Honors Physics Study Guide PDF

Physics Study Guide Made By Samay Parekh Equations 1. 𝑠 = 𝑑 2. 𝑣 = ∆𝑥...

Physics Study Guide Made By Samay Parekh Equations 1. 𝑠 = 𝑑 2. 𝑣 = ∆𝑥 3. 𝑎 = ∆𝑣 4. vf = vi + a∆t 5. vf2 = vi2 + 2a∆x ∆𝑡 ∆𝑡 ∆𝑡 You are solving for final You are solving for final velocity You are solving for speed with You are solving for You are solving for acceleration velocity with this formula. with this formula. this formula. velocity with this with this formula. 𝑣𝑓 = final velocity 𝑣𝑓 = final velocity d = distance formula. ∆𝑣 = final velocity minus initial 𝑣𝑖 = initial velocity 𝑣𝑖 = initial velocity ∆𝑡 = final time minus initial ∆𝑥 = final position minus velocity 𝑎 = acceleration 𝑎 = acceleration time. initial position ∆𝑡 = final time minus initial time. ∆𝑡 = final time minus initial ∆𝑥 = final position minus initial ∆𝑡 = final time minus time position. initial time. Unit 3 : This formula has both y and x axis (This formula is different from Unit 3 : This formula has both y versions and to solve for one axis, you Unit 3 : This formula has both y and x formula 4 because it helps you would need most of the variables in that axis versions and to solve for one axis, and x axis versions and to solve for solve for the same variable one axis, you would need most of axis you would need most of the variables in that axis without time). the variables in that axis Unit 3 : This formula has both y and x axis versions and to solve for one axis, you would need most of the variables in that axis 6. ∆x = vi∆t + ½ a∆t2 7. Fg = mg 8. Fnet = Fa -Ff 9. Fnet = ma 10. Ff = µFn You are solving for distance You are solving for The You are solving for Net Force You are solving for Net Force with this formula. Force of Gravity with this with this formula. with this formula. You are solving for the coefficient ∆𝑥 = final position minus initial formula. Fa = Push, pull, applied force m = Mass of Friction with this Formula position. m = Mass Ff = Force friction, resistance, 𝑎 = acceleration 𝑣𝑖 = initial velocity g = gravity - g ~ 10 N/kg drag Some other ways of writing Ff = Force of Friction ∆𝑡 = final time minus initial this formula are : time. 𝐹𝑛𝑒𝑡 A= 𝑚 or m = 𝑎 𝐹𝑛𝑒𝑡 Fn = Normal Force 𝑎 = acceleration µ = coefficient of friction Unit 3 : This formula has both y and x axis versions and to solve for one axis, you would need most of the variables in that axis 12. ∆PEg = mg∆h 13. ∆PEs = 1/2k∆x^2 14. KE = 1/2 mv^2 15. ME = PEg+PEs+KE 11. You are solving for You are solving for elastic You are solving for Kinetic You are solving for Mechanical gravitational potential Energy with this formula. Energy with this formula. You are solving for potential energy with this energy with this formula. KE is the Kinetic Energy KE is Kinetic energy Gravitational Force with this formula. m is the mass in m is the mass in kilograms PEg is gravitational potential formula ∆PEs is the elastic potential kilograms v is the speed of the object energy F is the gravitational force energy g is the acceleration due (Velocity). PEs is elastic potential energy. m1 and m2 = the mass of the k is the spring constant. The to gravity. On Earth this is two objects spring constant is the stiffness 10 m/s2 d = the separation between the of a spring and is measured in ∆h is the height above a objects N/m reference point G = The universal gravitation x is how much the elastic is constant which is 6.7 x 10^-11 compressed or stretched in Nm2/kg2 meters. 16. W =∆E= F d 17. 𝑃 = 𝑊 You are solving for Work with ∆𝑡 this formula. You are solving for Power ∆E = final energy minus initial with this formula. energy. W = work done on an d = distance or the separation object or thing. between objects. ∆t = final time minus F = force or usually net force. initial time. UNIT 5? UNIT 4 This Unit is all about Energy, Energy is the ability to do something, cause change, do anything. There are many types of energy, chemical energy, mechanical energy, nuclear energy, gravitational energy, light energy, radiant energy, sound energy, motion energy, thermal energy, and electrical energy. Yeah, A lot. Basic Definitions of Different Energy Concepts Mechanical Energy is all of your potential and kinetic energy added together at a single point, ME = PE + KE The unit for energy is a Joule ( J). Gravitational Potential Energy is the energy stored in an object based on its height above a reference point. Elastic Potential Energy is stored energy in an elastic (rubber band, string etc.) if an object is compressed or stretched. Kinetic Energy is energy of motion based on speed. Work is the ability to add or remove mechanical energy from a system. Thermal Energy is energy due to molecular motion. We will explore thermal energy later in the year. For now, think of thermal energy as heat. For example, if you rub your hands together, the kinetic energy of your hands transforms into thermal energy. Joule is the unit used for this section and it is a Newton times