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Download Day 1 Notes: Dealing with projectiles in two dimensions. There are
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Day 1 Notes: Dealing with projectiles in two dimensions. There are no forces acting on horizontal projectile. No acceleration. Ertical: negative 9.8 Projectile: an object that is acted upon only by gravity. It must be moving in two dimensions. LAB: Ball and ramp lab Hypothesis: The horizontal distance of a projectile can be calculated by the x and y chart and kinematics even when the vertical initial velocity is not provided. Data table: Calculations: Analysis: We set the vertical initial velocity to zero and we were able to calculate the horizontal distance by using the x and y chart and kinematic formula. However, there was 10% error from the photogate timer measurement. The result from the photogate timer was more accurate than the calculations. I think that there is a possibility of the vertical initial velocity not being zero. HOMEWORK: 1. What did you that you already understood from our class discussions? - I already understood the concept of projectile. A projectile is an object that continues in motion when it is projected. Gravity is the only force acting downward. Without the gravity, because gravity only influences vertically, a projectile will undergo a non stop horizontal motion. - I also understood that the projectile is in both vertical and horizontal ways and they are independent of each other. Horizontal movement is motion without acceleration. However, vertical motion is constantly acted upon by the force of gravity pulling the object down. Thus, increasing the speed of the projected object. - Horizontal displacement of a projected object can be found by the formula: x=V initial * T. I understand the calculations and the math of this lesson. 2. What did you read that was little confusing? - No concept was specifically confusing. However, I did not understand the fact that a projectile could continue moving without the force of gravity working downwards at first. I totally understand the fact now. Also, I had some trouble with finding hang time and range using the x and y chart. However, with the instructor’s(teacher’s) help, I do not have any problem with the math now. 3. What did you read that you still do not understand? - I basically understand every concept now. 4. What did you read that was not gone over during class today? - Day 2: We went over everything in the class. Frankly, I do not remember; there might be something that we did not go over but I think those things are too basic or trifling to go over during the class time. LAB: Objective: what is the relationship between the angle of incline nad the acceleration. Hypothesis: the greater the angle of incline, the faster the speed of an object. Data table: H Angle T1 T2 T3 Average Time Distance Acceleration Track 0.043 2.02 2.15 2.25 2.18 2.19 1.03 0.428 1.22 0.081 3.81 1.53 1.63 1.56 1.57 1.03 0.832 1.22 0.069 3.24 1.75 1.88 1.88 1.83 1.03 0.611 1.22 0.196 9.24 0.9 1.03 0.97 0.967 1.03 2.205 1.22 0.282 13.36 0.75 0.75 0.72 0.74 1.03 3.762 1.22 Graph: Analysis: The relationship between the angle of incline and the acceleration is proportional. The greater the angle of the incline, the faster the cart went dwon the track. The smallest angle was 2.03 degrees and the acceleration was 0.428 m/s/s. The biggest angle was 13.36 degrees and the acceleration for that angle was 3.76 m/s/s. In theory, the formula for the slope was g=sin theta, making the slope 9.8. However, the experimental result comes out to be 16.91. The percent error was 75.2%. This error comes from the reaction time between the student who let the cart go and the student who pressed the stop watch. This error could be minimized by using a photogate timer. Also, the error would be minimized if the same person did both works. Notes: Newton’s gravity law, Law of universal gravitation. Gravitation of force is directly proportional to the product of the mass of the two objects. Newton deduced that it is inversely proportional to the square of the distance. Distance is always measured center to center. G is universal gravitation constant. G=6.67 % 10 to the negative 11t hCappler’s planet laws planetsmove in elliptical orbits around sun with sun at one focus. Any given amount of time the planet will carve out equal areas in its orbit around the sun: law of equal areas The closer to the sun the faster you are moving. Period square divided by the distance by the sun cubed is constant for every planet in our orbit. HOMEWORK: A. Force board and head to tail method can be used to add ectors in 2-D problems. B. Forces that are not on either x or y axis can be broken in to two forces(one on x axis and another on y axis). If the force value and the angle is given, resolution of forces can occur using the trig soh cah toa. C. Equal liberium is reached when two forces exerted on an object balance out. There is no movement when reached the equal liberium. D. Diagonal forces can be split into x axis and y axis. Then, using trig functions, a student simply can plug the net force value in to Newton’s second law formula. E. When a student is encountered with an off centered plane questions, simply make diagonal lines x and y axis. Then, the original horizontal and vertical line will become diagonal line. From then, everything is the same as the mothod introduced in D. F. Two system problem solving is harder than a single system because they move or accelerate at the same rate but different direction. When encountered with these type of questions, split the two system and work each one out individually. A. Gravity is a force that pulls objects onto the Earth’s surface. 