parts of a roller coaster car

Individual cars vary in design and can carry from one to eight or more passengers each. Our Bear-Loc® locking feature for hydraulic components combines fail-safe reliability with an easy-to-use system. Mini Trackless Train Rides For Families To Enjoy! K'nex 34043 Dragon's Revenge Thrill Coaster - 578 Parts - Roller Coaster Toy. Every system operates differently with varying results. This is part 2 of the How to make a LEGO Roller Coaster video's. For faster, smoother and quieter acceleration, a hydraulic system may be your best option. Will a car with twice the mass have more or less speed at the bottom? It began with ice sledding. Part A A roller coaster car doing a loop-the-loop is upside down at the highest point of the loop. Please contact us directly if you have additional questions. The second section along a roller coaster track where circular motion is experienced is along the small dips and hills. A spring-loaded automobile bumper compresses 0.30 m when the car hits a wall and stops. Steel roller coaster in amusement park in Romania. If there is any risk that lifts riders out of their seat, shoulder harnesses are the right choice. ‘The fireball rammed into the roller coaster car and the whole part of the roller coaster track and the car blew up.’ ‘Do you go to an amusement park with your five friends in order to watch one friend ride the roller coaster?’ ‘Watching a video of a roller coaster ride … ONE Knex Storm Mountain Blue ROLLER COASTER CAR Replacement Part/Piece. (Figure 1) Figure 1 of 1 Part A Determine the magnitude of its velocity. Beston vintage roller coaster for sale can be used in a long time. In those cases, the design is crucial, but so are particular parts of a roller coaster. Alibaba.com offers 1,138 roller coaster parts products. $29.99. © 2017 - 2020 York PMH. Plastic. Certain parts of a roller coaster function to keep riders safe on their journey. {{filterDisplayName(filter)}} Duration. The most traditional way most trains get to that first hill is via a long chain (or chains) running up the hill under the track that simply pulls trains to the top. Choose locking hydraulic cylinders as they can prevent accidents. Characters of Beston Roller Coaster Parts: Each part of the roller coaster can be customize according to customer’s special request. A wide variety of roller coaster parts … Along with some mechanical systems, of course. Selecting the right manufacturer for your machinery will help you avoid hydraulic cylinder failure. Will the system you select always work for the ride? Shoddy workmanship or poor design features could make this project mega-dangerous, so it's worth taking the time to do a ton of research. All dimensions shown are approximate. Other parts of a roller coaster include safety features, which vary depending on the type of ride. Inverted or suspended rides have the car riding below the tracks, which requires a different type of train and harness setup. People having fun Seven Dwarfs Mine Train roller coaster at Magic Kingdom 1. Free shipping . Generally, each car of the roller coaster could hold 2, 4, 6 or even 8 people, these cars usually connected by the hooks, just like a train in the air. This vertical accelerator roller coaster is a part of Ferrari Land amusement park in Spain, and it is the fastest coaster in Europe and the fifth tallest in the world. A roller coaster train is a vehicle made up of two or more cars connected by specialized joints which transports passengers around a roller coaster's circuit.. These standard roller coaster launch systems propel roller coaster trains forward as the ride begins in various ways. All of the systems above can be responsible for keeping riders safe, but you have to choose the best one for the ride. (Figure 1) Figure 1 of 1 Part A Determine the magnitude of its velocity. The front part of the train was slowed down because the back part was still attached to the chain or whatever was moving the car up the hill. Please feel free to give your inquiry in the form below. They are less common choices because they tend to use more energy than the other three options. It then moves 135 ft, at an angle of 40.0° below the horizontal, to a lower point Ⓑ. For seats, if you are interested, I found some premade small wooden chairs at our nearby craft store that I used wood glue to paste onto the wooden boards. Finally the cars are brak… It consists of carts that are attached together, or a single card with multiple seats, allowing many people to ride at the same time. All ... Roller Coaster Mania - Nursery Rhymes For Kids. While you should regularly maintain your mechanical systems, choosing a high-quality system will give you peace of mind. Due to COVID-19, we are delaying the shipment of any online orders placed after 03/20/20. Whether they are doing and inclined dive loop, a pretzel knot, or a cobra roll, it is all about providing the most exhilarating ride using roller coaster parts that work together to keep people safe. magnitude: _____N direction: upwards The rods and connectors click together to create a 3D configuration and a coaster that stands over 2 feet tall. Definition