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SPH4U Physics 12
Independent Study Unit
| Rube Goldberg Machine Project: Raising a Flag
Akmal Farhan Ab Rahman
1007C10603
Mr Tan Swee Chuan, Period 2
Eddy Arief Zulkifly
1007C10605
Mr Tan Swee Chuan, Period 2
Mohd Afiq Mohd Asri
1007C10609
Mr Tan Swee Chuan, Period 2
A k m a l , E d d y & A f i q | 1
THE STEPS:
EXPLANATION OF ACTIVITY AND PHYSICS CONCEPTS/PRINCIPLES
Our Rube Goldberg machine project consists of 16 distinct steps. The final product of the
machine is raising a Malaysian flag. The machine encompasses various Physics concepts and
principles.
Step 1: Projectile motion from an incline
A marble goes down an incline. At the end of the incline, the marble goes
airborne momentarily before falling into the plastic bottle.
Physics concepts/principles::
- Along the incline, the marble experiences gravitational, frictional and
normal forces. The force of gravity is resolved into components parallel
and perpendicular to the incline.
- using the Principles of Conservation of Energy, the potential energy of
the marble at the top of the incline is converted into kinetic energy as the
marble rolls down the incline. The velocity at the end of the incline is
given as v = 2𝑔ℎ
- The marble undergoes projectile motion launched at an angle below
horizontal. The final velocity of the marble from the incline becomes the
initial velocity of the projectile.
A k m a l , E d d y & A f i q | 2
Step 2: Helix rotational motion
As the marble enters the plastic bottle, the
marble undergoes circular motion due to
the high velocity gained from the incline.
As the rotation approaches the bottom of
the funnel, it falls onto the mousetrap.
Physics concepts/principles:
- The circular motion is caused due to the
centripetal force supplied by the normal
forces acted upon the marble by the walls
of the plastic bottle.
- As both centripetal force and gravitational force is acting upon the marble, the marble
experiences a helix shaped rotational motion.
- At the bottom of the funnel, the marble free falls onto the mousetrap.
Step 3: Mousetrap
The marble fell onto the mousetrap. The
mousetrap snaps and pulls the string
horizontally.
Physics concepts/principles:
- The elastic potential energy stored in the spring of the mousetrap supplies the restoring
force of the spring. The strong restoring force is larger than the tension in the string, Fs > T,
causing the string to be pulled.
A k m a l , E d d y & A f i q | 3
Step 4: Series of pulleys
The pulled string undergoes a series of high friction pulley
system. The string pulls the lever.
Physics concepts/principles:
- The tension in the string provides the force to pull the
lever. As the string is pulled across high friction pulleys,
energy is loss to overcome the friction, hence lowering the
force. The energy loss is approximately ½ for each pulley.
As there are 3 pulleys along the system, the force in the
string, T to pull the lever is approximately 1
2𝑛 =
1
23 =
1
8 of the
force supplied by the mousetrap.
Step 5: Knock the marble
The string pulls the lever. The lever turns and hits the
large marble.
Physics concepts/principles:
- The lever is a first class lever, where the fulcrum is
in the centre.
- The string pulls the lever at from an angle θ ≈ 90°.
The torque produced by the lever is given as 𝜏 =
𝐹 𝑟 sin𝜃. As the F = T and sin 90° = 1, 𝜏 = 𝑇 𝑟 ,
where r is the distance between the fulcrum and the
force.
A k m a l , E d d y & A f i q | 4
Step 6: Split steps – Newton’s cradle and opening the trapdoor
The large marble collides with another large marble. Both marbles hit the Newton’s Cradle and
the falls into a basket. The basket pulls the strings across a pulley that opens the trapdoor in Step
9.
Physics concepts/principles:
- The inelastic collision between the marbles obeys the Principles of Conservation of
Momentum.
- The collision with the Newton’s Cradle is elastic.
- The gravitational force acting on the marbles as it falls into the basket is greater than the
tension in the strings, mg > T. A net force acted on the basket and the trapdoor, causing the
basket to move downwards and trapdoor to move upwards. The trapdoor opens with the lower
acceleration as the basket, as force due to tension is also used to overcome friction of the pulley.
A k m a l , E d d y & A f i q | 5
Step 7: The see-saw
The Newton’s cradle hits a
domino piece, which falls
onto a makeshift elastic ruler
see-saw. The see-saw tilts a
horizontal runway and
releases a marble along the
incline into the corrugated
tubing.
Physics concepts/principles:
- The kinetic energy from the Newton’s marble is transferred to the levers.
