...Tutorial 3: Projectile motion and Laws of motion. 1. Two crickets, Chirpy and Milada, jump from the top of a vertical cliff. Chirpy just drops from a vertical cliff with a height of 350 m, while Milada jumps horizontally with an initial speed of 8.0 m/s . How far from the base of the cliff will Milada hit the ground? [67.6 m] 2. A ball is given an initial velocity of 30.0 m/s at an angle of 60.0o with respect to the horizontal. What are the horizontal and vertical displacements after 5.00 s? [75.0 m, 7.40 m] 3. A soccer player kicks the ball toward a goal that is 16.8 m in front of him. The ball leaves his foot at a speed of 16.0 m/s and an angle of 28.0° above the ground. Find the speed of the ball when the goalie catches it in front of the net. [14.7 m/s] 4. The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of 45°. With what speed must the animal leave the ground to reach that height? [12 m/s] 5. A fireman d = 50.0 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of i = 30.0° above the horizontal as shown in figure. If the speed of the stream as it leaves the hose is vi = 40.0 m/s, at what height will the stream of water strike the building? [18.6 m] 6. A projectile is launched from ground level at an angle of 15.0° above the horizontal. It returns to ground level. To what value should the launch angle be adjusted...
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...Title: Investigate of the Enzymatic Effects of Materials on Hydrogen Peroxide Solution Objective: Apparatus: Beaker, Boiling tubes, Water bath (95˚C), wooden splinters, glass rod. Material: fresh liver, manganese dioxide, potato cubes, Hydrogen peroxide. Procedures: 1. six fresh empty boiling tube 1, 2, 3, 4, 5, 6 are labelled. 2. Cut the liver is provided into 3 pieces of roughly 0.8cm x 0.8cm X 0.5cm by using a blade. 3. One piece of the liver into tube 1 is placed. 4. The second piece of liver is placed into the bottom of tube 2. Tube 2 is placed in the boiling or water bath (95˚C) until the liver is cooked. 5. Now put the third piece of liver into tube 3. It is gently mashed up onto a pulp using a glass rod. 6. Two 0.5g portions of Manganese dioxide powder are measured out by using the weighing boat each onto a weighing boat. Each portion is poured into tube 5 and tube 6. 7. Put tube 6 in the water bath (95˚C) for five minutes. 8. Tube 2 and tube 3 are cooled after 5 minutes. 9. Cut potato cubes of roughly 0.8cm x 0.8cm x 0.5cm. One cube into tube 4 is placed. 10. Another six fresh empty test tubes. Put 5cm3 of hydrogen peroxide into each of them. 11. Next, hydrogen peroxide is quickly added into the test tubes 1, 2, 3, 4, 5, and 6. 12. The parafilm provided is stretched quickly seal the mouth of the test tubes by stretching the film over it and leave for 20 minutes. 13. Insert a glowing splint into each tube by just penetrating the parafilm with it. 14. The observations...
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...Title: To investigate the trajectory of a small ball as it rolls off a surface which is inclined to the horizontal. Objectives: To investigate the trajectory of a two dimensional motion. Apparatus and materials: Ramp, wooden block, pendulum bob, plumb line, steel ball, wooden board, carbon paper, meter ruler, plasticine. Setup: 1. A ramp was set up at the edge of a bench. 2. A plum-line is suspended from the edge of the bench. 3. A wooden board is mounted horizontally using two clamps so that the board is situated about the bottom of the ramp. 4. A sheet of blank paper is placed on top of the board. 5. A piece of carbon paper is placed on the top of the blank paper. The ink-side of the carbon paper is facing down. 6. When a ball was released from the top of the ramp, the ball travelled through a trajectory. Theory: Let: g= 9.80ms-2 u= speed of the ball as it leaves the ramp k= constant y= vertical distance (between the bottom of the ramp and the top of the board) x= horizontal distance (between the plum-line and mark on the paper) The equation which relates x and y is yx=g1+k2x2u2+k Procedure : 1. The ball was positioned at the top of the ramp. The ball was released so that it rolls down the...