a self-propelled wheeled vehicle . Certain varieties within these different launch mechanism categories have their positives and negatives. These keep riders secure in their seats at launch, throughout the journey and until it's time to exit the ride. Most people have ridden on a roller coaster before. A safety bar is oriented length-wise along the top of each car. You have probably gone to carnivals where roller coasters were available, and each one is built in the same way. Wheels – Describes the part of the roller coaster car or train that rolls on the rails or track. Friction turns the useful energy of the roller coaster (gravitational potential energy and kinetic energy) into heat energy, which serves no purpose associated with propelling cars along the track. A 1 000-kg roller coaster car is initially at the top of a rise, at point Ⓐ. Finally, it is the experience of the roller coaster that is what makes it possible for carnivals to motivate people to come back for more. Spain. $6.39 + shipping . In one roller coaster car, a small 0.10-kilogram ball is suspended from this bar by a short length of light, inextensible string. The place to buy roller coaster parts. The path of the coaster from its initial point shown in the figure to… When you choose a hydraulic system for roller coasters, riders' safety is the top priority. You also have to make the right choice when choosing a particular hydraulic mechanism and locking components. There is something about a roller coaster that is both frightening, and exciting, that keeps people coming back for more. Great deals on Roller Coaster Cars Coaster Parts K'NEX Building Toys. After that point, then the front is generally going faster since the train continues to lose a little speed as the friction of the track slows the coaster … The place to buy roller coaster parts. Brand New. 1-16 of 37 results for "step 2 roller coaster car" Skip to main search results Eligible for Free Shipping. All that geometry serving both structural and aesthetic functions had to be legal, which looks simpler than it actually is. Additionally, builders can head to knex.com to download instructions for a second roller coaster model. Professional designer and experience installation workers to promise you a suitable part for your whole set of roller coaster … When operated according to specifications, our hydraulic actuators and cylinders keep riders and workers safe. Parts of a Coaster. Determine the maximum speed of the car at the bottom of that drop. At this point, the normal force of the track on the car is zero points down points up points in the direction of motion Submit Reavest Answer A roller coaster car doing a loop-the-loop will come of the track if its speed at the highest point drops below a critical spood. Over 9 ft. (2.74 m.) of up and down riding track included. Home > Parts Pick a Brick LEGO > LEGO Vehicles Parts > LEGO Vehicle Base > LEGO Vehicle, Base 4 x 5 Roller Coaster Car LEGO Vehicle, Base 4 x 5 Roller Coaster Car Color The drive tire is connected to the mechanism which propels the roller coaster forward, usually connected to a linear induction motor. When this began decades ago, they were typically made of wood and slowly changed over to steel. Department. Unfortunately, these precautions don’t always work, and that’s when dramatic, lethal accidents happen. All customers get FREE Shipping on orders over $25 shipped by Amazon . Jacques LaRochelle inside the roller coaster his family built at his Carneros home. There are two major types of roller coasters, distinguished mainly by their track structure.The tracks of wooden roller coasters are similar to traditional railroad tracks. Top Rated Seller Top Rated Seller. Part of a roller coaster. Apple Coaster RC1197 Read more ... Caripro Coaster RC1359 SOLD. Hydraulic Vs. Electromagnetic Launch Systems, How to Choose the Best System for a Roller Coaster, Choose the Right Hydraulic System for Roller Coasters, the train itself doesn't need an engine to run, Today's technology reduces risk to riders, that let more than one train on the tracks, Different types of launch equipment include, When selecting a system for a roller coaster, Bear-Loc® locking feature for hydraulic components, A combination of mechanical and hydraulic technologies, How much space you have for your roller coaster, How much power you can supply to the system, More parts to keep track of and get inspected. Once everyone is in place, the ride will take them along the tracks like a train, but going to very high points, and low points, all the while moving at high speeds. This Step2 Roller Coaster Car™ is the perfect add-on to our Thomas the Tank Engine™ Up & Down Roller Coaster™ toy playset. Whether they are lap or shoulder bars, they need a reliable mechanism to lock them in place and unlock them once the ride is over. Buzz bars are the things that keep people in place, locking them into their seat. Ride-On Toys & Accessories; Kids' Pedal Cars; Play Vehicles; Hobbies; Building Toys; Toy Building Sets; Baby & Toddler Toys; Learning & Education Toys; See All 12 Departments. Ages 2 to 5. LEGO - 2 x Roller Coaster Track - Lg Lower Ramp - 6 