- The marble rolls down along the incline.
Step 8: Corrugated tube
The marble rolls inside the corrugated tubing and exits
into a semi-circular channel, which leads to Step 10.
Physics concepts/principles:
- The motion inside the corrugated tubing causes
energy loss to the marble due to the high frictional
force acted by the walls of the tubing. This reduces
the speed of the marble before it goes into the channel.
A k m a l , E d d y & A f i q | 6
Step 9: Marbles and plane with obstacles
When the trapdoor moves upward, it allows 9 marbles to move down the transparent incline
plane. Using gravitational potential energy, the 9 marbles move down the plane, knocking the
vertical pole obstacles along way and fall into a slightly-inclined horizontal track at the end of
the plane. The marbles then follow down the inclined path onto the semi-circular channel.
Physics concepts/principles:
- Along the incline, the marbles experiences gravitational, frictional and normal forces. The force
of gravity is resolved into components parallel and perpendicular to the incline.
- using the Principles of Conservation of Energy, the potential energy of the marble at the top
of the incline is converted into kinetic energy as the marbles are released and roll down the
incline. The velocity at the end of the incline is given as v = 2𝑔ℎ
- The collision with the obstacles causes loss in mechanical energy due to work done on
negative direction.
- The sudden change in direction and inclination angle between the plane and the horizontal track
causes the magnitude of velocity of the marbles to reduce greatly.
A k m a l , E d d y & A f i q | 7
Step 10: Marble accumulation
The marble from the Step 8 and the nine marbles from Step 9
are channeled through the semi-circular channel and are
directed into a narrow inclined track. A small slit is cut at the
side wall of the track. As the marbles accumulate in the track,
the first nine marbles fill in all the spaces of the track, causing
the last marble to fall through the side of the track wall.
Physics concepts/principles:
- Along the incline, the marbles experiences gravitational,
frictional and normal forces. The force of gravity is resolved
into components parallel and perpendicular to the incline.
- the mass of the nine accumulated marbles is greater than the last marble (9m >> m), causing it
to exert a force on the last marble upon collision.
- the marble momentarily experiences free fall.
A k m a l , E d d y & A f i q | 8
Step 11: The slippery satin cloth
The marble falls onto a stretched satin cloth. The cloth absorbs the impact of the fall, and then
slides down the smooth cloth. The marble is launched airborne over a gap, before landing on
another platform of stretched satin cloth.
Physics concepts/principles:
- The stretched cloth absorbed the force from the falling marble as it is slightly deformed, hence
increasing the interaction time, Δt between the marble and the cloth. Impulse, J, is constant
during contact as it is affected by the change of velocity of the marble before contact. Reducing
the force is important to avoid the marble from bouncing off.
- The smoothness of the cloth greatly reduces the frictional force acting on the marble as it
slides down.
- As the marbles reaches the gap, it is launched to a projectile motion before landing on another
cloth. The cloth again absorbs the force and avoids the marble from bouncing.
A k m a l , E d d y & A f i q | 9
Step 12: Chain reaction
The marble rolls down the cloth and hits the first trigger, moving the first marble from rest. The
marble knocks the next trigger, and releases all the subsequent three marbles. The last marble
rolls down the incline before it stops on the steel wire loop, and falls onto the track below it.
Physics concepts/principles:
- The momentum from the rolling marble is transferred through the triggers and the marble. The
kinetic energy loss during the inelastic collision between the marbles and the triggers is
compensated by the kinetic energy gained as the marbles rolls down the incline.
- The last marble experiences a large change of momentum at the end of the inclined track as it
is abruptly stopped by the steel wire loop. The change in velocity becomes Δv = 0 –vi. The
marble momentarily undergoes free fall.
A k m a l , E d d y & A f i q | 10
Step 13: Sideways motion transfer
The marble rolls along the track and hits the pivot. The pivot stops the marble. The force by the
marble is transferred at an angle by the pivot to the stationary large marble. The large marble
rolls down the steep incline to the banked curve.
Physics concepts/principles:
- The pivot transfers the initial force, Fi from the marble, to the large marble. The resultant
force (assuming energy absorbed by the pivot is negligible) is given as |Fnet|2 = |Fi|
2 + |Ff|
2 –
2|Fi||Ff| cos θ, at an angle θ which is the bend angle of the pivot.
- The final kinetic energy of the marble is given as Ekf = Epi + Eki + W, where work done is the
energy transferred to the marble by the pivot.
