UNIT 1 - ENERGY & MOTION
Physics Lab 1.1
Pendulums & Energy
This lesson deals with
some practical examples of gravitational potential
energy, kinetic energy, work and power. The video
presentation for this lesson illustrates the following
experiments:
- Pendulum –
Conservation of energy
- Estimate the speed of
a pendulum
Optional Physics Lab 1.1B
- Estimate the amount
of solar radiation reaching the earth's surface.
Get
Started
After watching the video presentation, answer the
questions in the list of exercises below.
The solutions are on the last page of this document.
Experiments
Carry out the experiments described below.
Record the results of the
experiments using the data tables provided. Enter the
experimental results in the appropriate columns and
calculate the values needed to complete the data tables.
Answer the questions that
are associated with the results of the experiments.
- When a pendulum
swings back and forward, all of its mechanical
energy takes the form of gravitational potential
energy when it reaches each of the two extremes.
(The highest points in the cycle.) Why does the
pendulum not reach the same height after each
cycle?
- A pendulum,
consisting of a weight on the end of a piece of
string, is allowed to swing by pulling it to the
side and letting it go. If a wooden peg is used
to block the movement of the pendulum by placing
it about half the length of the pendulum below
the upper end of the pendulum, why does the
weight still swing in such a way that it
approaches the height that it was released from?
- If a pendulum bob
with a mass of 200 grams is pulled to the side
until it is 45 cm above the lowest point, what is
the gravitational potential energy of the bob
relative to its lowest point?
- If the pendulum bob
is then released and it accelerates towards the
lowest point, how much kinetic energy will the
bob have as it passes the lowest point? (Assuming
that no energy is lost due to friction.)
- If a pendulum bob
with a mass of 300 grams has kinetic energy of 0.12
Joules, what is its speed?
- If a pendulum bob
with a mass of 50 grams is allowed to swing from
a height of 35 cm above its lowest point, what
will its velocity be as it passes the lowest
point?
- If the bob were
replaced with a larger one with a mass of 150 g.
would the speed at the lowest point be different?
Why?
Experiment
1.1.1 Conservation of Energy
The purpose of this
experiment is to illustrate the conservation of energy.
Equipment
Tape measure – 1.5m
About 1.5 meters of thin rope or string
2 metal weights – anything between 20g and 400 g
Board - roughly 1m x 2m
Wooden peg
A hook to support the pendulum on a board
Procedure
- Tie the weight to one
end of the string and support the pendulum by
attaching the other end of the string to the
pendulum support.
- Starting at the
height of the bob at its lowest point, draw a
series of horizontal lines above this point on
the board behind the pendulum. Space these lines
evenly: 2cm or 5cm apart.
- Draw the weight to
one side and note the height from which it starts
to swing. The pendulum should reach approximately
the same height at the other end of its swing.
- Fix the wooden peg to
the board about half the length of the pendulum
below the support point.
- Repeat step 3 above.
Note the height to which the bob swings.
- Vary the height of
the wooden peg and establish whether this affects
the height to which the bob swings
Results –
Experiment 1.1.1
Length of pendulum :
……………………..cm.
Height of bob at start
of swing
|
Height of peg
|
Height of bob at other
end of swing
|
| 1. ………….
cm above lowest point.
|
No peg
|
…………. cm above
lowest point. |
| 2. |
No peg
|
|
| 3. |
No peg
|
|
| 4. |
……..……cm above
lowest point |
|
| 5. |
……..……cm above
lowest point |
Change the length of
the pendulum: Length of pendulum :
……………………..cm.
Height of bob at start
of swing
|
Height of peg
|
Height of bob at other
end of swing
|
| 1. ………….
cm above lowest point.
|
No peg
|
…………. cm above
lowest point. |
| 2. |
No peg
|
|
| 3. |
No peg
|
Experiment
1.1.2 Estimate the speed of a pendulum
The purpose of this
experiment is to demonstrate the conversion between
gravitational potential energy and kinetic energy as a
pendulum swings
Equipment
As for Experiment 1.1.1
above
Scale to weigh pendulum
bob
Procedure
- Measure the length of
the pendulum and the mass of the bob (weight) at
the end of the pendulum.
- Mark the lowest point
of the pendulum’s swing on the paper mounted
behind the pendulum.
- Pull the pendulum a
distance of about 50% of its length away from its
lowest point – keep the string straight.