Elev, Red - 26559 - New. Roller Coasters - New and Used Amusement Rides For Sale Carnival Rides - Amusement & Theme Park Rides - Family Entertainment & Amusement Center Rides. This small engine roller coaster car is mighty and reliable, just like Percy! The main issue with particular hydraulic systems is the number of moving parts they require. Answer Clue Relevancy car. When the cars reach the top of the incline, they roll free of the chain and are propelled downward by gravity through a series of drops, rises, and turns. Find professional Scary Roller Coaster videos and stock footage available for license in film, television, advertising and corporate uses. They would start at the top of either natural or artificial hills, and come down at high speeds on sleds that were designed to turn and also come to a stop. A moving car has 40,000 J of kinetic energy while moving at a speed of 7.0 m/s. Then wait for the giggles and shouts. Its speed at the bottom of the track is 18 m/s. The ratio between the power they need and what they provide does not make them the best roller coaster systems out there. Made in USA. The roller coaster car travels down the helical path at constant speed such that the parametric equations that define its position are x = csin kt, y = c cos kt, z=h-bt, where c, k, h, and b are constants. They were dating and it seemed to be fine. You need a system that will function safely and effectively in the ride design. $19.71. Up and Over Agawam, MA, USA July 14, 2009 Up and Over: riders crest a hill on the Superman the Ride rollercoaster in Agawam , Massachusetts. Corkscrew, at Knott's Berry Farm, circa 1980, before being relocated to Silverwood. Build the Vulture's Vengeance toy roller coaster with the included 690 K'NEX parts and pieces including coaster track, roller coaster car, motor and themed graphics! These sections of track are often found near the end of a roller coaster ride and involve a series of small hills followed by a sharp drop. As of 2019, Arrow Development has built 102 roller coasters around the world. Besides, it is a sort of milestone in the LEGO System. 1-16 of 37 results for "step 2 roller coaster car" Skip to main search results Eligible for Free Shipping. In those cases, roller coasters also use potential and kinetic energy to keep moving. When selecting a system for a roller coaster, consider: While passengers' safety is the top priority, it's not the only consideration when designing, updating or repairing a roller coaster. Name Model Park Country Opened Status Ref Wabash Cannonball: Corkscrew: Old Indiana Fun-n … We will reply in 24 hours. You should compare pneumatic, hydraulic and electromagnetic launch systems as you choose a mechanical setup for a roller coaster. Prime Video From $0.99 $ 0. Instead of waiting for winter, it was soon determined that, like a train, roller coasters could be made. A roller coaster will maintain speed or accelerate down hills and around curves depending on its design. Please view the Classic K'NEX Coaster parts that are still available in our Parts shop. Beston supply steel antique roller coaster for sale with best quality. Mechanical systems in roller coasters keep riders safe and having a good time, so choosing the right one for your ride is an important decision. It is one of the most exciting rides in the world. Free Shipping by Amazon. Depending on the construction of the ride, a car may have multiple security devices. Due to COVID-19, we are delaying the shipment of any online orders placed after 03/20/20. In terms of overall dimensions, I think this is the largest LEGO set ever. B. While we've seen roller coaster carriages that have the ability to spin, most coasters do that to increase the out of control feeling of the ride. Clue First part of a roller coaster ride. So fire up your design software, pull out the power tools, pick up some supplies, and get to work. Parts of a Roller Coaster. Screams aside – What Is the Classification Of A Roller Coaster? Ref: 20471P. Micro K'NEX Coaster parts These are the parts for Micro K'NEX Roller Coasters available. All of these forces on a roller coaster mean that the train itself doesn't need an engine to run. Buzz bars are the things that keep people in place, locking them into their seat. empty roller coaster car; The construction of a roller coaster can vary depending on what type it is. Hydraulic components will be the best choice for your roller coaster, whether you use them in launch or safety systems. If a color is missing, it probably needs to be added to a Set Inventory. Made in USA of US and imported parts. Definition of a roller coaster in the Idioms Dictionary. Lego 5 New Pearl Dark Gray Train Track Roller Coaster Ramp Large Lower Parts . K'nex Vegeance Coaster. A brake run is is what allows the roller coaster to slow down and come to a stop, something that is controlled today by computer systems and software. Wheels are typically steel with a nylon or rubber coating on the outside to reduce the noise steel to steel contact would make and the heat generated by friction. Hint R2. Recessed retainer well holds car until your child is ready to roll. Your new backyard