GateWay CC
PHY101 Physics Lab:
TO GRAVITY
ACCELERATION
DUE
Purpose

To determine the value of the gravitational acceleration
Theory
When we use the word “acceleration” we mean the rate at which the velocity of a moving
object changes with time. Acceleration is always caused by force – gravitational force as
one of the fundamental forces of nature. This is the essence of Newton’s first law. In
today’s lab we will measure the acceleration due to the gravitational force exerted by the
earth on two different types of objects, a tennis ball, baseball and a ping-pong or golf
ball.
An object falling near the surface of the earth experiences constant gravitational
acceleration. If we drop the object from the certain distance on a free fall, the distance
traveled by an object in a free fall after “t” seconds is:
d  y  vo  t 
1 2
gt
2
(1)
The velocity of an object in free fall after “t” seconds is:
v  vo  gt
(2)
Here, the parameters vo and g are, respectively, the initial velocity and the acceleration.
Galileo first demonstrated this result when he dropped cannonballs of different masses
(weights) from the Leaning Tower of Pisa to show that although they had different
masses, when dropped together, they landed together. This happened in this manner
because they both experienced the same acceleration. A similar experiment can be done
by dropping a coin and a feather. When dropped in air, the coin always lands first, but
when they are dropped in a vacuum, an environment where there is no air, they land
together! In the coin and feather case, the different velocities are due to the presence of
a force, the frictional force on the coin and the feather due to the presence of air.
In this experiment, you will be dropping an object from rest, so that vo = 0. We will
assume that the only acceleration present is due to the force of gravity. We then obtain
the relation that describes the distance the object falls as a function of time
d
1 2.
gt
2
(3)
Equation (3) can be used to measure g. All we need to do is to drop an object through a
known distance y and then measure the time t it takes to hit the ground. If we know both
y and t, we can solve equation (3) for g,
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GateWay CC
g
2d
t2
(4)
By measuring the travel distance y and the travel time t for an object falling from rest,
gravitational acceleration can be determined.
Procedure
Each group will drop three types of objects: Ping-pong ball, Tennis ball, and baseball.
1. One student from the group will stand on the laboratory desk and drop a ping pong ball,
tennis, and a baseball from the same height of d = 1.5 m from the floor. During the lab
you will measure the time it takes each ball to hit the floor. You also need to measure
very accurately distance from which each ball is dropped.
2. Each lab group should select 1 ping-pong ball, 1 tennis ball and 1 baseball. In order to
measure the distance you can use a motion sensor, computer set-up or meter stick.
3. Time it takes each ball to hit the floor is measured using a stopwatch.
4. The balls should each first be dropped from rest from the height of about 1.5 m above
the floor. Measure the time it takes the ball to hit the floor. Record this number in
seconds, in the data table. Perform 4 drops for each ball.
5. Lab partners should take turns dropping the balls so that everyone has dropped all balls
four times each.
6. Using the meter stick or computer set-up, measure the drop distance, in units of meters,
from the dropping point to the floor. Record this value in your data table as y.
7. Find the second dropping point of 2.5 m above the floor.
8. Drop and time all balls four times each. Record the drop times in the tables below.
9. Lab partners should alternate positions so that everyone has dropped both balls four
times each from the height of 2.5 m from the floor.
10. Calculate the value of gravitational acceleration g.
11. Determine the percentage difference between the calculated value of g and the actual
value near the surface of the earth, which is 9.80 m/s2. The percentage difference is
found using the following equation: (
g  9 .8
) x100%
9 .8
12. Calculate the velocity of an object just before it hits the ground:
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v  vo  gt .
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GateWay CC
Data Table
Part I: Dropping Ping-pong or golf Ball
Objects: Ball with mass: m = _______ kg, distance dropped d = 1.5 m
Ball type
Mass of
ball
(kg)
Dropping
Distance d
(m)
Velocity just
Time t
(sec)
Calculated
gravity g
(m/s2)
g  9 .8
(
) x100% before it hits
9 .8
the ground
(m/s2)
(m/s)
Ping-pong
Ping-pong
Ping-pong
Ping-pong
Average
Objects: Ball with mass: m = _______ kg, distance dropped d = 2.5 m
Ball type
Mass of
ball
(kg)
Dropping
Distance d
(m)
Velocity just
Time t
(sec)
Calculated
gravity g
(m/s2)
(
g  9 .8
) x100% before it hits
9 .8
the ground
(m/s2)
(m/s)
Ping-pong
Ping-pong
Ping-pong
Ping-pong
Average
Part II: Dropping Tennis Ball
Objects: Tennis ball with mass: m = _______ kg, distance dropped d = 1.5 m
Ball type
Mass of
ball
(kg)
Dropping
Distance d
(m)
Velocity just
Time t
(sec)
Calculated
gravity g
(m/s2)
(
g  9 .8
) x100% before it hits
9 .8
the ground
(m/s2)
(m/s)
Tennis ball
Tennis ball
Tennis ball
Tennis ball
Average
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GateWay CC
Objects: Tennis ball with mass: m = _______ kg, distance dropped d = 2.5 m
Ball type
Mass of
ball
(kg)
Dropping
Distance d
(m)
Velocity just
Time t
(sec)
Calculated
gravity g
(m/s2)
(
g  9 .8
) x100% before it hits
9 .8
the ground
(m/s2)
(m/s)
Tennis ball
Tennis ball
Tennis ball
Tennis ball
Average
Part III: Dropping the Baseball
Objects: Baseball with mass: m = _______ kg, distance dropped d = 1.5 m
Ball type
Mass of
ball
(kg)
Dropping
Distance d
(m)
Velocity just
Time t
(sec)
Calculated
gravity g
(m/s2)
g  9 .8
(
) x100% before it hits
9 .8
the ground
(m/s2)
(m/s)
Baseball
Baseball
Baseball
Baseball
Average
Objects: Baseball with mass: m = _______ kg, distance dropped d = 2.5 m
Ball type
Mass of
ball
(kg)
Dropping
Distance d
(m)
Velocity just
Time t
(sec)
Calculated
gravity g
(m/s2)
g  9 .8
(
) x100% before it hits
9 .8
the ground
(m/s2)
(m/s)
Baseball
Baseball
Baseball
Baseball
Average
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GateWay CC
Questions
1. Is travel time varies with the mass of the ball? Why?
2. Which ball has the largest velocity just before they hit the floor and why?
3. What is the gravity at h = 1000 km above the ground?
4. What happened to the value of gravitational acceleration as you move closer to the center of
the Earth?
6. At what point on the Earth the gravitational acceleration is maximum?
Value of "g" Acceleration due to gravity at different locations
Place
Latitude
Altitude
"g" in m/s2
North Pole
90o
0m
9.832
Green Land
70o
20m
9.825
Stockholm
59o
45m
9.818
Brussels
51o
102m
9.811
New York
41o
38m
9.803
Chicago
42o
182m
9.803
Denver
40o
1638m
9.796
San Francisco
38o
114m
9.800
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GateWay CC
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