Date:__________
Partners:______________________________________________________________________
APHY201 – Lab – Work and Energy
Introduction
The apparatus you will construct today will allow you to study the relationship between
work and mechanical energy. The simple pendulum is a mass connected to a string and allowed
to swing in a plane. The period of a pendulum is the time it takes to move from A to B then back
to A again. As the mass moves, its potential and kinetic energy changes due to work done by an
external force.
B
A
You will also experiment with two simple machines: an incline plane and a lever. To
compare 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 =
L
h
Note that the TMA has no units.
force
L
h2
weight
h1
1
Neil E. Miller
3/6/2016

The actual mechanical advantage (AMA) is the ratio of the weight of the object being moved to
the force moving the object:
mcart g
weight
AMA =

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:
work output
Efficiency =
work input
If we use the information in the figure to define the work output and work input, then the
efficiency becomes
weight  h
Efficiency =
force  L
Note that the efficiency also has no units and is usually written as a percentage.
Procedure
Part A – The Simple Pendulum
Equipment: Metal Stand, Meter Stick, Pendulum Clamp, String, 20g Hooked Mass, Protractor,
Photogate
1. Measure the mass m and width d of the hooked mass and record the values in Table 1.
2. Construct a pendulum between 40 and 80cm long using string and the hooked mass. Adjust
the pendulum clamp so that the center of the hooked mass is y1 = 15cm above the table with the
mass hanging straight down. Displace the mass to the side about 10°, keeping the string tight.
Measure this new height y2 and determine Δy.
3. Calculate the initial GPE of the pendulum using Δy.
Table 1
m (kg)
Δy (m)
d (m)
GPEi (J)
4. Place the photogate so that the mass will activate the gate when it passes the lowest point in
its motion. Make sure the mass will not hit the gate as it swings.
5. Put the photogate in GATE mode and position the mass at y2. Release the mass and record
the time t in Table 2 after each set of 10 swings. You will have to reset the photogate after each
measurement. Use t and d to determine v and KE to 4 decimal places for the pendulum.
2
Neil E. Miller
3/6/2016
6. Calculate KElost per swing to 4 decimal places after each set of 10 swings. For example, the
1
KE10  GPEi  and after 20 swings is 1 KE20  KE10  .
KElost after the first 10 swings is
10
10
Table 2
number of swings
10
20
30
40
50
60
t (s)
v (m/s)
KE (J)
KElost per swing
Is the KElost per swing approximately constant? Explain.
Part B – Machines
Equipment: Meter Stick, Inclined Plane w/pulley, Hall’s Cart, Metal Stand, Clamp, Dowel,
Small Mass Hanger, Slotted Masses, String, Protractor, Hooked masses
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
Neil E. Miller
3/6/2016
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. Repeat for other values of 
 ()
55
50
45
40
35
L (m)
 ()
55
50
45
40
35
h1 (m)
weight (N)
 ()
55
50
45
40
35
h2 (m)
mhanger+masses (kg)
Work output (J)
h = h2 - h1
force (N)
Work input (J)
TMA
AMA
Efficiency
5. What is the relationship between the mechanical advantage and the efficiency for the incline
plane as the angle changes?
6. Based on your data, what would be your TMA value if the inclined plane’s angle was 90?
Explain.
4
Neil E. Miller
3/6/2016
For what angle will your AMA value be a maximum value? Explain.
7. 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)
weight (N)
Lweight (m)
mforce (kg)
0.5
force (N)
Lforce (m)
TMA
AMA
8. 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
5
Neil E. Miller
3/6/2016
mweight (kg)
1
weight (N)
Lweight (m)
force (N)
Lforce (m)
TMA
AMA
9. 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
fulcrum in position so it does not move upward as you apply the force.
force
fulcrum
Lweight
weight
Lforce
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.
weight of 1 kg = __________ N
Name
Lweight (m)
Lforce (m)
6
Neil E. Miller
3/6/2016
TMA
force (N)
10. Comment on the force values and remember that 1 N ~ ¼ lb.
11. Which type of lever has the largest mechanical advantage? Explain why this must be the
case.
7
Neil E. Miller
3/6/2016