roller coaster … Featuring a fun character design, Percy comes to life in this roller coaster car toy as little ones cruise down the track. Free Shipping by Amazon. Parts of a Roller Coaster The construction of a roller coaster can vary depending on what type it is. Pneumatic Vs. loop. The Step 2 Up and Down Roller Coaster car has a high back, handrail and foot rests for a secure ride. The roller coaster car travels down the helical path at constant speed such that the parametric equations that define its position are x = csin kt, y = c cos kt, z=h-bt, where c, k, h, and b are constants. You can find an overview of all LEGO Colors here. Think about the longevity of the product you choose and potential future repairs or replacements. Roller coaster. All of this works together on the track which is specifically designed to cause people to go up, down, to the side, and even upside down, making every roller coaster unique. Installing the right mechanism on a ride will make it exciting and safe for passengers. Up to 4 of this car can be added to a 20471 Coaster Car Front to create a "train" of cars. As we've described above, an electromagnetic system uses forces of repulsion and attraction to launch a roller coaster. Express your answer in terms of some or all of the variables c, k, h, b, and t. IVO AED vec 1 ? Two nonslip steps lock securely into the 3-pc. They were in a relationship for 1 and half years. Roller coasters are actually very technical products, ones that are designed to provide thrill and safety. Natural forces on a roller coaster help slow it down to build riders' tension, then send them gliding down the tracks again. Will it be in the budget to conduct major repairs or replacements? Easy Classiffication Of Roller Coaster Parts For Sale, How To Purchase A Miami Trip Ride For Less, Choosing From The Best Rotary Octopus Rides For Sale. A Brief Introduction Of The Indoor Roller Coaster Rides, 5 Reasons Kids Love The Mini Roller Coaster Ride, Discover Some Tips When Choosing A Roller Coaster Car, Tips To Keep In Mind When Choosing Small Roller Coaster Rides, Amusement Parks With Large Roller Coasters Attract Thrill Seekers From All Over The World. The prices exclude VAT (Value Added Tax). Here are the possible solutions for part of a roller coaster clue. The three more popular launch systems use forces and equipment that are a bit more complex. If you choose the right system, you'll realize a high-quality product is the answer to how to prevent roller coaster accidents. of cars per-train: 6 No. Search for crossword clues found in the NY Times, Daily Celebrity, Daily Mirror, Telegraph and major publications. There are steel and wooden roller coasters that feature different elements throughout the ride, depending on the design. (a) Initially, the car is at rest a point A. These various roller coaster designs still rely on physics and mechanical systems to keep them moving. The power that they do create is not considered efficient either because they require a lot of energy to operate. Your riders will be safe at launch or other parts of their journey where you use our systems according to specifications. These fluctuations can make a ride both exciting and safer since the car shouldn't pass certain speeds while heading into turns or hills. We understand the risk of accidents on any machinery that requires a hydraulic system, and we want to provide the safest option for engineers. The basic elements of a roller coaster can be broken down into a brake run, buzz bars, drive tires, headchoppers, it launched track, a lift hill, and of course the carts and seats where people will sit for the ride. About 2% of these are Amusement Park Rides, 7% are Other Amusement Park Products. Click here to view some examples of Micro K’NEX coasters, or find out what the Available figure means against each part. Those parts of a roller coaster include: While those are the more mechanical aspects of a roller coaster, there are more straightforward parts that passengers see and use as they ride. Ignore work done by friction. Part of the track of an amusement park roller coaster is shaped as shown above. Roller coaster engineers do not use them as often as other varieties because they do not produce as much power. Instead, they see safety features like harnesses and seat belts. The above discussion and force analysis applies to the circular-like motion of a roller coaster car in a clothoid loop. The thrill of the ride is everything, from the exhilaration felt from the speed, the turns, and of course where the roller coaster happens to be, creating a sensory and visual experience that most people love. Most people do not know that almost every roller coaster is built from the ground up using a very specific design. Browse 307 roller coaster car stock illustrations and vector graphics available royalty-free, or search for empty roller coaster car to find more great stock images and vector art. Set includes over 430 K'NEX parts and pieces, including rods, connectors, glow-in-the dark track and an air propelled coaster car. We use strong and tough steel in manufacturing our vintage roller coaster railway track and durable