Calculations

To find the physics behind the my Rube Goldberg Machine, I used my Physics Everything Sheet as a tool to help find solve these following equations:

velocity = rate of covered distance in a direction (v)
acceleration = rate of change of velocity (speeding up or slowing down) (a)
force = push or pull on an object can cause a change in motion (F)
Mechanical Advantage = the ratio of the force produced by a machine to the force applied to it, used in assessing the performance of a machine. (MA)
Gravitational Potential Energy = energy an object has due to its position at a height or in a gravitational field (PEg)
Kinetic Energy = energy due to motion (KE)

Velocity

To find the velocity on my steps, I calculated it by recording the step in motion on my phone to find the time and measured the ramp with my meter stick. The ball I measured rolled down a ramp that was 1.32m in 0.95s so I divided both values and got 1.39m/s as its average velocity.

Acceleration

To find the acceleration of the ball, I had to divide the velocity which was 1.39m/s over the time which was 0.95s. I already knew the velocity from the previous calculations and after dividing both values, I got 0.37m/s^2 as the acceleration.

Force

The force exerted on the load is the weight of the ball which is 0.86N or 0.088kg because that's the force that initializes the pulley step. It can also be the force of gravity that is acting upon it when it pulls it directly down while the revert force pulls in its opposite direction making the force of gravity equal.

Mechanical Advantage

There are two types of mechanical advantage which are ideal and real. They are represented in variables such as MAi and MAr. MAi is how much further (more distance) you have to push due to using a tool and MAr is how much easier (less force) a tool makes a task. For my calculations towards my steps, I used MAi for my pulley which makes it really easy since the ideal mechanical advantage is equal to the number of rope segments pulling up on that object. Since the rope is wrapped around 2 segments representing a pulley, the MAi is 2 and the more the rope segments the less force that is needed for the job since there are more ropes supporting the lifting work.

Gravitational Potential Energy and Kinetic Energy

There are two main types of energy, Potential and Kinetic. Potential energy is an energy that is stored in an object due to its position relative to some zero position. The equation for potential energy or PE is simply (mass)(acceleration due to gravity)(height) and will look like this, PE=mgh. The higher the object is on a ramp, for example, the faster it falls down making the PE higher. As the ball glides through the inclined plane, its potential energy starts to deteriorate and creates kinetic energy. Kinetic energy, also variabled as KE, is an energy of mass in motion. To find the KE of an object, you have to multiply the mass by 2 and multiply that by its velocity squared. So the equation will look like this, KE=1/2(mass)(velocity)^2. If we go back to the example, as I let go of the ball from the top of the ramp, the motion of the ball that is descending down will start to gain KE as its PE starts decreasing. So when an object is at its highest amount of PE, its KE is 0 but when its KE is at its highest amount through motion, its PE is 0. I contributed PE on my inclined plane/pulley step by taking the mass of the ball which is 0.088kg multiplied by the acceleration due to gravity which is 9.8m/s^2 and lastly multiplied by the height which is 0.05m. After multiplying the three units together, I got the total PE of 0.043J. I contributed KE on those same simple machines by taking the ball's mass, 0.088kg, and multiplying it by its velocity, 1.39m/s, and square it to get 0.170kg. Since the KE formula is 1/2mv^2, I multiplied the 1/2 by 2 to make the sides even and with the value of 0.170kg, I divided it by 2 and got 0.085J as the KE. In conclusion, I got the PE of 0.043J and the KE of 0.085J of that step.

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