Funnest swing design

Process:

We set out to create a device that could resemble harmonic motion.To accomplish this we set out to make an outdoor swing on campus that we could then use to calculate the different forces occurring during its oscillation period as well as then apply a torque upon the swing and calculate the physics of that.

We first set out with rope and created our swing by throwing a rope around a tree twice and connecting a wood board. With this we then set out to find the following calculations of our rope swing design.


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Background info:

mass of person: measured with a scale

time period : measured with a stop watch accounting a full harmonic rotation

frequency: 1/time period

max amplitude at 50 degrees

equations:

rope length using Time period= 2pi*square root of (rope Length/gravity)

change in Y: Length of rope- L*cos(50 degrees)

Ug= M8g*(y)

ke=ug because of conservation of energy

Velocity max= 2*pi* frequency *amplitude

Force of tension:

tension maximum will be at the bottom of the swing: M*g+M*V^2

57kg (9.8 m/s) + 57kg ( 5.77m/s squared / 3.2 m )

= 558.6N + 593.029 N

= 1156.62 Newtons for both ropes

→ 575.8 N per rope

tension minimum : at the highest point of swing = Tmin = sin(40) = F/m*g

Ft= 558.6N * sin (40)

Ft= 359.06N

Ft= 359.06 N for two ropes

Ft= 179.53 N per rope



calculations:

moment of inertia using 1/2 m *r^2 = 57kg (3.2m)^2= i=583.6 kgm^2

rotaitonal velocity= change in radians over change in time (0.873 rad)/(0.9 sec) = w=0.97 rad/s

rotational acceleration= change in roational velocity over time:

started out at a rot velocity of zero and then was accelerated to a rotation velocity of 0.97 rad/s over a time of 3.6 seconds

0.97 rad/s /3.6 seconds= Arot 0.269 rad/s^2

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Bonus:

Rotational velocity: 2pi/time

momentum of inertia: for this we had to use a new moment of inertia due to using a different amound of mass and spinning in a horizontal direction rather than vertical from harmonic motion

using the mass of the legs off the swing we found the mass to be 60% of the mass of the whole person

to find moment of inertia = 1/2 (0.6*m) (r^2)

Torque calculations:

first recorded the rotational velocity of our person by recording the time for them to complete a complete rotation about their cener of axis and divided it over the time taken to do so. We did this for the very first roationa and then the very last one. With this we were able to find the change in these two velocityes and get our rate of acceleration over time. we found a de-acceleration over time as you can see below which we hypothesize is due to friction between the ropes. we then used the acceleration and the moment of inertia as well as the amount of time the torque was enacted upon the person to find our ending torque value. Torque *time = moment of inerita* rotaitonal acceleration

Angular Momentum Calcs (rotated 4 times)

1st: 6.28 rad/1.35 sec. = 4.65 rad/s

4th: 6.28 rad/ 2.1 sec. = 2.99 rad/s

ΔW/ΔT= (0+4.65 rad/s ) /0.36 sec. = initial α = 12.91 rad/s2

(4.65rad- 2.99 rad) / (3.8 seconds)= final α = -0.44 rad/s2

Tt=I*W

T*0.36s= 4.104* 12.91 rad/s2

T= 147N is about 33 pounds of force

So how did torque create the rotational momentum:

first we know it had to be the torque because it was enacted upon outside the center of mass of the person creating a force about an axis thus creating rotational momentum.

and secondly we can relate it to the equation Torque is equal to angular momentum divided by angular acceleration T= L/w


Funnest Tree Swing

Reflection:

two things I did well on were excelling in critical thinking by being helping contribute to the team and find out how our calculations would work and how we could make the swing at school, this along with having to think for myself and figure out how we would calculate for values such as the new moment of inertia showcased some of the critical thinking that took place. I also did well as a conscientious learner due to goal setting the team by splitting up work as well as managing the group and helping initiate some calculations and brain storming sessions with my team.

Two things I could work on are character, as during this last project I tried to lead too much which I could work on by leaving space for others to initiate in the group and implement more of their ideas and creativity into the project. Lastly I could also work on communication, our group struggled a bit with this when we attempted to do some of the project at home, as well as running out of time near the end. This along with practicing the presentation before hand wold also be one of my weak point for communication.