mass Energy Conservation This topic is kind of confusing because in the lab we did, many people got different answers. Energy for an isolated system is always conserved. It may change forms, but the total amount of energy in an isolated system is constant. Energy can, however, be converted from one form to another form. This would mean that a cart pushed will lose Mechanical energy and the excess will be converted into friction or thermal energy. Even though the ME goes down the total energy stays the same. This photo above shows the transformation of PE into KE back into PE, it also shows how the total energy (without friction) does not change. The width of the arch under the pendulum stays the same throughout meaning that the total energy stays the same. If outside (external) forces are not acting on the system (friction), the total mechanical energy is the same throughout the entire system, and MEi = MEf Problems (ME, PEg, KE and energy conservation) Here is one of the problems taken from the hw but I will explain it more in depth - “A roller coaster has a starting height of 45 meters. The rollercoaster train has a mass of 1000 kg and it is at rest on the top of the first hill. The roller coaster has been constructed on the Earth. ” (no friction) 1. The train continues its way around a corner, then rises to the final hill, 40 meters above the ground. a. Identify the total mechanical energy of the train. The total mechanical energy is just the KE + PE and because in a system mechanical energy is conserved, we can calculate it from any point, ex : when it is not moving. When something is not moving, there is no KE meaning that ME = PE (in this case). PE an be calculated by plugging 45 for h, 1000 for m, and 10 for g in formula 12 to get the final answer of 450,000 J b. Calculate the gravitational potential energy of the train on top of the 40 meter high hill. Show your work. This question is asking us to find PEg which we can do by using formula 12 again. The only difference is that the height is now 40 meters. When we plug everything in, it should look like this and you will get 400,00 J as your answer - PEg = 1000 kg 10 N/kg 40 m PEg =400,000 J c. Determine the kinetic energy of the train on top of the 40 meter tall hill? Show your work or explain your answer. To find kinetic energy we could use 14 but we do not have the velocity of the coster meaning we will need to find this another way. We can do this by using the ME = PE + KE formula to see that when we plug in what we already know we get 450,000=400,000 +KE Simple subtraction will get us KE = 50,000J d. How fast is the train moving on top of the 40 meter tall hill? Show your work. This problem wants us to find velocity and that is only in formula 14. So if we plug what we have into formula 14, we will get this, 50,000 J = ½ 1000kg v^2 the next step is to do some simple math to get 100 = v^2 and by square rooting both sides, we get this v = 10 m/s Some concepts to understand after doing the problem are, When an object is not moving, it has no KE When an object is moving and you know KE and m, you can solve for v. When in object has no height, KE = ME and PEg = 0 Work and Power Work is when energy is added or removed from a system. This could mean you have negative work because energy was lost during a system to maybe thermal energy for instance. You can find Work by doing Force times distance. Work is measured in Joules. Work can be positive or negative. If energy is added to the system, positive work is done. (This usually only happens when something has a motor or is speeding up). If energy is taken away from the system, negative work is done. Power is how much work is done over a certain time. I like to think of it as the velocity vs time graph of a position in time graph where Work is the position time and Power is a step up or, the velocity v time graph. Kinda confusing but to be simple, it is how much work happened over a certain time period. It is measured in Watts. Work and Power Practice Problems 1. 0.5 kg-cart is traveling down a 2 meter high ramp. The cart is released from rest and has a speed of 4 m/s at the bottom of the ramp. How much work was done on the cart? There are 2 ways to find work, MEf - MEi and f times d, we do not have a force or a distance so, we should use MEf - MEi = W. Because it starts from rest, this means it is not moving, so MEi = PEg. At the end, there is no height meaning that MEf = KE. By using formulas, 13, 14 and 16 we can get a final formula of W = KE - PEg or W =½ mv2 - mg∆h By plugging in values, we can get = ½ (0.5kg) (4m/s)2 - 0.5kg 10N/kg 2m which simplifies to =4J - 10J or =-6J This answer shows us some main things and because it is negative, we lost energy throughout the experiment. 