Download Physics Principles Step 1 The physics principle used in the first step

A) Physics Principles
Step 1
The physics principle used in the first step is the transformation of energy. An elastic band is
placed on the first level, which is stretched to a certain distance and gains elastic potential
energy. Once the elastic band is released, it goes back into its equilibrium position and strikes the
marble. Then, all of the elastic potential energy is converted into kinetic energy and as a result,
the marble starts to accelerate. This is an example of the law of conservation of energy. The
elastic potential energy has to have a greater magnitude than the work done by the force of
kinetic friction on the marble throughout the distanced travelled in order to reach the next step.
Step 2
The physics principle used in the second step is the motion of connected objects involving an
Atwood’s machine. A wooden block is placed on the incline setup in step three in order to block
the second marble from moving along the incline. An Atwood machine consisting of a block and
a plastic cup connected by a massless string over a pulley is installed on the first level. As
learned in class, if the objects have different masses, they will experience uniform acceleration.
Thus, a plastic cup is placed at the end of step one so that when the first marble with kinetic
energy falls into the cup, all of its kinetic energy transforms into gravitational energy causes the
wooden block to move.
Step 3
The physics principle used in the third step is the motion of objects along an incline. In order for
the second marble to achieve enough kinetic energy to knock down the series of dominos setup
in step four an easy yet effective step had to be installed on the second level. By placing an
incline on the second level and adjusting the angle higher off the ground the marble’s
gravitational potential energy is converted into the necessary kinetic energy required to knock
down the series of dominos. The net force acting on the marble is found by using the equation
F=mgsinθ and then subtracting the force of friction from it.
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Step 4
The physics principle used in the fourth step is the conservation of energy. Since the series of
dominos consists of a few dominos, the loss of energy due to friction is negligible for this step.
In order for the last domino to hit the big third marble and knock it down to start the fifth step it
needs enough kinetic energy to start moving, as it is initially at rest. The amount of kinetic
energy the last domino has is equal to the initial kinetic energy that the marble had the moment it
rolled down the incline. This holds true as we have learned in physics class that energy can’t be
destroyed nor created.
Step 5
The physics principle used in the fifth step is centripetal motion and transformation of energy.
The third level consists of a bridge supporting a much larger series of dominos that is crucial in
turning on the circuit setup as the final step. An effective yet different way had to be found to
enable the large marble to travel from the second level to the third level with sufficient kinetic
energy. The solution to the problem is centripetal motion; a relatively light 21 cm long string is
attached to the bottom of the second level which allows the big marble to transfer its
gravitational energy into kinetic energy and knock down the dominoes.
Step 6
The physics principle used in this step is the transformation of energy. A single domino did not
have enough gravitational potential energy to be converted into kinetic energy in order to fall on
the circuit and turn it on due to its lack of mass which result in gravitational potential energy
with a small magnitude. This is known due to the equation Eg =mg∆h. Thus, two separate
dominos were taped together to have a greater mass. This additional mass is important in
allowing the two taped dominos have enough gravitational potential energy so that when they
fall the transfer from gravitational potential energy to kinetic energy is enough to strike the
switch and turn on the circuit.
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A) Calculations
In the first step, the elastic band is stretched for 4.0 cm to store elastic potential energy in it. The
spring constant of the elastic band was found by attaching it to a Newton scale and stretching it
and recording the results.
Force ( N )
Displacement
(m)
Trial 1
- 3.05
0.097
FE = −𝑘𝑥 => k =
Trial 2
- 2.90
0.097
𝐹𝐸
−𝑥
=
− 2.93 𝑁
− 0.097 𝑚
Trial 3
- 2.85
0.097
Trial 4
- 2.95
0.097
Trial 5
- 2.90
0.097
Average
- 2.93
0.097
= 30.2 𝑁⁄𝑚
The energy stored in the elastic band was calculated by the following:
1
1
2
2
Eband = 𝑘𝑥 2 =
× 30.2 𝑁⁄𝑚 × (0.040 𝑚)2 = 0.0247 J
Once the elastic band is released and gets back to equilibrium, all of this energy transfers into
kinetic energy in the marble and it starts travelling on the wooden surface. As it travels, friction
between the surface and the glass marble reduces some of this energy.
µk = 0.36 (glass and wood), Mass of the marble = 0.00485 kg
Fnormal = mg = 0.00485 kg × 9.8 𝑚⁄𝑠 2 = 0.0475 N
Ffriction = µk × Fnormal = 0.36 × 0.0475 N = 0.0171 N
Efriction = Ffriction × ∆d, ∆d = 0.38 m, Efriction = 0.0171 N × 0.38 m = 0.00650 J
Ekinetic – Efriction = 0.0247 J – 0.00650 J = 0.0182 J
The marble then drops into a cup which is located 0.09 m below the surface and is attached to a
block by a string using an Atwood’s machine. The gravitational potential energy of the marble
transfers into kinetic energy and pushes the cup down and as a result the block moves up and
gains gravitational potential energy.
