)
force (N)
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Lforce (m)
TMA
AMA
8. This type of lever system is similar to the human forearm. Determine the force, using a spring
scale, necessary to make the lever horizontal and complete the table. You will have to hold the
lever in position so it does not move upward as you apply the force.
force
fulcrum
weight
mweight (kg)
0.5
weight (N)
Lweight (m)
force (N)
Lforce (m)
TMA
AMA
Complete the table for each person in your group assuming they are holding a 1 kg mass in their
hand with their forearm level with the ground. The force can be found by weight / TMA.
Your
Hand
Lforce
Lweight
weight of 1 kg = __________ N
Name
Lweight (m)
Lforce (m)
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TMA
force (N)
Analysis
1. What happens to the mechanical advantage and the efficiency for the incline plane as the
angle increases? Why does this happen?
2. What would be the TMA value if the inclined plane’s angle was 90? Explain. For what
angle will the AMA value be a maximum value? Explain.
3. Explain why the AMA depends on friction but not the TMA.
4. Which type of lever has the largest mechanical advantage? Explain why this must be the
case.
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