2. Calculate the power of a crane that lifts a load of construction materials. The crane does 250,000 Joules of work in 120 seconds. The answer to this question is not very hard to get because the formula for power is work over time. We have both those variables so we can plug in the different terms to get, P = W / ∆t = 250,000 / 120 = 2,083 Watts - This is the unit for power. Main Topics to Understand and Things to Study - ME is the addition of PEg PEs and KE - When things are at rest, there is no KE because velocity would be 0 - When things are on the ground (usually) they do not have any PEg. - ** FORMULA 11 is on the Exam and technically part of the unit so make sure you know it (It is below under Unit 3.) ** - Work is the difference in the mechanical energy or force time distance.  - Power is the rate at which that work gets done (how much time it takes.) UNIT 3 This unit is about 2d motion which is the motion of an object that has both an X and Y value. This unit is also freefall but that is only in the Y direction. Free Fall One main thing applied to all objects in free fall (neglecting friction) on earth is how their acceleration due to gravity is - 9.8 (-10 is also fine). This is the case for all objects that do not have a motor to accelerate them. Their FBD would be one line going down and the force of gravity which is the mass times the acceleration due to gravity (-9.8). Problems - free fall Let's say that a ball was dropped from a cliff and it took 3 seconds to hit the ground. How high was the cliff? To answer this type of question we need to use the distance formula (formula 6) and plug in 0 for vi, -10 for acceleration, and 3 for t. The next step is solving for t when you have every other variable. Usually free falling objects have no initial velocity resulting in the first part of the distance formula to be 0. This is not always true but most free fall objects have no initial velocity. To solve for t, you need to first plug in all the variables you have and then you can do some algebra until you get ___ = t^2 To fix this, you can square root both sides of the equation and get an answer. Don't forget that time cannot be negative and that it applies to both x and y axis. Free Fall P2 - Vertically launched projectiles/objects Main points - There is one force that makes an object accelerate and that is gravity - it will still accelerate but just in the negative direction. - Now that objects are going in both directions - positive and negative, Which is which? - down is usually the negative direction and up is usually the positive direction. - When an object is thrown in the air, the FBD is still the same as the one before because only the force of gravity is acting on it. Maximum height - this is a concept with some differences. When a vertically launched projectile is at its maximum height, there is no velocity because the projectile is not moving. There is still the force of gravity because that doesn't ever go away. Graphs: These are the two graphs for a vertically launched projectile. The maximum height is when the x = 0 for the velocity graph and for the position graph, it is where the vertex is. If the object lands where it is launched from the final velocity is the negative of the initial velocity. 2D Motion and Horizontally Launched Objects Now we are adding another axis, the x axis. There are some very key things to remember when thinking about this new axis - - The acceleration in the x axis is always 0 for projectiles without a motor. - The x axis velocity is always the same so if the initial velocity was 20 m/s that will stay the same. Here are some visuals that will help. As you can see, the x velocity does not change where as the y velocity does. X Axis - ∆x = vix∆t - ax = 0 m/s2 - vx is constant Y Axis - ∆y = viy∆t + 1/2ay∆t2 - vy = viy + ay∆t - ay = -10 m/s2 - vy = 0 m/s at the top of its path These are the formulas for the individual axis - In most problems with this you need to solve for a blank with only one axis of information, You cannot use the acceleration in the y axis in the same formula as something from the x axis. Time is the only universal variable (for this unit). Problems - HLP One very good question that was given to us is Mrs. Powers is trying to hit Mr. Shapiro with a water balloon. She is on top of a 45 meter tall building and throws the balloon horizontally with a horizontal velocity of 10 m/s. Neglect friction in the questions below. 