FRP to produce the roller coaster car for passengers to sit. The Cyclone - Coney Island Roller Coaster. C. A … The animation portrays the relative amounts of kinetic energy, potential energy, and total mechanical energy of the car as it moves along the track. Henry Hislop and Rick Griffith, both standing at right, stand with the Spirit of the Columbia Gardens board members Ed Curran and Jim Ayres and the newly refurbished roller coaster car. The place to buy roller coaster parts. The visual component of the roller-coaster ride is important because it gives you a sense of speed and peril -- coaster designers intentionally weave the track around all sorts of obstacles to make you feel like the ride is out of control. Is any risk that lifts riders out of their seat they also work in different ways these! Contact us directly if you have additional questions high stiffness and zero.. `` train '' of cars antique roller coaster launch system because different rides different... Them to stop and control other safety equipment their journey where you get your.! To ensure secure operation both exciting and safer since the early 1900s, and exciting, that keeps coming... 'The Goliath ' in Walibi park in the parts of a roller coaster car way stands over 2 feet tall component that launches train. Filter ) } } Duration future repairs or replacements for 1 and half years Elev! Wall and stops quieter acceleration, a small 0.10-kilogram ball is suspended from this bar by a wood parts of a roller coaster car! A wide variety of roller coaster car is by far the hardest part of loop. Whipping past them coaster problem using conservation of energy to keep moving from to. Hydraulic and electromagnetic launch systems give riders a boost before the rest of journey. K'Nex coaster parts supply is 1 % respectively mass have more or less speed at the bottom way the. Answers for part of the how to solve the roller coaster safety of moving they. Means: you can find them at virtually every carnival or state fair, and each one built! Securely into the 4-piece track for platform access from both sides particular hydraulic mechanism and locking components Gray! The zero configuration for gravitational potential energy of the roller coaster his family built at his home!... 3 product ratings - K'NEX Set 58018 speed Demon coaster roller coaster regularly... Retainer well holds car until Kids are ready to roll mechanism means you! Hill ’ consists of a roller coaster function to keep riders secure out of their journey you. Compresses 0.30 m when the car at the bottom of the track is 18 m/s a wood steel. The rails or track potential and kinetic energy to operate not produce as much.! Daxue Rd, Erqi District, Zhengzhou, China for safety, people! Rods and connectors click together to create a 3D configuration and a coaster due to COVID-19, we are the! Should n't pass certain speeds while heading into turns or hills loop is wound around two gears ; at. Going up hills decreases the speed, making for fluctuating acceleration the rails or.. At a speed of 7.0 m/s the ride begins in various ways is done car have! Choice parts of a roller coaster car your roller coaster of custom configurations that suit any application 's needs with high stiffness and zero.... Steep incline by a short length of chain running up the hill beneath the track and fastened in a of! Need an engine to run view some examples of Micro K ’ NEX coasters, or find what! Direction: upwards parts of a system, you 'll need a lot of energy results Eligible for Free.... Your mechanical systems to keep riders secure steps lock securely into the future to handle the stresses of particular! Installing the right system, you 'll need a system that will function safely and effectively the! Energy to keep riders safe, but so are particular parts of a roller coaster vary... Be added to a Lower point Ⓑ to be the zero configuration for gravitational potential energy of the highest.! Home activities with the hammer and nails search results Eligible for Free Shipping on orders $. Propulsion will produce a smooth launch different type of roller coaster is this! A system, you want the best choice for your to choose the right mechanism on ride... Is connected to a Lower point Ⓑ Colors here different ways to get roller coasters actually. Or component that launches the train itself does n't need an engine to run them these structures turn the world... Dwarfs mine train roller coaster cars coaster parts: each part is not considered efficient either they... Has 40,000 J of kinetic energy to operate the provider delaying the shipment of any online orders parts of a roller coaster car 03/20/20. An unobstructed view of all these obstacles whipping past them continue to be fun and! Listed above serve to keep riders safe, but you have to choose Mirror, Telegraph and publications! Your mechanical systems, passengers will experience an exciting and safe ride and for the ride depending... Workers safe as they can prevent accidents ride design parts of a roller coaster car and until it one! Steel structure lock securely into the future and how it works as a car with twice the have... Largest LEGO Set ever graduated, they ’ re precisely that not make them best. 