Experiment 5 – RATE OF ACCELERATION DUE TO GRAVITY

25 Jun Experiment 5 – RATE OF ACCELERATION DUE TO GRAVITY

Question
Experiment 5 – RATE OF ACCELERATION DUE TO GRAVITY
BACKGROUND:
Because of the lack of proper measuring tools, Galileo did not use the Leaning Tower of Pisa
as is often illustrated to determine that all objects regardless of mass will fall to the earth at the
same rate of acceleration. Instead he used an inclined plane on which he rolled balls and
measured the time it took to for the ball to pass a measured distance. Later the same results were
obtained by use of a pendulum which Galileo reasoned was a constantly falling object. The rate
of fall of an object was found to increase with time, according to the equation: d = 1/2at 2, and
a = 2d/t2, where d = distance, a = acceleration, and t = time. When air resistance is insignificant,
“a” is equal to “g”, the gravity constant. Near the earth’s surface, g = 9.8 m/s2.
When analyzing the movement of a pendulum, “g” is calculated by an equation that is
specific for pendulum motion – g = 4 π2L/t2 , where L = the length of the pendulum. Thus,
g = 39.4 L/t2. Notice the similarity of the pendulum equation to the general equation shown
above: a = 2d/t2.
OBJECTIVES:
To determine the acceleration of a falling object due to gravity
– To understand the concepts of acceleration and gravity in a pendulum system
PROCEDURE:
The required equipment includes: ring stand and clamp (alternately, pencil and tape, as
shown here), string with attached hook at one end, large metal washers, stop watch, and meter
stick.

A: The Pendulum Motion
Open a paper-clip into a kind of hook and tie one end to a length of string. Hook one washer
onto the other end of paper-clip. The other end of the string will be attached to a support, which
is either the prong of a clamp mounted on a ring stand and extending outward into the aisle space
or (as shown above) a pencil taped to the bench, where about half of the pencil extends outward
into the aisle space. Tie the upper loop so that the length (L) from the bottom of the support
(prong or pencil) to the “center” of the washer is approximately one half meter; i.e., 49.0 -51.0
cm (equal to 0.490 – 0.510 m), measured with a meter stick to the nearest 0.1 cm. Record below.
1

Pull the pendulum back to a position about 45 degrees from vertical (as in above picture),
and without pushing, release and let the pendulum swing freely for exactly one minute (60
seconds). [If the washer hits the lab bench or other object, start the run again]. One lab partner
should count the swings and another partner should time the run. A full swing is one out and
back, and a half-swing is out-but-not-back from the release point. Count each complete swing,
and if it has occurred at the 60 seconds mark, a half swing. Record the number of swings to one
decimal place (e.g., as 20.0, or 20.5 swings). Do this procedure at least three times to obtain an
average number and as accurate a count as possible.
L = __________ cm
Number of swings (1 washer):

Convert from centimeters to meters: L = _________ m .
______ _______ _______

Time of one swing = 60 seconds
Average # of swings

t=

Acceleration = 39.4 L = __________m/s2
t2

Average: _______
s

(for 1 washer)

Any change in experimental conditions that might affect the outcome of an experiment is
called a Variable. Parts B, C, and D examine the effects of some variables on the measurement
of “g”.
B.

Effect of Height of Release
Repeat Part A, but this time, release the pendulum from a smaller angle, i.e., about 30
degrees from vertical.
L = _________ m (should be same as in Part A)
Number of swings (1 washer):

______ _______ _______

Time of one swing = 60 seconds
Average # of swings

t=

Acceleration = 39.4 L = __________m/s2
t2

Average: _______
s

(for 1 washer)

Does a different release point, i.e., a different initial length of swing and swing height, have a
significant effect (more than about 10%) on the calculated value for “g” ?
______________
C.

Increased Mass of a Pendulum
2

1). Increase the mass of the pendulum by adding two more washers (total = 3). Again
measure L, as there may be a slight increase in the length of the pendulum because of the
added mass stretching the string; use this new value of L in the calculation below. Then
follow the procedure in Part A to see the effect, if any, that the added mass has on the rate
of acceleration. Again, it is suggested that each trial be done 3 times.
Measure the pendulum length, to nearest 0.1 cm. L = ________ cm

L = ________ m

Number of swings (3 washers): _______ _______ _______ Average ________
Time of one swing = 60 seconds
Average # of swings

t=

s

Acceleration = 39.4 L = ________ m/s2
t2

(for 3 washers)

Did the added mass have a significant effect on the rate of acceleration? ________
2) Increase mass again by two more washers (total = 5), and measure L again. Count the
number of swings in one minute and then calculate the rate of acceleration.
Measure again the pendulum length.

