Physics
Lab 1.10 Pendulum Projectiles
Purpose: The
purpose of this experiment is to determine the speed of a
pendulum at the bottom of its swing by measuring the
distance traveled by a marble as it is released from the
pendulum bob.
Materials and Equipment
- Table
- A large glass marble
- A pendulum consisting
of a small metal cradle held by two pieces of
string.
The cradle should be shaped to hold the glass
marble while it swings. A slight indentation in
the metal assists in keeping the marble in
position. A protruding section below the cradle
tips the cradle as it hits a barrier at the
bottom of its swing.
- A tape measure
- A sheet of carbon
paper & a large sheet of white paper
Procedure
- Mount the pendulum
above the edge of the table. The bottom of the
pendulum should be about 10 cm above the edge of
the table at the lowest point in its swing.
- Place the marble
inside the cradle.
- Pull the pendulum
away from the edge of the table, measure the
height of its launching position above the
tabletop and allow it to swing in the direction
of the edge of the table.
- The barrier should
tip the metal hoop as it reaches the bottom of
the swing. The marble should continue moving and
drop to the floor.
- Note the region in
which the marble strikes the floor. Place a piece
of white paper covered with a downward facing
piece of carbon paper in this part of the floor.
- Repeat steps 3,4 and
5 and identify the exact location where the
marble strikes the floor from the carbon mark on
the white paper.
- Measure the vertical
distance from the edge of the table to the floor.
Mark a point on the floor directly below the
point on the edge of the table where the marble
left the metal hoop.
- Measure the distance
from this point to the point at which the marble
landed.
Calculations
The speed of the marble at
the lowest point of the pendulum’s swing can be
calculated from the height that it was launched from.
Compare this with the
distance that it traveled in the air before it hit the
ground.
Assuming it was traveling
horizontally when it left the metal hoop, it started
accelerating towards the floor at a rate of 9.81 m/s2
as soon as it left the hoop. The time taken to reach the
floor can be calculated from the equation: d = ½gt2
where d is the distance in meters (The height of the
table plus the height of the hoop at its lowest point
above the table), g is 9.81 m/s2 and time, t,
is measured in seconds.
The speed of the marble
can be calculated from the distance from the point on the
floor below where it left the hoop to the point at which
it landed on the floor divided by the time taken.
Results
Mass of marble =
……………grams
Height of table top above
floor = ……………….cm.
Height of cradle at its
lowest point – above table =
……………cm.
Height of cradle at its
lowest point – above floor =
…………….cm.
Time for marble to drop
this distance = …….……seconds.
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Height of cradle at
launch
(cm
above table top)
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Horizontal distance from
lowest point of cradle to point at which it
landed on the floor
(cm)
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Distance that cradle
dropped as cradle moved to lowest point
(cm)
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Gravitational potential
energy of marble that was converted to kinetic
energy
(Joules)
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Velocity of marble at
bottom of swing
(m/s)
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Horizontal velocity of
marble after leaving cradle
(m/s)
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| 6 |
30
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76
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20
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0.01962
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1.981
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1.882
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For the test reported
on line #6 above:
Mass of marble =
………20…grams
Height of table top above
floor = ………70 .cm.
Height of cradle at its
lowest point – above table = ……10 cm.
Height of cradle at its
lowest point – above floor = ……80 .cm.
Time for marble to drop
this distance = 0.4039 seconds
Question
- How does the speed
calculated using the time to fall to the ground
compare with the speed calculated from the
kinetic energy of the marble at the bottom of the
pendulum’s swing?
- A pendulum bob with a
mass of 0.2 kg has gravitational potential energy
equal to 0.025 J at the highest point in it’s
cycle. (Relative to it’s lowest point) What
is it’s kinetic energy at the lowest point
in it’s cycle?
- If the horizontal
speed of a marble traveling through the air is 2
m/s, how far will it travel in 0.2 seconds?
- If an object travels
30 m in 5 seconds, what is its speed?
- If an object
traveling horizontally has a mass of 0.2 kg and
kinetic energy equal to 0.025 Joules, what is it’s
speed?
- A marble that rolls
slowly over the edge of a table accelerates
towards the floor at a rate of 9.81 m/s2.
If the equation: d = ½gt2 can be used
to determine the distance, d (meters) traveled in
t seconds as it falls, how far will it fall in 0.1
seconds?
- How long will it take
for the marble to fall 0.5 meters?
- A marble with a mass
of 20 grams is attached to a pendulum and
released to swing from a height of 20cm above its
lowest point. How much kinetic energy will the
marble have when it reaches its lowest point?
- If a marble is
launched horizontally from the top of a table,
and the table-top is 80cm above the floor, how
long will the marble spend in the air before
landing on the floor?
- What is the
horizontal speed of the marble as it leaves the
table-top if it lands 40cm from a point directly
below the edge of the table?
- 0.025Joules: Neglecting friction,
all of the potential energy is converted to
kinetic energy at the lowest point in the cycle
of the pendulum.
- 0.4m: 2 m/s x 0.2 s = 0.4 m.
- 6 m/s: 30 m ÷ 5 s = 6 m/s.
- 0.5 m/s: ½mv2 = 0.025
J. v = Ö (0.025 x 2 ÷ 0.2) = 0.5 m/s.
- 0.0491 m: d = ½gt2 = 0.5
x 9.81 x 0.12 = 0.0491 meters.
- 0.319 seconds: t = Ö (0.5
x 2 ÷ 9.81m/s2) = 0.319 seconds.
- 0.039 J: Kinetic energy =
gravitational potential energy at launch.
Gravitational potential energy = mgh = .02 x 9.81
x .2 = 0.039 Joules.
- 0.404 s: d = ½gt2: t =
Ö (0.8 x 2 ÷ 9.81m/s2) = 0.404
seconds.
- 0.99 m/s: Time spent in the air =
0.404 seconds.
Horizontal velocity = 0.4m ÷ 0.404s = 0.99 m/s.
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