# Investigating the Factors that Affect the Acceleration of a Ball Bearing Down a Ramp

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Investigating the Factors that Affect the Acceleration of a Ball Bearing Down a Ramp I intend to investigate what factors affect the acceleration of a ball
bearing down a ramp. I will measure how long the ball bearing takes to
roll down a ramp, and my other variable will be to measure the final
velocity of the ball bearing rolling down the ramp. Using this
information I will then be able to work out the acceleration of the
ball bearing down the ramp. I will be able to work out the velocity of
the ball bearing, and therefore be able to work out the acceleration
using a different formula above.

I will conduct two experiments and for both there will be only one
variable with everything else fixed. In the first experiment, my
variable will be the mass of the ball bearing which rolls down the

ramp. In the second experiment, I will keep the mass of the ball
bearing the same but change the angle of the ramp that the ball
bearing rolls down.

CHANGING THE MASS OF THE BALL

In this experiment the only factor I will change will be the mass of
the ball bearing which rolls down the ramp.

Apparatus

To do the experiment, I will need to use the following equipment:

a plastic ramp,

a stand,

a clamp,

a nail,

a metre rule,

a selection of ball bearings with varied masses,

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four metal electrodes,

four crocodile clips,

four wires and

a stop-clock.

The ramp will be set up originally to get a 5° angle. I have worked
out using the sine function that the start of the ramp needs to be
10.9cm off the ground. The ball bearing will be released from the top
of the ramp and will roll down. The ball bearing will be rolled down
twice. On the first roll, the final velocity of the ball bearing as it
rolls down the ramp will be measured. This will be measured by
connecting wires to the stop-clock and set points on the ramp. The
electrodes are placed close together either side of the ramp. As the
metal ball rolls over them the circuit is completed and starts the
stop-clock. As it then rolls over the second set, it again completes
the circuit and stops the clock. I must use an insulator for a ramp
because if I used a conductor the electricity would run from one
electrode, through the ramp to the other electrode and start the
stop-clock. For this reason, I am using a plastic ramp. This is much
more accurate than me timing the ball. I will take three readings, and
in the end take the average. I will then work out the final velocity
by using the formula below. I will take three readings, and in the end
take the average.

Distance travelled in a given direction (m)

Time taken (s)

1. Velocity (m.s-1) =

On the second roll, the time it takes to roll from the top to the
bottom will be measured. As the metal ball rolls over the electrodes
at the top, it completes the circuit and starts the stop-clock. As it
then rolls over the second set of electrodes, it again completes the
circuit and stops the clock. Again I will take three readings, and in
the end take the average. I already know the initial velocity to be
zero, so using the final velocity and the time it takes the ball to
roll down the ramp; I can work out the acceleration of the ball. I can
work this out using the formula below.

Change in velocity (m.s-1)

2. Acceleration (m.s-2) = Time taken for the change (s)

Once I have worked out the acceleration for one ball, a different ball
with a different mass will then be used and the procedure repeated. I
will do this with four balls with different masses, as I believe I
will be able to obtain a good graph with the amount of results.

I will use the masses 6.06g, 7.30g, 8.63g and 9.07g. From my
preliminary work, these seemed like a good range of masses to use. To
make it a fair test I will need to release each ball from the same
height on the ramp. The further the ball falls, the faster it will go
so if I release them from different heights the acceleration of the
balls will be different. The most important thing to keep the same is
the angle of the ramp, I will keep it at 5°. If the angle changes then
the acceleration of the ball bearing will change automatically. I have
chosen to use the angle of 5° because from my preliminary work, which
I carried out before the experiment, it seemed like a good angle to
use.

I predict that the difference in the mass of the ball will not affect
the acceleration of it. I am able to make my prediction by using my
own knowledge and information from textbooks. The greater the mass of
an object, the greater force needed to accelerate it. Therefore when
two objects fall in a gravitational field, although the object with
twice the mass has twice the gravitational force acting on it, it
needs twice the force to accelerate it at the same rate as the smaller
mass. For this reason ALL objects accelerate at the same rate ignoring
air resistance.

Prediction

Using the sin function I can find out how high the ramp has to be for
a 5°

angle. The length of the ramp is 124.8cm.

124.8 sin 5° = 10.88cm(this is the height the ramp must go)

I know that by dropping a ball straight down, at a 90° is roughly
9.8m.s.-2. By dividing 9.8 by 90 and

multiplying it by 5, I can effectively get the acceleration of the
ball due to gravity.