- Mark the position of
the bob on the board behind the pendulum and
allow the pendulum to swing.
Results
Measure the difference in
height between an extreme and the bob’s position at
the lowest part of its swing.
Calculations
Use the difference between
the two heights of the pendulum bob to calculate its
gravitational potential energy relative to its lowest
point.
The kinetic energy of the
pendulum bob at the lowest point of its first swing
should be very close to its gravitational potential
energy at the start of its swing. The speed of the bob at
its lowest point can be calculated from the relationship:
KE = ½mv2.
Results
Mass of bob =
…………………g.
| |
Height of bob at start
of swing
(cm)
|
Gravitational potential
energy of bob at start of swing (J)
|
Kinetic energy of bob at
it’s lowest point. (J)
|
Speed of bob at its
lowest point (m/s)
|
| 1 |
|
|
|
|
| 2 |
|
|
|
|
| 3 |
|
|
|
|
| 4 |
50
|
1.619
|
1.619
|
3.132
|
Question
- Does the mass of the
string contribute to the energy of the pendulum?
Experiment
1.1.3 Measure the power used in climbing a flight of
stairs
The purpose of this
experiment is to measure the rate at which a person can
increase the gravitational potential energy of their body
as they climb a flight of stairs.
Equipment
Stopwatch.
Bathroom scale
Tape measure
Safety Instructions
This experiment
involves moving quickly on stairs. Use extreme care to
avoid slipping or tripping on the stairs.
Procedure
- Measure the mass of
the person who will climb the stairs.
- Measure the
difference in height between the top and bottom
of the flight of stairs.
- Use a stopwatch to
measure the time taken to climb to the top of the
stairs.
Results
Record the mass of the
weight, the height that it was lifted and the time taken.
Repeat the experiment 2 or
3 times.
Calculations
The gravitational
potential energy imparted to the person = mass of person
x the height of stairs.
Power is the rate at which
energy is converted. 1 Watt = 1 Joule per second.
Divide the number of
Joules imparted to the weight by the number of seconds
taken. This gives the number of Watts.
Horsepower can be
calculated using the conversion factor: 745.7 Watts = 1
HP
Average height of each
step = ……………….m (A)
Number of stairs =
………………… (B)
Height of flight of stairs
= (A x B) = ……………. m
| |
Mass of person
(kg)
|
Time to reach top of
stairs
(seconds)
|
Work done
(Joules)
|
Power used
(Watts)
|
| 1 |
|
|
|
|
| 2 |
|
|
|
|
| 3 |
|
|
|
|
| 4 |
|
|
|
|
| 5 |
|
|
|
|
| 6 |
82
|
3.5
|
2574
|
735.5
|
Physics Lab 1.1
Energy
Answers
to Questions
- Some energy is lost
to friction as the pendulum moves through the air.
The friction with the air and (to a lesser extent)
friction in the string, cause a reduction in the
mechanical energy of the pendulum.
- In order to convert
kinetic energy back to gravitational potential
energy, the bob approaches the same height as it
occupied at the start of the swing.
- PE = 0.883 J. The
gravitational potential energy of an object is
calculated using the formula: mgh where: m is the
mass in kg, g is the acceleration due to gravity
(9.81 m/s2) and h is the height above
a reference point in meters. (In this case, the
reference point is the lowest point of the
pendulum.)
mgh = 0.2kg x 9.81m/s2 x .45m = 0.883
J.
- KE = 0.883 J. All of
the gravitational potential energy is converted
to kinetic energy.
- v = 0.894 m/s: 0.12 J
= ½mv2. m = 0.3 kg. v = Ö (2 x 0.12 / 0.3) = 0.894 m/s
- v = 2.62 m/s: PE = 0.05kg
x 9.81 m/s2 x 0.35m = 0.172 J. v = Ö (2 x 0.172 / 0.05) = 2.62 m/s
- No. Mass occurs in
the equation for PE and the equation for KE. PE
and KE are each affected to the same extent by an
increase or decrease in mass.
Typical
Results
Experiment
1.1.1
Height
of bob
|
Height
of Peg
|
Height
of bob at
|
at
start of swing
|
|
other
end of swing
|
(cm
above lowest point)
|
(cm
above lowest point)
|
(cm
above lowest point)
|
50
|
No peg
|
45
|
40
|
No peg
|
37
|
25
|
No peg
|
22
|
50
|
60
|
44
|
50
|
50
|
45
|
|