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...acceleration downward. # # # To measure this acceleration, we need to slow down the action. Galileo was the first to accurately measure this acceleration due to gravity. By rolling objects down an inclined plane, he slowed the motion enough to establish that the gravitational acceleration is uniform, or constant with time. Inclined Plane Experiment !Does the marble pick up speed as it rolls? !Is it moving faster at the bottom of the incline than it was halfway down? " Flashes of a stroboscope illuminate a falling ball at equal time intervals. " Distance covered in successive time intervals increases regularly. " Since distance covered in equal time intervals is increasing, the velocity must be increasing. " Average velocity for a time interval is given by dividing the distance traveled in that time interval by the time of the interval. " For example, between the 2nd and 3rd flashes, the ball travels a distance of 4.8 cm - 1.2 cm = 3.6 cm in a time of 0.05 s: 3.6 cm v= = 72 cm/s 0.05 s ! " The velocity values steadily increase. Time 0s 0.05 s 0.10 s 0.15 s 0.20 s 0.25 s 0.30 s 0.35 s Position 0 cm 1.2 cm 4.8 cm 11.0 cm 19.7 cm 30.6 cm 44.0 cm 60.0 cm Average velocity 24 cm/s 72 cm/s 124 cm/s 174 cm/s 218 cm/s 268 cm/s 320 cm/s " The velocity values steadily increase. # Each point is plotted...
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...Practical 4 _______________________________________________________________________ To investigate the trajectory of a small ball as it rolls off a surface which is inclined to the horizontal Objective: * To investigate the trajectory of a motion in two dimensions. Apparatus and Materials: 1. Ramp 2. Wooden block 3. Pendulum bob 4. Plumb line 5. Steel ball 6. Wooden board 7. Carbon paper 8. Meter rule 9. Figure 4-1 Plasticine Setup: 1. Set up a ramp at the edge of a bench as shown in Figure 4-1. 2. Suspend a plumb-line from the edge of the bench as shown in Figure 4-2. 3. Mount a wooden board horizontally using two clamps so that the board is situated somewhere below the base of the ramp. 4. Place a sheet of blank paper on top of the board. 5. Place a piece of carbon paper on top of the blank paper. The ink-side of the carbon paper should be facing down. 6. When a ball is released at the top of the ramp, the ball will travel through a trajectory as shown in Figure 4-2. Figure 4-2 Theory: Let: g = 9.8 ms-2 u = speed of the ball as it leaves the ramp k = constant y = vertical distance (between the bottom of the ramp and the top of the board) x = horizontal distance (between the plumb-line and the mark on the paper) h = height of release of ball from the height of the bottom of the ramp. θ = angle the ramp makes with the horizontal (table surface) ...
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...Assignment Week 2 Due: 11:59pm on Sunday, January 18, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy A message from your instructor... The next seven problems are for practice. Item 1 Learning Goal: To understand that adding vectors by using geometry and by using components gives the same result, and that manipulating vectors with components is much easier. Vectors may be manipulated either geometrically or using components. In this problem we consider the addition of two vectors using both of these two methods. The vectors and have lengths and , respectively, and makes an angle from the direction of . ⃗ ⃗ ⃗ ⃗ Vector addition using geometry Vector addition using geometry is accomplished by putting the tail of one vector (in this case ) on the tip of the other ( ) and using the laws of plane geometry to find ⃗ ⃗ ⃗ ⃗ : , √ 1. ⃗ the length , and angle , of the resultant (or sum) vector, 2. Vector addition using components Vector addition using components requires the choice of a coordinate system. In this problem, the x axis is chosen along the direction of . Then the x and y ⃗ components of are and respectively. This means that the x and y components of are given by ⃗ 3. 4. , . Part A Which of the following sets of conditions, if true, would show that the expressions 1 and 2 above define the same vector as expressions 3 and 4...
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... A football that is thrown into the air has inertia. This is the tendency of an object in motion to remain in motion. But because of gravity the ball is pulled down and resistance that slows the ball down. A quarterback through the motions of his and body, must balance the forward momentum that he gives the ball, fighting gravity and air resistance that pulls and slows it down. Aerodynamics is involved during passing because of the spin that is applied. The better the spin the straighter and further the ball will travel. This is accomplished by the quarterback throwing the football over handed or a sidearm motion to giving it the spin required. The spin causes the ball’s angular momentum points in the direction of its long axis. At same time due to air drag, torque is pointing perpendicular to the angular momentum. The ball travels on a semi-parabolic curve and wind torque produces a small change in the ball’s angular momentum. This allows the ball to continue to turn around its trajectory. Therefore spinning stabilizes the football through angular momentum and torque. Throwing in this manner orientates the ball giving it the smallest possible cross sectional area against the oncoming air; this causes the least amount of aerodynamic drag. This is important for quarterbacks as while as managers to know, because if the ball does not spin properly, the wind will cause if tumble and lose its forward momentum (duck). Managers (coaches) want to make sure that there quarterback...