1. How long is the balloon in the air? To solve this - you need to use the y axis because you have more information (the distances and the vi which is 0 and the acceleration which is -10m/s^2) 2. If Mr. Shapiro is standing 30 meters away from the building on the ground will the balloon hit him? Now we are in the x axis and we have to use the values in the x axis to answer the question. There is no acceleration in the x direction so the second half of the equation is 0, and the first is the initial velocity (10 m/s) times 3 seconds which we found out in the problem before 3. What is the final speed of the water balloon? Hint: what is the velocity in the x and y direction? To solve this problem you need to know the velocity of both the x and y to use the pythagorean theorem. By using the vf formula and plugging Y values into it, we get a velocity of -30 m/s. And because vx never changes, it is still 10 m/s. We can now plug this into the pythagorean theorem - 10^2 + 30^2 = s^2 once doing the math we get the speed is 31.6 m/s Universal Law of Gravitation The Law of universal gravitation says that every object attracts every other object in the universe. The force that it attracts something else with is determined by the mass and the distance of the objects. Different forces : The moon and the Earth both give out forces to each other - they are the same force but in opposite directions. F is the gravitational force m1 and m2 are the mass of the two objects d is the separation between the objects G is the universal gravitation constant which is 6.7 x 10^-11 Nm2/kg2 Inverse Square Law This law is very confusing until… you understand it. It basically says that however much the distance between two things is, the area of the gravitational field is the inverse squared. For example the butter gun example - when the distance is 1, one bread will be covered but when the distance is doubled the amount of bread covered is the square of the one before plus one (4). I like to think of this algebraically, for example if you were given a distance of x,if one was added to the distance, the amount of things the field covers is (x +1)^2 It is very confusing but the two photos explain it pretty well. Problems for ISL One great problem is this one : Assume the force between two masses is F. If the distance between the two masses triples, how much will the gravitational force change? The gravitational force between the two masses will decrease if the distance decreases. It will decrease by 1/9 because the distance is squared. Scientific Notation and Using Formula 11 All info taken from this video →https://app.nearpod.com/presentation?pin=YUNZE Scientific notation is a very important topic when discussing big numbers like those associated with the planets and gravitational force. Scientific notation is also a shorter way of expressing big numbers by moving the decimal place. For example, 3 x 10^2 = 300 and 4.57 x 10^6 = 4570000 and 8.383 x 10 ^-3 = 0.008383 This is just dealing with one number but the equation involves dividing and multiplying these numbers so that is what I will focus on. This is some key vocabulary to understand Now let's get on to adding, subtracting, multiplying and dividing them. if the exponents aren't, → This is the same for subtracting where you subtract the coefficients and if the exponents are not the same you want to change one of the numbers decimals places so that the exponents line up. Next is multiplying and dividing,  for example, Dividing is almost the same as multiplying but you just divide coefficients and subtract exponents. Now that we know all this, we can start solving for formula 11 which uses the scientific notation of 6.7 x 10^-11 as the variable G. Let's do a problem to understand it better, (Taken from the hw). Problem : If we know that G=6.7×10^-11 Nm2/kg2 and d is the center-to-center distance. Mass of Earth = 5.97×10^24 kg. Mass of moon = 7.35×10^22 kg. Earth-moon distance = 3.84×10^8 m Calculate the force of gravity on the moon due to the Earth? The first this to do is plug all know values into formula 11, −11 24 22 →= (6.7𝑥10 )(5.97𝑥10 )(7.35𝑥10 ) 8 2 From here we need to simplify the top and (3.84𝑥10 ) bottom, we can do this by multiplying all the top and the bottom to get this 37 2.94𝑥10 = 17 then we can divide to get our final answer of, 1.47𝑥10 = 2.0 x1020 N Common Problems (Whole Unit) and Major Things to Remember - Problems asking about the distance an object falls when launched with an x velocity. - Problems asking the acceleration of an object when it accelerates from a certain value to another over a specific time interval - The velocity of an object when it is in freefall (Vf) - The time it takes for an object thrown off a building to hit the ground **** - One big thing to remember is that two objects that are thrown off a build at DIFFERENT horizontal velocities will hit the ground at the SAME time - think about the bullet mythbusters clip we watched  - When something is thrown off a building with only a horizontal velocity, it will not have any y (vertical) initial velocity at all. UNIT 2 Forces definition and introduction The simple definition of a force is a push or pull. Force is also a vector quantity with direction and magnitude There are 7 different types of forces : 1. Contact Forces - They are forces that have two objects having a physical impact on each other. 2. Field Forces - Does not have contact between objects. 