7-2 Project Analysis Report

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1 7-2 Project Analysis Report Jessica Infante Southern New Hampshire University PHY-101: Principles of Physics Professor Alison Lockman December 11, 2022

2 Step Selection: Pictured above is my Rube Goldberg device. The selected step in my Rube Goldberg Device is what is considered the second step in the device. This step starts with a 1.25 kg stone ball hitting a 1.25 rubber ball. When the stone ball hits the rubber ball, the rubber ball it pushed forward, rolling across the plane before hitting a 0.5 kg stone ball, thus starting the third step in the device. Previous Step: The previous step in my Rube Goldberg device, also considered the first step, is considered the previous step. This step starts by a 1.25 kg stone ball being dropped on a -30 ° incline. The ball then rolls down the incline and collides with a 1.25 kg rubber ball. “ Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force” (NASA, 2022). Based off of this law, the stone ball remains in uniform motion in a straight line unless compelled to change its state, which happens when the stone ball collides with the rubber ball. The kinetic energy from

3 the stone ball is transferred to the rubber ball when they collide at the bottom of the incline, thus pushing the rubber ball forward. To determine potential energy, the equation Potential Energy = mass x gravity x height must be used. According to the conservation of energy, potential energy is equal to kinetic energy. We can use the equation for kinetic energy KE= 1/2 mv 2 to solve for velocity. Then using the velocity, we can calculate for momentum, which is p=mv. Starting with the potential energy equation, Potential energy= (1.25 kg)(9.8 m/s 2 )(1.654 m) = 20.26 J. To solve for velocity, we can simplify the equation for kinetic energy to v = √((2*20.26)/1.25kg) = 5.69 m/s. We can then use the momentum equation p=mv to solve for momentum, which is p = (1.25 kg) (5.69 m/s) = 7.11 kg m/s . Selected Step: The initial velocity of the rubber ball is 0 m/s because the ball is at rest before it is pushed by the ball from the previous step. Since the mass of both the stone ball and rubber ball are the same and considering the conservation of energy, we can assume that the kinetic energy transferred from the stone ball to second ball remains the same. The rubber ball is at rest until the stone ball collides with it, so the change in velocity is 5.69 m/s – 0 m/s = 5.69 m/s . To calculate the acceleration, we timed that the rubber ball takes t = 2.33 s to reach the next step, using the equation a = (v f – v i ) / t we find

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4 that a = 2.44 m/s 2 . We can then use the equation F=ma from Newton’s second law of motion to calculate that the force acting on the rubber ball is F = (1.25 kg)(2.44 m/s 2 ) = 3.05 N To determine the change in kinetic energy across the step, I would need to use the equation K=1/2m(v 2 f-v 2 i). When I plug in the numbers for this equation, it looks like: K=1/2(1.25 kg)(5.69 m/s – 0 m/s)= 3.56 kg m/s. Next Step: The next step, and the third and final step in my device starts with the 1.25 kg rubber ball colliding with a 0.5 kg stone ball. When the stone ball gets hit, it is propelled forward, where it eventually falls off the edge of the plane. Once off the edge, the ball continues to roll forward, eventually hitting a 0.15 kg steel plate, thus making the steel plate fall. This step demonstrates Newton’s first law as the steel plate is at rest until acted upon by the stone ball. The kinetic energy from the stone ball is transferred to the steel plate, making it fall over. To determine potential energy, the equation Potential Energy = mass x gravity x height must be used. According to the conservation of energy, potential energy is equal to kinetic energy. We can use the equation for kinetic energy KE= 1/2 mv 2 to solve for velocity. Then using the velocity, we can calculate for momentum, which is p=mv. Starting with the potential energy equation, Potential energy=(0.5 kg)(9.8 m/s 2 )(1.172 m) = 5.74 J To solve for velocity, we can simplify the equation for kinetic energy to v =√ ((2*5.74)/0.5 kg)= 4.79 m/s

5 We can then use the momentum equation p=mv to solve for momentum, which is p =(0.5 kg) (4.79 m/s)= 2.4 kg m/s Electromagnetic Spectrum: The tool I have chosen that uses electromagnetic waves to measure velocity is a radar gun. Radar guns are used by police officers to detect how fast a car is going down the road. Speed guns give off radio waves that bounce off cars, and the reflected radio frequency is shifted by the speed of the car (Doppler Effect & Shocks, n.d.). After the gun receives the frequency, it calculates the velocity, or speed in mph in this case. “ By detecting and timing microwave echoes, radar systems can determine the distance to objects as diverse as clouds and aircraft. A Doppler shift in the radar echo can be used to determine the speed of a car or the intensity of a rainstorm” (OpenStax, n.d.). Radar guns use radio waves to determine velocity. In the electromagnetic spectrum, radio waves lie in the low frequency end. “ These correspond to frequencies as low as 3 Hz and as high as 1 gigahertz (10 9 Hz)” (Britannica, n.d.). With the waves being very low, this means they are longer in length, allowing the radar guns to detect frequencies from farther distances. A transmitter inside the radar gun sends waves in the direction the gun is pointed through the antenna inside. When the waves are reflected, they are sent back through the antenna and to the receiver. A duplexer is inside the gun which allows a singular path to allow duplex communication. When the receiver gets the frequency, it displays the speed on the screen read in mph.

6 References Encyclopædia Britannica, inc. (n.d.). Radio Wave. Encyclopædia Britannica. Retrieved December 11, 2022, from https://www.britannica.com/science/radio-wave Doppler Effect & Shocks . Doppler effect & shocks. (n.d.). Retrieved December 11, 2022, from https://physics.highpoint.edu/~jregester/potl/Waves/Doppler/doppler.htm NASA. (2022, October 27). Newton's laws of motion - Glenn Research Center . NASA. Retrieved December 11, 2022, from https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/newtons- laws-of-motion/#newtons-first-law-inertia 24.3 The Electromagnetic Spectrum - College Physics . OpenStax. (n.d.). Retrieved December 11, 2022, from https://openstax.org/books/college-physics/pages/24-3-the-electromagnetic- spectrum

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