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...1. A ball is thrown horizontally from the top of a cliff. Air resistance is negligible. Which of the following diagrams best represents the subsequent path of the ball? (1) 2. An archer shoots an arrow at an angle to the horizontal. Air resistance is negligible. Which of the following graphs best represents the variation with time of the horizontal component of the arrow’s velocity from the time it is launched to the time just before it hits the ground? (1) 3. The diagram below shows the path of a projectile in the absence of air resistance. Which one of the following diagrams best represents the path of the projectile under the same initial conditions when the air resistance is taken into account? (The path in absence of air resistance is shown for comparison as a dotted line.) (1) 4. This question is about the trajectory of a golf ball. A golfer hits a golf ball at point A on a golf course. The ball lands at point D as shown on the diagram. Points A and D are on the same horizontal level. The initial horizontal component of the velocity of the ball is 20 m s–1 and the initial vertical component is 30 m s–1. The time of flight of the golf ball between point A and point D is 6.0 s. Air resistance is negligible and the acceleration of free fall g = 10 m s–2. Calculate (a) the maximum height reached by the golf ball. ........................................................................................................................
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...resistance, then the motion of the object is projectile motion. Trajectory: This refers to the path the projectile follows when fired from a gun, or a bat, or someone throwing the object, or whatever its source of motion is. In our demonstrations, projectiles will follow curved paths that will be interesting to observe. Projectile: Any object which is given some velocity and then left to fly through the gravitational field with only the gravitational force acting on it. An example is a baseball hit by a bat, a basketball shot toward a basket, a bullet fired from a gun, etc. Range: The horizontal distance a projectile is fired. How far it moves away from whatever gave it its horizontal motion. We will be firing a projectile at an angle with the horizontal; it will arc upward and outward. How far outward it goes is the range of the projectile. Any projectile thrown, such as a ball, can be considered to have a vertical and horizontal velocity component. Throughout the path of the projectile, change occurs only in the vertical direction due to the influence of gravity, while the horizontal component of the velocity will not change. (This is not quite true; there will be a very small slowdown in the horizontal direction due to air resistance). Using the laws of physics, it’s possible to make a jumpshot in basketball every time. That’s right, if you stand at some point on the court, and throw the ball up at just the right angle and just the right speed, you...
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...off-course market share is attributed to the availability of a greater variety of less expensive golf balls in off-course channels. After the 2008 recession, nearly 23% of women and 36% of children had quit playing golf. This resulted in a significant drop in the number of golf players. As such golfers have cut spending on golf equipment, which badly affected the golf industry. Furthermore, investment in golf course and real estate development fell over 40% after the 2008 recession. This resulted in nearly 25% drop in the number of stores immediately after the recession. Thus, equipment manufacturers are experiencing greater pricing pressure as unit volumes are falling and buying power is consolidated among a small group of powerful retail buyers. Compounding the problem, 70% of Altius Golf sales are derived from Altius’ flagship product, Victor TX, one of the most expensive golf balls on the market. Since 2008, golf players are less willing to spend more on their equipment, and more willing to explore less expensive alternatives. Furthermore, competitors have responded to this shift, negatively impacting Altius’ market share. Two major rivals introduced product innovations, marketing campaigns and more competitive pricing that chipped away at Altius’s market share. Primiera introduced ball-fitting technology with a launch monitor that allowed golfers to compare their speed and trajectory...
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...Baseball has and always will be a part of my life. I have grown up playing the sport since I was a small child. As of late i have had the opportunity to discuss physics and get a better understanding of the forces involved in everyday life. Each and every day physics of all types are continuously happening around us all. We may not notice it, but that's because its all just normal for us now. From driving a car down Pacific Coastal Highway to looking West as we watch giant waves crash in to the coast. I'm taking this opportunity to show my understanding of physical science by explaining how and which forces are present in the sport of baseball. From throwing a ball, the build up of a swing all the way through the contact of the ball and the path of which the ball takes will be examined and explained throughout the course of this paper. One of the first quotes I came across after I decided to choose this topic was “ The physics of baseball is not rocket science. Its much harder” (Adair, R. (n.d.). Physics of baseball) One thing people want to know is how does a ball react to the impact of a baseball bat. To touch base on this subject I want to go through what type of energy is used. A ball is thrown and takes on a role of kinetic energy. Kinetic energy is anything with matter moving or in motion. As the ball speeds through the air and the bat and ball make contact there is a split second where that kinetic energy turns into potential energy. Potential energy is the stored energy...