Egravitational = Ekinetic, Egravitational = mg∆h = 0.00485 kg × 9.8 𝑚⁄𝑠 2 × 0.09 m = 0.00428 J
The kinetic energy before the drop needs to be added to the kinetic energy resulted by the falling.
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Total kinetic energy = 0.00428 J + 0.0182 J = 0.0225 J
Mass of the block = 0.0260 kg, ∆h =
𝐸𝑛𝑒𝑟𝑔𝑦
𝑚𝑔
0.0225 𝐽
= 0.0260 𝑘𝑔 × 9.8 𝑚
⁄𝑠2
= 0.0883 m => change in height
of the block
As a result of the block moving up and clearing the path, a second marble starts traveling down
the incline. As the marble starts accelerating, the gravitational potential energy of the marble
transfers into kinetic energy. It should be noted that only a portion of gravitational vector is
acting on the marble due to the angle.
Mass of the second marble = 0.00534 kg, Angle of elevation = 30 ̊
Distance travelled (∆d) = 0.15 m
Egravitational = Ekinetic
Eg marble = Fg sinθ∆d = 0.00534 kg × 9.8 𝑚⁄𝑠 2 × sin 30 ̊ × 0.15 m = 0.00392 J
Friction between the glass marble and wooden surface decreases some of this energy again.
µk = 0.36 (glass and wood), Mass of the marble = 0.00534 kg
Fnormal = mg = 0.00534 kg × 9.8 𝑚⁄𝑠 2 = 0.0523 N
Ffriction = µk × Fnormal = 0.36 × 0.0523 N = 0.0188 N
Efriction = Ffriction × ∆d, ∆d = 0.15 m, Efriction = 0.0188 N × 0.15 m = 0.00283 J
Ekinetic – Efriction = 0.00392 J – 0.00283 J = 0.00109 J
At the end of the incline, the marble hits a series of 4 wooden dominoes and causes them to fall one after
another. There is a little or no friction between the dominoes. Thus, all of the kinetic energy of the marble
is conserved and no energy is lost during the collision of the dominoes.
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The last domino will hit a large marble and causes it to fall. The large marble is attached to the ceiling of
the lower level by a string and thus goes through centripetal motion. During its motion, the gravitational
potential energy is being transferred to kinetic energy.
Egravitational = Ekinetic, mass of the large marble = 0.0945 kg, change in height = 0.24 m
Egravitational = mgh = 0.0945 kg × 9.8 𝑚⁄𝑠 2 × 0.24 m = 0.222 J
Total kinetic energy of the large marble = 0.00109 J + 0.222 J = 0.223 J
At its lowest point, the large marble will hit a series of 4 dominoes. Since the friction between
the dominoes is negligible, all the energy is conserved and perfectly transferred by them. The last
domino will hit a wooden cube and causes it to fall on the switch and turn the light on. As the
mass changes height, its gravitational potential energy transfers into kinetic energy and then
pushes the switch down.
Egravitational = Ekinetic, mass of the cube = 0.0340 kg, change in height = 0.22 m
Egravitational = mgh = 0.0340 kg × 9.8 𝑚⁄𝑠 2 × 0.22 m = 0.0733 J
Total kinetic energy of the cube = 0.0733 J + 0.223 J = 0.296 J
Total energy that causes the switch to go down and complete the circuit in order for the light to
turn on is 0.296 J.
B) Materials and Equipment
Materials: Two pieces of wood (30 cm by 60 cm), one piece of wood (30 cm by 1 m), pulley
(one), one piece of wood (1 m by 60 cm), Styrofoam cup (one), one piece of wood (50 by 14
cm), two pieces of wood (50 cm by 30 cm), one piece of wood (10 cm by 23 cm), one small
piece of wood (15 cm by 10 cm), one small piece of wood (20 cm by 10 cm), Dominoes (nine,
different sizes), elastic band (one), marbles (2 small and 1 large), wooden block (incline),
wooden mass (turning on the switch), electric wire (0.5 m), string (1 m), small light bulb (one),
AA batteries (two), tape (one), plastic bag (one), nails (4), toy bridge (one), play dough (50
grams)
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Equipment: hammer (one), screw driver (one), electric saw (one), screws (46), L brackets (16),
super glue (one), battery holder (one), light bulb socket (one), plier (one), meter stick (one),
electric switch (one)
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