L = ________ cm

L = ________ m

Number of swings (5 washers): _______ _______ _______ Average ________
Time of one swing = 60 seconds
Average # of swings

t=

Acceleration = 39.4 L = ________ m/s2
t2

s

(for 5 washers)

Did the added mass have a significant effect on the rate of acceleration? ________
D: Larger Pendulum Length
Lengthen the pendulum (with one washer) to about 73.0-76.0 cm (L = 0.730-0.760 meter),
measure L to the nearest 0.1 cm. Once more count the number of swings for one minute. Do
three trials. Then calculate the acceleration due to gravity.
3

L = ________ cm

L = ________ m

Number of swings (1 washer): _______ _______ _______ Average ________
Time of one swing = 60 seconds
Average # of swings

t=

Acceleration = 39.4 L = ________ m/s2
t2

s

(for 1 washer)

Did the changed length have a significant effect on the acceleration of the pendulum? ______
E. Experimental Error.
At or very near sea level, e.g., in our location, the accepted value (AV) for acceleration due to
gravity is 9.8 m/s2. Let us now calculate the experimental error in our measurements!
1. Obtain an average for the five values for ‘acceleration’ found in Parts A, B, C, and D.
Average = _________ m/s2

(called here the ‘experimental value’ (EV))

2. Calculate % Error, using the equation: % Error = 100 (EV – AV)
AV
% Error = ____________ %
F. Questions
1. The time on your grandfathers’ clock is too slow. How should the pendulum be adjusted to
make the time more accurate? Explain briefly.

4

Experiment 9 – CALCULATING WORK & POWER
BACKGROUND:
Work is done when an object is moved some distance. The general formula for work is W = Fd
(Work = force x distance). The formula for determining the work output in a vertical direction
(i.e., against gravity) is W = wd (work = weight x distance). Remember: weight is a force. Work
is expressed as foot-pounds (ft-lb) in the English units. For example, when an object weighing 55
lb is moved 3.0 ft, there is 165 ft-lb of work done. In the metric (SI) system, vertical work can be
calculated by the equation; W = mgh, where m = mass, g = the gravity constant (9.8m/s2), and
h = height distance. The standard unit for work in the SI metric system is the Joule (J).
Power is the rate at which work is done, i.e., the work done in a given period of time. Power can
be determined by the general formula P = W/t (Power = work divided by time). In the English
System, the standard unit for power is ft-lb/s. Another English unit of power is horsepower (hp),
where 1 hp = 550 ft-lb/s. When the two formulas for work and power are combined and
converted to horsepower, and then applied to vertical lift, the equation becomes:
horsepower = weight x height =
Work
.
time x 550
time x 550
In the metric (SI) system, the standard unit for power is the Watt (W), where 1 W = 1 J/s.
For power generated during vertical work, we can use the equation:
P = mgh
t
OBJECTIVE:
– To determine the work that is done and power (in horsepower and in Watts) that is
generated when a person climbs a set of stairs at different rates
MATERIALS:
bathroom scale, meter stick, stopwatch.
PROCEDURE:
A. Determination of height of stairs, and mass and weight of traveler
1. Choose a teammate to be the climber, i.e., the walker and runner, in Part B. The climber
should weigh his/herself and then calculate mass.
Weight of climber = _________ lb

Mass of climber = ________ kg

Remember: 1 kg = 2.2 lb
2. Other teammates will do the measurements below and will be the timekeeper for Part B.
Go to the stairwell and measure the height of a step in centimeters and then count the number of
steps from one floor to the next one up (assume all steps have the same height), Then calculate
the height of the floor level. Record your measurements and calculations below.
Height of 1 step = _________cm

Number of steps _______ Total height _______ cm

Calculate: Total height of steps, in ft = _______ ft Total height of steps, in m = ______ m
1

Remember: ft = cm / 30.5
Remember: 1 m = 100 cm
B. Climbing the stairs
1. Walking: The climber will go to the bottom of the steps and will be timed by another
teammate as he/she walks up the flight of steps at a relatively normal pace.
Time of walking = _________s
2. Running: Now repeat Part B1, but this time the climber (same person) is to go up the stairs
at a faster speed, i.e., by running.
Time of running = _________s
C. Work and Power Calculations – – SI Metric Units
Use the appropriate height, mass, and time values from Parts A and B in the calculations. [We
are going to ignore the work done when moving horizontally across the landing since this work
will be much less than the vertical work].
1. Work (W) done while walking = _______ J

Power (P) while walking = _________Watt

2. Work (W) done while running = _______ J

Power (P) while running = ________ Watt
Remember:
W
=mgh
P = W/t = mgh/t
D. Work and Power Calculations- – English Units
Use the appropriate height, weight, and time values from Parts A and B in the calculations.
1. Work (W) done while walking = _______ft-lb

Power (P) while walking = _______ft-lb/s

= _________
hp
2. Work (W) done while running = ______ft-lb

Power (P) while running = _______ ft-lb/s
= _________
hp

Remember: W = wd = wh

P = W/t

hp = W/550t

.
Analysis
1] Does the running activity require more work than does walking? _____________________
2] Which activity requires more generation of power?

2

_______________________
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