9.8 / 90 = 0.108 Þ 0.108 * 5 = 0.54

The acceleration of the ball is 0.54m.s.-. As stated earlier the mass
of the ball does not affect the acceleration, all the accelerations
should be the same.

Mass of the ball / g 6.06 7.30 8.63 28.07

Predicted acceleration / m.s-2 0.54 0.54 0.54 0.54

CHANGING THE ANGLE OF THE RAMP

In this experiment I will keep all aspects of the experiment constant
except for the angle of the ramp

that the ball rolls down. For this experiment I will need to use

a plastic ramp,

a stand,

a clamp,

a nail, a metre rule,

a ball bearing,

four metal electrodes,

four crocodile clips,

four wires

stop-clock.

The set up of the apparatus is the same as the last experiment, as
shown below. The ramp will be initially set up to get a 5° angle. From
the previous experiment we know that to achieve a 5ÿ angle the ramp
will be set up 10.9cm off the ground. I have gone through the method
for this later. The same method will be used as before. I will use the
same ball which weighs 28.07g each time even though all masses should
accelerate at the same rate. I do this just so that the environment is
completely fixed apart from the angle of the ramp. The metal ball will
be released from the top of the ramp and allowed to roll down. The
ball will be rolled down twice. On the first roll, the final velocity
of the ball as it rolls down the ramp will be measured. This will be
measured by connecting wires to the stop-clock and set points on the
ramp. The electrodes are placed close together either side of the
ramp. As the metal ball rolls over them, it completes the circuit and
starts the stop-clock. As it then rolls over the second set, it again
completes the circuit and stops the clock. I will take three readings,
and in the end take the average. I will then be able to work out the
velocity by using the formula as shown on the next page.

Distance travelled in a given direction (m)

1. Velocity (m.s-1) = Time taken (s)

On the second roll, the time it takes to roll from the top to the
bottom will be measured. As the metal ball rolls over the electrodes
at the top, it completes the circuit and starts the stop-clock. As it
then rolls over the second set of electrodes, it again completes the
circuit and stops the clock. Again I will take three readings, and in
the end take the average. I already know the initial velocity to be
zero, so using the final velocity and the time it takes the ball to
roll down the ramp; I can work out the acceleration of the ball. I can
work this out using the formula below.

Change in velocity (m.s-1)

2. Acceleration (m.s-2) = Time taken for the change (s)

I will do this with six different angles. I will use the angles 5°,
10°, 15°, 20°, 25° and 30°. From my preliminary work, these seemed
like a good range of angles to use. To make it a fair test I will need
to release each ball from the same spot on the ramp. On the second
roll, the time it takes to roll from the top to the bottom will be
measured. As the metal ball rolls over the electrodes at the top, it
completes the circuit and starts the stop-clock. As it then rolls over
the second set of electrodes, it again completes the circuit and stops
the clock. Again I will take three readings, and in the end take the
average. I already know the initial velocity to be zero, so using the
final velocity and the time it takes the ball to roll down the ramp; I
can work out the acceleration of the ball. I can work this out using
the formula below.

The further the ball falls, the faster it will go so if I release them
from different heights the acceleration of the balls will be
different. When I measure the times for the balls, In theory it should
not matter

what ball I should use as mass should not matter to the acceleration.
However to make it a 'proper' fair test, I will only use one ball for
all the readings. I have chosen to use a ball with a mass of 28.07g
because from my preliminary work, which I carried out before the
experiment, it seemed like a good weight to use. It is big enough to
connect both electrodes easily, but small enough to roll properly
through along the ramp. A bigger ball could catch on the crocodile
clips. I predict that the closer the angle is to 90°, the faster it
will accelerate. I am able to make my prediction by using my own
knowledge and information from textbooks. When objects fall naturally,
they fall at a 90° angle. On earth, the acceleration due to gravity
acting on an object is 9.8m.s.-2, when the angle decreases, so does
the acceleration due to gravity. For this reason, I predict that the
closer the angle is to 90° the greater the acceleration the ball will
have.

I have worked out using the sin function how high the ramp has to be
for a 5°,

10°, 15°, 20, 25° and 30° angle. The length of the ramp is 124.8cm.