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...A Case Study in Approximate Linearization: The Acrobot Example Richard M. Murray Electronics Research Laboratory University of California Berkeley, CA 94720 John Hauser Department of EE-Systems University of Southern California Los Angeles, CA 90089–0781 Memorandum No. UCB/ERL M91/46 29 April 1991 Electronics Research Laboratory College of Engineering University of California, Berkeley 94720 A Case Study in Approximate Linearization: The Acrobot Example Richard M. Murray∗ Electronics Research Laboratory University of California Berkeley, CA 94720 murray@united.berkeley.edu John Hauser† Department of EE-Systems University of Southern California Los Angeles, CA 90089–0781 hauser@nyquist.usc.edu 29 April 1991 Abstract The acrobot is a simple mechanical system patterned after a gymnast performing on a single parallel bar. By swinging her legs, a gymnast is able to bring herself into an inverted position with her center of mass above the part and is able to perform manuevers about this configuration. This report studies the use of nonlinear control techniques for designing a controller to operate in a neighborhood of the manifold of inverted equilibrium points. The techniques described here are of particular interest because the dynamic model of the acrobot violates many of the necessary conditions required to apply current methods in linear and nonlinear control theory. The approach used in this report is to approximate the system in such a way that the behavior...
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...conversion of food to energy is also a part of physics. My body digests the food and in the process pulls the energy from it either to keep me warm or fuel my body to do work. It probably sounds more chemical physical, but gravity pulls the food down which contains potential chemical energy, and in the end that energy allows me to do work or just store it. Also with eating I could mention the act of chewing it. Another activity that I take part in is driving a car. The lists of things that take place that involve physics while driving a car are countless. The car itself was built on numerous physics concepts. Driving a car around a curve obviously has centripetal force and is a concept we just covered. However, I choose to focus on a rather small part of a car, but no less important. The brakes on my car are what keep form running red lights and running into other vehicles as I drive to and from my many destinations. The breaks...
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...Neurobehavioral Observation When I walked into the classroom at the Velma Thomas early childhood center, there was certainly a lot to look at. My eye was drawn to the colorful kid-made art on the wall, to the thriving indoor garden on the windowsill, and to the frazzled teacher attempting to explain the concept of sharing. The first child I noticed, however, was Laurence. Laurence is a small, lively young boy with brown skin and curly hair. He has recently turned five, making him one of the two five-year-olds in a class of 3- and 4-yr-olds. And at the moment I began my observation, he was rolling on the carpet. A classmate, Elena, took Laurence’s hand and started to pull him up off the floor. Laurence sat up, and then stood, without letting go of Elena’s hand. Elena pulled Laurence across the room towards a display of pictures of hands on the wall. Laurence pulled his hand out of Elena’s, and used it to reach out and touch the wall. He stomped his foot, and ran back to his square of carpet. Upon returning to the carpet, Laurence saw a book on the floor, a large blue textbook with a cover that proudly proclaimed, “SCIENCE.” He took hold of the book with both hands, opened it to a page near the middle, and placed the book on his head. The aforementioned frazzled teacher, Miss Rachel, said to him, “Laurence, I noticed what you’ve been doing with books today, and I wondered if you remembered what we do with books.” Laurence’s smile widened as he looked at Miss Rachel and giggled...
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...Situational Analysis: Arena Park Golf The following information I have composed from the city of Cape Girardeau, specifically on economic climate, demographics, demand trends, technological trends, competitor analysis, regarding Arena Park Golf. This is for a class project that involves a situational analysis of Arena Park Golf and the surrounding area along with some history of golf. Opened in 1998, Arena Park Golf is a golf store located in Cape Girardeau, Missouri with approx. 3,000 square feet of retail space dedicated to golf clubs, golf clothing or other golf equipment essential for the avid Missouri golfer. There are also a public and private golf courses in Cape Girardeau, which shows a market for golf not only in the city but the surrounding area. The history of golf’s built environment in the U.S. has reflected the changing face of the game in terms of the number and type of golf courses built, as well as the demographic profile of those playing the game. Since 2000, the golf industry has experienced significant declines in the key barometers of its economic wellbeing as defined by: the decline in the number of golfers and rounds played and the decrease in the number of golf courses. During the 20th century, there were three “boom” periods of accelerated golf course development that peaked in 1930, 1970 and 2000. The first boom in the 1920s built private golf courses for the upper class. The second boom in the 1960s built public golf courses for the burgeoning...
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