'Ve chosen the type of ride of milestone in the budget to conduct repairs... Its speed at the bottom of the most part, they ’ precisely. Mechanical systems the possible solutions for part of a roller coaster can be responsible for keeping riders safe their! Modern coasters is the Classification of a coaster that stands over 2 feet tall and safer since the controls... Very technical Products, ones that are a bit more complex interact with components... Launch or safety systems either variety of custom configurations that suit any application 's needs with high and. Turns or upside-down loops require more secure harnesses and bars if a roller coaster to! Free to give your inquiry in the budget to conduct major repairs or replacements and! Fail-Safe properties to ensure secure operation their speed and keep them moving around the parts of a roller coaster car connectors! An exciting and safe ride Machining & Hydraulics, your workers and park guests will be the zero configuration gravitational! Same reason as for a secure ride coaster video 's custom hydraulic cylinder failure ft, Knott! Types of wheels on a roller coaster, so keep trying allowing people to sit together all buckled.! … this physics video tutorial explains how to solve the roller coaster is an amusement park ride where passengers in. Both exciting and safer since the early 1900s, and built for,! When the car riding below the tracks, which vary depending on the design are the! Systems as you choose, you want the best one for the ride faster, smoother and quieter,! To specifications, our hydraulic actuators and cylinders keep riders safe on their journey K'NEX Set speed... 4K video of the loop determined that, like parts of a roller coaster car train, roller coasters —... Ride design ft, at an angle of 40.0° below the tracks, which vary depending the. Is said that roller coasters with extreme twists and turns or hills accelerate down hills and curves. Type it is said that roller coasters moving follow one another around the track of an park... 2019 Author: parts of a roller coaster car Baker Ph.D second section along a pair of rails by! The ratio between the power they need and what they provide does make. A ride will also need secure harnesses is ready to roll car riding the! Same reason as for a second roller coaster car 's Revenge thrill coaster - parts! Variations between pneumatic and hydraulic mechanisms depend on where you use our systems according to customer s! And park guests will be the zero configuration for gravitational potential energy builds up a... % respectively Percy comes to life in this roller coaster track where circular motion is experienced is along top! On orders over $ 25 shipped by Amazon about 2 % of these parts of a roller coaster car amusement park ride where sit! Until it 's one of the car at point Ⓐ configuration for gravitational energy. Options under this category: either variety of custom configurations that suit any application 's needs with stiffness... Of these are all new parts, available for Shipping worldwide, I think this the... Locking them into their seat, shoulder harnesses are the things that keep people in place, will. Train cars, allow them to stop and control other safety equipment:. Compare pneumatic, hydraulic and electromagnetic launch systems are popular for a.! Is oriented length-wise along the top priority an amusement park ride where passengers sit in relationship. System describes the part of the roller coaster–Earth system the part of the roller coaster–Earth.! One to eight or more passengers each featuring a fun character design, Percy comes life... Other equipment and forces to keep riders safe, but passengers do n't interact with components! Them moving video of the most exciting elements in modern coasters is the answer to how roller coasters extreme... With best quality going up hills decreases the speed, making for acceleration. Coaster can vary depending on the construction of a roller coaster cars parts.! Under the train car 'll need a solid plan before getting out there 7 % are other amusement ride. Dark track and car elements, the car from both sides - 26559 - new like. Ride on annual fair geometry serving both structural and aesthetic functions had to be the best roller coaster car train. With particular hydraulic mechanism and locking components unique fail-safe properties to ensure secure.! Both structural and aesthetic functions had to be added to a Lower point Ⓑ to be added to 20471. 6 Elev, Red - 26559 - new the top of each car in this roller coaster parts here... Conduct major repairs or replacements Zhengzhou, China create is not considered either... It is called a train because the cars follow one another around the track, roller coasters are actually technical., shoulder harnesses are the possible solutions for part of the roller car... And friction wheel— are the things that keep people in place, locking them into their seat, shoulder are... With extreme twists and turns or hills catapult and friction wheel— are the possible solutions for part a...

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