3. Tension Force - This force can only pull objects and cannot push. This force is implemented through a cable, rope, string, or wire. 4. Normal Force - This is a contact force between two perpendicular surfaces. It starts from the surface and goes to the object on it. 5. Friction Force - There are two main types of friction which are Static and Kinetic Friction. Static friction is friction where no movement is happening and it is greater than kinetic friction. This is the case because getting an object to move is much easier than keeping it moving. Kinetic friction happens when objects are sliding past each other. 6. Weight - Also known as the gravitational force (Fg = mg) where g = 10 N/kg. 7. Air resistance - This force/drag happens when objects fall through air or get pushed into air. If they are falling, they will reach terminal velocity at a certain point and their acceleration will slowly cease. Signs and symbols Contact Forces Field Forces - Applied Force (Fa) - Gravitational Force (Fg) - Tension (FT or T) - Electric Force (Fe) - Normal Force (FN or N) - Magnetic Force (Fm)  - Friction (Ff or f) - Nuclear Forces - Air Resistance (Fair) - Spring Force (Fs) Force Diagrams Force diagrams are a great way to see how objects are moving and by how much. “Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation.” Is what “The Physics Classroom” has to say. Some examples of force diagrams are listed here The first one could be an object being pulled up by a string and the force acting on it is 400N up. The second could be an object falling through the air where the force acting on it is 200N down. The 3 diagram could be a hockey puck sliding on the ice where the forces acting on it is 20N to the left because the normal force and the gravity force are in equilibrium. Equilibrium In order for an object to have an acceleration, it must have a net force. Objects that are either at rest or moving with constant velocity are said to be in equilibrium. Therefore if an object is in equilibrium, the net force is 0-N. For example, an object moving at a constant velocity with no friction force, will have no net force. Drawing Force Diagrams and Finding Net Force From Them Drawing force diagrams have some thinking to them, for example when an object is moving does not mean it has a net force in that direction. The clues in the question are what will lead you to your diagram. No arrows on your diagram should be going into the dot. Usually… when there is a mention of the object moving at a constant rate, there is no net force because there is no acceleration. 1. The first step is starting with the things you already know, for example each diagram starts with a dot and the force of gravity because everything on earth has gravity. This is what almost every force diagram will have. 2. The next step is to look for other clues in the question like, “is at rest on a table.” This would mean that there is a normal force on the object that is in equilibrium with gravity. There might be something saying, “Person A is pushing to the right while person B is pushing to the left.” This would mean that there was a push force going to the left and the right. In both of these diagrams, there is no Net Force. If the question said something , “The hockey puck you just hit is sliding along the ice towards the right. The force of friction on the puck is 0.50 N. ” This would mean that there would be an unbalanced force resulting in the FBD looking like this : The force of friction is 0.50 N resulting in a net force of 0.50 N to the left.  Finding Net Forces with Formulas 7, 8, and, 9 Net Force is one very important topic in this unit and a majority of the questions will be about it. There are 3 main ways to find net force, the first one is looking at a Free Body Diagram and finding the net force, the other is using formula 8 and the last one is using formula 9. In the case where there is only one unbalanced force, the net force will equal that force. Free falling objects have Fnet = Fg Coefficient of Friction (Formula 10) These are the coefficients of friction in different situations, you can plug this into the coefficient of friction in order to get the answer or Ff or Fn. Static vs Kinetic Friction Kinetic and static friction are both different types of friction, usually static friction comes before Kinetic friction because static friction is the force needed to make an object move (It is usually bigger) - whereas static friction is the force needed to keep something in motion. Study Tactics/Common Questions One main question that is asked a lot is questions involving what objects have the greatest inertia, in this case, the answer is usually the object with the greatest mass no matter the speed or acceleration. Another question that is asked a lot is finding net force when given friction and applied force (Formula 8) or Mass and acceleration (Formula 9). The Open response part will also probably include a question or two with Force diagrams - make sure you draw these with somewhat accurate measurements to insure that there is no confusion. The answer to all the test is gyta