9.8 m/s/s is the acceleration dueto gravity. B. Every object has its own gravitational pull. This is the reason planets orbit the sun. The law of ilypsis explains that the orbit of planets around the sun, being the one focus, is ilyptical. The law of equal area says that the distance between the center of the sun and the center of each planet will carve out the same amount in the same amount of time. The law of harmony= period^2/average distance from the sun^3. C. The distance is measured from the center of one to the center of another. As two objects get farther apart, the gravitational attraction will lessen as well. D. G is constant for the gravitational attraction(G= 6.67^10^-11). Little g is the acceleration due to gravity(g=9.8m/s/s). E. Day 3: Changing velocity – changing speed- changing direction Uniform circular motion- constant speed but changing direction. EF=ma What’s different is how we find acceleration. We cannot use kinematics. A c= V2/R Centripetal acceleration- center seeking Tention is much bigger in the bottom. LAB 1: Part A: Find max tension of string at static equilibrium Part B: Find min v at top of loop Part C: Find Max v at bottom of loop Data table: Mass (Kg) Radius(m) Revolutions Distance (m) Max Load(kg) Time of period (s) Minimum Velocity (m/s) Average Velocity 0.02 0.37 10 2.325 0.950 6.34 3.667 0.02 0.37 10 2.325 0.950 6.41 3.627 0.02 0.37 10 2.325 0.950 6.5 3.577 0.02 0.37 10 2.325 0.950 6.38 3.644 0.02 0.37 10 2.325 0.950 6.5 3.577 0.02 0.37 10 2.325 0.950 6.54 3.555 3.608 Mass (kg) Radius(m) Revolutions Distance (m) Max Load (kg) Time of preiod (s) Max Velocity (m/s) Average Velocity 0.02 0.37 10 2.325 0.950 3.77 6.167 6.237 0.02 0.37 10 2.325 0.950 3.72 6.249 0.02 0.37 10 2.325 0.950 3.64 6.387 0.02 0.37 10 2.325 0.950 3.81 6.102 0.02 0.37 10 2.325 0.950 3.7 6.283 0.02 0.37 10 2.325 0.950 3.73 6.233 0.02 0.37 10 2.325 0.950 3.73 6.233 Calculation: Analysis: The theoratic and experimental results were too different from each other. The percent error was approximately 75 pecent. This difference in results came from errors resulting from human’s reaction time when we pressed the stop watch and also the inability to spin the mass and the string in constant rate. Data table and calculation are helped by group members. Graphic is from Lawrence because he had all the calculations. LAB2: Conical pendulum Objective: what happens to the period as you change the radius. Hypothesis: The radius and the period is inversely proportional to each other. 10 cm radius 4 20 cm radius 1 40 cm radius 2 60 cm radius 3 100 cmradius 5 3.315 s 3.277 s 3.297 s 3.16 s 3.291 s 3.259 2% Cos =r/l Cos= 0.10/2.64 Theta= cos-1(0.10/2.64) Theta= 87.8 V= 2 pie r/period Solve for period= 2 pie r/v EFy=may Ty-w=0 T sin theta= mg T=mg/ sin theta 0.60% 3.24 3.218 3.142 0.90% 2% 0.50% g/tan theta=v squared/r Rg/tan theta=v (0.10)(9.8)/tan87.8= v squared 0.194 m/s=v = 2 pie (0.10)/0.194 = 3.238 seconds 0.388 = velocity Analysis: This experiment proves that the period and the speed of the ball is inversely proportional to each other. This lab was done as a clas and the percent error was less than 2 percent. This slight error results from human’s slow reaction time to press the stop watch. Also the angle at which the students view the pendulum might have altered the time and thus resulted the wrong data. HOMEWORK: Q: What is uniform circular motion? A: When a circle is a perfect circle with the same radius and when the speed of an object going around it is constant. Q: What is the formula for the average speed? A: The equation is 2pi r/T Q: What is the relationship between the magnitude of the velocity and the direction of velocity? A: While magnitude stays the same, the direction might change every second. The best word describing the direction change of velocity is tangential. Q: What is the forbidden f word? A: the forbidden f word is “centrifugl circular motion. This concept is impossible because the object in circular motion tends to move inward than outward. Q: What is centripetal circular motion? A: It is an opposite concept of centrifugal. When an object spins aound, the object has an intuition to move inward than out ward. Day 4 Notes: Work- Three components, work is caused by force acting in the direction of motion of an object and this object should move. On the axis of direction of motion. The force and the direction of motion cannot be perpendicular. Symbol: W Kinetic energy: Energy due to an object moving. Any object that is moving has kinetic energy. Symbol: Ke Gravitational potential energy: energy possessed by an object because it is above or below zero level. So it can fall. The zero is relative. Symbol: Gpe Elastic potential energy: Energy possessed by an object due to a compressed spring or stretched spring. Symbol: Epe Units for all of theses is Jouls. J is short hand. Equations: Work=force * distance* cos phi. Phi is the angle between force and direction of motion. Ke= 1/2mv squared GPE= m*g*h EPE= ½ little k X squared. K stand for springy your spring is spring force constant. X is the distance it was compressed or stretched. Cue for work: tention normal and friction but not weight Kinetic: if object is moving Gpe: above or below zero position. Law of conservation of energy: you have constant amount of energy the types of energy can change but the total amount must remain constant. The enrgy can be increased by doing work. Work out is mostly due to friction.