- Along the steep inclined track, the large marble experiences gravitational, frictional and normal
forces. The force of gravity is resolved into components parallel and perpendicular to the
incline.
A k m a l , E d d y & A f i q | 11
Step 14: The banked curve
The large marble undergoes semi-circular motion as it corners via the banked curve. The large
marble then rolls along the horizontal track and knocks the bottom of the long vertical lever.
Physcs concepts/principles:
- The banked curve provides the centripetal force to allow the marble change its direction. The
velocity of the marble is given such that v = rg tan θ.
- The kinetic energy from the marble is transferred from the bottom of the lever to the top of the
lever.
A k m a l , E d d y & A f i q | 12
Step 15: Long vertical lever and horizontal see-saw
The vertical lever pulls back and releases the horizontal see-saw. The horizontal see-saw tilts
towards the weight.
Physics concepts/principles:
- The vertical lever holds the horizontal see-saw with a small frictional force. As force is
applied on the vertical lever by the large marble from Step 14, the frictional force is overcome
and releases the horizontal see-saw. The see-saw (first class lever) tilts towards the load i.e the
weight.
A k m a l , E d d y & A f i q | 13
Step 16: Raising the flag
The weight falls downwards and pulls the
string down across the pulley. The flag is
raised upwards.
Physics concepts/principles:
-This step is based on the concept of an
Atwood Machine where 2 masses are
connected to the end of a single string. The
mass with a higher weight will be pulled
downward as the downward force
experienced; gravitational force is higher
than the tension of the string, mg > T. As a
result, the weight goes down with a
constant acceleration due to gravity. At the
same time, the mass with the lower weight
will move upward with certain
acceleration. In both cases, both objects
experience the same tension however, since the masses of each object are different, they would
also have different accelerations, as Fweight = m(g+a) and Fflag = m(g-a) and mweight > mflag.
A k m a l , E d d y & A f i q | 14
Problems Faced and Solutions/Modifications
Our project is based on a whole original concept of combined contraptions involving many
physics principle which at most time seemed easy to make but we realize that in the real world
everything required calculation and testing. The final design of the project has deviated much
from the original plan however; we believe that it was worth it as most of the original designs
were problematic and hard to design. While constructing the contraptions, we encountered many
problems and we solved the problems along the way instead of just adding steps and piling the
problem which in long term is beneficial.
Problem #1:
A wobbly wooden support for Step 1.
Due to the fact that the support system for the first step is wobbly and it’s fragile, we found out
that screwing/nailing the wooden pillars are weak. We used wood glue to attach the support
system to the base. Furthermore, we added an extra support pillar from the original pillars to the
wall.
Problem #2:
Inaccurate Centripetal Force trajectory in Step 2.
We wanted the ball to land into the plastic bottle at an angle and therefore making the marble
spin as long as possible in the bottle. We used a bottle with no patterns in it (such as coke
bottles). To increase the centripetal force, we had to estimate the position of the bottle. So we did
more than 40 tests to make sure the rotational motion of the marble was to our expectations.
Problem #3:
Marble shoots out at a random direction from the plastic bottle in Step 2.
To overcome the problem, we added a channel made out of paper so that the marble would land
directly on the mousetrap (which is the next step). To ensure that the marble always triggers the
mousetrap, we added a platform above the trigger, which will be lowered onto the trigger every
time the marble falls onto the platform.
Problem #4:
Mousetrap in Step 3.jumps up and down and affects tension of the string
When the mousetrap is not at a fixed position and moves around (because the spring force is
strong), the tension of the spring which is on the next step is greatly affected – not being able to
provide the maximum force. To overcome this, we glued the mousetrap to the base using wood
glue and we nailed it to fix its position.
A k m a l , E d d y & A f i q | 15
Problem #5:
The tension of the string in Step 4 was not strong enough to pull the lever up.
The solution to this is that we placed several brackets at strategic locations on the wall as to
provide maximum tension so that the lever is able to be lifted up at a reasonable force (more than
enough to move the marble). Also, instead of pivoting the lever to the wall using nails, we
decided to glue the lever to a door hinge which has less friction, allowing more force to be
transferred to the lever.
Problem #6:
Constructing a Newton’s cradle for Step 7.
A retail Newton’s cradle costs in excess of more than a few hundred Ringgit which was out of
our budget. Using our creativity we managed to make our own mini newton’s cradle by
encapsulating 3 marbles with metal wire. The wire acts as a supporting frame to tie the rope on
the marble to the overhead beam above it.