124.8 sin 5° = height (10.9cm)

124.8 sin 10° = height (21.7cm)

124.8 sin 15° = height (32.3cm)

124.8 sin 20° = height (42.7cm)

124.8 sin 25° = height (52.7cm)

124.8 sin 30° = height (62.4cm)

I know that at 90° gravity is roughly 9.8m.s.-2. By dividing 9.8 by 90
and

multiplying it by whatever the angle is, I can effectively get the
acceleration

of the ball due to gravity.

9.8 / 90 = 0.108 È 0.108 * 5 = 0.54

9.8 / 90 = 0.108 È 0.108 * 10 = 1.08

9.8 / 90 = 0.108 È 0.108 * 15 = 1.62

9.8 / 90 = 0.108 È 0.108 * 20 = 2.16

9.8 / 90 = 0.108 È 0.108 * 25 = 2.70

9.8 / 90 = 0.108 È 0.108 * 30 = 3.24

The acceleration of the ball for a 5° angle is 0.54m.s.- , for a 10°
angle it is 1.08m.s.-2 , for a 15° angle it is 1.62m.s.- 2, for a 20°
it is 2.16m.s.- 2, for a 25° angle it is 2.70m.s.-2 , and for a 30°
angle it is 3.24m.s.-2 . As the mass of the ball does not affect the
acceleration, all the accelerations should be

the same.

Steepness of ramp / ° 5 10 15 20 25 30

Predicted acceleration / m.s-2 0.54 1.08 1.62 2.16 2.70 3.24

RESULTS

Changing the Mass of the Ball

Mass of the Ball (g) 6.06 7.30 8.63 28.07

Acceleration (m.s.-2) (Reading 1) 0.50 0.53 0.56 0.54

Acceleration (m.s. -2) (Reading 2) 0.52 0.52 0.55 0.53

Acceleration (m.s. -2) (Reading 3) 0.54 0.50 0.52 0.53

Average/ (m.s. -2) 0.52 0.52 0.54 0.53

Changing the Angle of the ramp

The angle of the ramp (ÿ) 5.0 10.0 15.0 20.0 25.0 30.0

Acceleration (m.s. -2) (reading 1) 0.54 1.01 1.60 2.10 2.71 3.23

Acceleration (m.s. -2) (reading 2) 0.53 1.03 1.62 2.18 2.63 3.26

Acceleration (m.s.-2) (reading 3) 0.53 1.12 1.64 2.19 2.70 3.23

Average (m.s. -2) 0.53 1.05 1.62 2.16 2.68 3.24

Conclusion

As you can see from the graph as the angle of the ramp goes up so does
the acceleration and it goes up very steadily the smallest gap between
was 57m.s.-2. These results show that when the angle of the ramp is
increased the speed increases in turn whereas the acceleration between
the 5ÿ intervals is roughly the same around 54m.s. -2. Between these
intervals the acceleration between 5ÿ angles does not change but the
speed does. I predicted these accurately by using my previous
knowledge, which is that at 90ÿ, objects accelerate at 9.8m.s. -2 so
by dividing the acceleration at 90ÿ by 90 you get the acceleration at
1ÿ then you can multiply that by the angle e.g. at 10ÿ you would
multiply 0.108 by 10 to obtain an acceleration of 1.08m.s. -2.

When the variable was the mass of the ball, the times of the
accelerations were all in a range of 0.02m.s. -2. This reinforces the
fact that all masses, ignoring air resistance, accelerate at the same
rate. This is because the greater the mass of an object the more force
it needs to accelerate it. In my prediction I was very close to the
actual results, as I knew that all objects accelerated at the same
rate and as I knew that at 90ÿ it accelerated at 9.8m.s-2 so by
dividing the acceleration at 90ÿ by 90 I could tell the acceleration
at 1ÿ would be 0.108m.s.-2 so by multiplying by 5 I could find out
what the acceleration should be for all of the ball bearings. When the
variable was the mass of the ball I had to repeat one of my readings
when the ramp slipped.

Evaluation

I think the experiment was carried out successfully when I drew my
graph I could spot no anomalous results. If I were to do this
experiment again I would use a smoother ramp, the ramp that I used may
have caused the ball to bobble and this would be remedied with a
smoother ramp. When the variable was the mass of the ball I had to
repeat one of my readings when the ramp slipped this should not have
been a problem but I did not fasten the clamp enough.

Future experiment improvement

I could take more readings to iron out any anomalous results and get a
more definite average.

In a follow-up experiment I could see how different materials reacted
in this experiment.

In a further experiment I could see what affects an obstacle in the
middle of the ramp would have.