Problem #7:
Newton’s cradle in Step 7 did not swing properly.
The solution was to align the marbles in such a way that they are at their closest distance and are
exactly parallel to each other. To further strengthen this, we taped the exact positions of the
string to ensure the string did not change position due to subsequent trials.
Problem #8:
The marble in Step 7 was stuck at the funnel and did not fall into the corrugated
tube.
The solution was to tape pieces of card to form inclines that directs the marble straight into the
tube.
Problem #9:
Trapdoor for Step 9 did not open when the basket was pulled down.
The solution was to shorten the trapdoor such that it no longer depends on the slits to hold it in
place, instead only depends on the weight of the marbles. Therefore, the door only experiences
friction with one surface instead of two surfaces.
Problem #10:
Marbles in Step 9 move too fast that they flew off the plane.
The solution was to build a barrier using paper cups covering the end of the incline plane.
A k m a l , E d d y & A f i q | 16
Problem #11:
There is no proper method to channel the marbles from Steps 8 and 9 to Step 10.
The solution was to construct a semicircular canal using paper cups. Semicircular shape was
chosen instead of tubular shape because it channels the marble properly while not obstructing us
to make any adjustments.
Problem #12:
Marble did not slide down the cloth in Step 11 when the marble landed on it.
The solution was to stretch the cloth using chopsticks and wires placed at strategic spots.
Problem #13:
Last marble from Step 12 got stuck between the steel wire loops.
The solution was to enlarge the size of the loop, and to form a wall at the sides of the track below
the loop using mounting board to avoid the marble to run off-track.
Problem #14:
The large marble bounces off as it reaches the bottom part of the banked curve for
Step 14.
The solution was to add an extra ramp using cardboard to create a smoother path transition from
the inclined track to the banked curve.
Problem #15:
The flag was not raised after the weight is released.
The solution was to adjust the pulley system of the flag at the beginning of every trial to ensure
the string lies on the pulley wheel and not stuck between the axles. The mass of the
counterweight tube is increased by adding marbles into the tube.
A k m a l , E d d y & A f i q | 17
Skills Learned While Doing Project
Throughout the construction of our Rube Goldberg machine, we gained many useful technical
and interpersonal skills that are very valuable for our development as future leaders and
engineers.
1. While constructing our Rube Goldberg Project, an important skill that we gained was
learning to make the best out of everything. We did not have a relatively high budget
for our project and most of the tools used were mostly from friends or leftover items
from home. Rather than buying items from stores, we instead learned the art of
recycling old materials from previous projects as well as rummaging in the garbage
for useful items. For example, the red cloth for the slide came from Akmal and
Eddy’s Calculus and Vectors project while the black tube which brings down the flag
came from a model ship which was left lying beside garbage inside the Taylors
Wisma Subang Jaya building.
2. Another important skill that we learned was connecting theory to practice. Students
are mostly taught about the theoretical aspects of Physics but are rarely exposed to the
real life application of Physics concepts in daily life. Banking curves were easy to
understand in the textbook, but in real life they are definitely much harder to recreate.
This was due to additional factors that were needed to be put into consideration such
as the orientation of the marble ball as it moves on the curve, the effect of gravity and
friction on the marble as well as the direction the marble moves while travelling on
the banked curve.
3. The Rube Goldberg project also helped us develop our divergent thinking skills.
Humans are normally taught that there is only one way to do things. For example, to
make a marble move from one place to another, you would require cable or anything
that can channel the marble in a particular direction. However, from the project we
learned that this need not be the case. For example, rather than using a cable to
channel the last marble to the multilevel marbles step, we instead used red cloth
which functioned like a ramp. To ensure the marble fell in a particular direction, we
adjusted the position and height of the cloth to ensure the marble jumped with a
particular angle. As the marble dropped from the cloth, it gained kinetic energy and
jumps of the cloth, landing exactly around pivot which activates the next step. Thus,
we creatively solved the problem of moving the marble around the base while
showing a few physics concept at the same time.
A k m a l , E d d y & A f i q | 18
4. Lastly and most importantly, while completing our Rube Goldberg project, we
learned the value and skill of teamwork. Like in any football match, a team of players
will always win a match rather than a group of individuals. Everyone in the group
offered something different to the table whether it was Akmal’s creativity, Afiq’s
craftsmanship or Eddy’s management skills. A strong team composes of people with
different skills sets rather than people of similar strengths and backgrounds. We as a
team were able to compensate each other’s weaknesses and produce the best quality
work possible.