STUDYSOUP___1_physics_1.pdf Phys 211
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This 10 page Class Notes was uploaded by Habibah Dawodu on Sunday September 4, 2016. The Class Notes belongs to Phys 211 at Slippery Rock University of Pennsylvania taught by Dr Herat Athula in Fall 2016. Since its upload, it has received 32 views. For similar materials see Physics 1 in Physics at Slippery Rock University of Pennsylvania.
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Date Created: 09/04/16
Motion simply is the change of a physical body’s position with time. There are 4 fundamental types of motion which are: Linear motionExample, A skateboarder moving along a straight line. Circular motionThis involves motion along a circular trail. Example, walking round a circular fountain. Projectile motionIt involves launching an object in air and the then it coming back down due to the law gravity. It always forms a curved path. Example, shotput, javelin or shooting an arrow in the air Rotational motion: it involves motion of a stiff body rotating about its axis. Example, a ball spinning on the ground about its axis. The first three motion listed above are all called translational motion. This is because they move their whole body freely through space. Important point: Trajectory can be defined as the trail or pathway in which a body moves. This pathway can be unswerving or swerving (straight or bent). The fourth motion (Rotation motion) on the other hand differs from the other three because it involves movement of a body but without change in position of the body. Making a Motion Diagram. Motion diagram is defined as the combined or edited image which shows a body’s position at equal time interval. Making a motion diagram is not difficult at all because it involves only the use of a video camera which can take up to 30 images per second. Every image it takes, is individually known as a frame. Imagine you lay all the frames on top each other to create a combined image, this combined image you created will show different position of the body at constant time interval. For example, Bob takes a picture of a moving body, the time interval between each position can be maybe 12ms. It can only be 12ms, not any other time interval because the time interval is equally spaced. So if there are six positions, the first position from the starting point will be 12ms, the second from starting point will be 24ms, the third from the starting point will be 36ms etc. Examples of Motion Diagrams. There are three examples of motion diagrams: 1. The motion diagram that shows the body at constant speed, as a result of equal distance between the physical body during motion. 2. The motion diagram that shows the body with increasing speed, as a result of increasing distance between the physical body during motion. 3. The motion diagram that shows the body with decreasing speed, as a result of decreasing distance between the physical body during motion. Models and Modelling. Modelling can simply be defined as Removing details in order to concentrate on vital features. Model is a realistic and simplified version of something but still captures the essence of what is being studied. It is a simplified version of something complex but will still help us understand the complex thing. For example, summary of an essay or a novel in which you are expected to give important information and remove all unnecessary details OR the figures 0,1,2,3,4,5,6,7,8,9 that are the simple figures we all know that gives us trillions of other complex figures. German born theoretical physicist, Albert Einstein once said, “Physics should be as simple as possible but not simpler.” Types of Models There are two types of model 1. Descriptive model: It is used to describe a phenomenon or a system. 2. Explanatory model: It is usually based on physics law to explain a phenomenon or system. It also is used to test against experimental data. The Particle Model A particle is defined as a body that can be depicted as a mass at a single point in space. It does NOT consist of a size, shape, or a distinction between its top and bottom or its front and back. The good thing about the particle model is that it allows us to treat a physical body as though all of its mass is concentrated into a single pint. This further allows us to denote it as a single dot. . Important information: Particle model can only be used represent translational motion. (Linear, circular and projectile motion). Rotational motion on the other hand cannot be depicted with Particle model because its axis is fixed. Position, Time and Displacement. When using a motion diagram, it is likely that you want to know an object’s position and time at that position. You can measure a position by using a coordinate system grid over the motion diagram. You will then trace the object’s (x, y) coordinates. A coordinate system is used in analyzing motion. The origin of the coordinate system can be placed anywhere depending on the writer’s preference. Time can also be a coordinate system. To understand this, you can visualize it this way. Pick any point during motion and label it as t=0 seconds. This time t=0 can be the time you resolve or decide to start your stop watch. This time t=0, you start is regarded the origin of your time coordinates. For example, Brooke and Taylor are about to go for a walk around their community. Brooke decides to start her stop watch just after she comes out of the house, while Taylor walks half of community before she starts her stopwatch. Brooke’s origin starts at the time she comes out of the house while Taylor’s origin starts at the time she walked half the community. NOTE: It is possible for an object to be in motion before you start your stop watch like in Taylor’s situation. All those time before you start you stop watch is denoted as negative, mainly because it occurs before or to left of the origin. Position Vector: is an arrow that is drawn from the origin to a position on the motion diagram. The position vector is denoted with r . r is always equal to the length of the position vector and the angle of the position vector. The previous sentence explains an alternative form to coordinate (x, y). Scalar vector Is a sole number with a unit that is used to Cannot be described as a lone number, rather describe a physical quantity. (has only as a quantity with magnitude and direction. magnitude, no direction). Example: Temperature, time, distance, mass Example: displacement, acceleration, force, etc. velocity, momentum etc. Can be positive, negative or zero Can be positive negative or zero Scalar symbols are indicated without arrows. Vector symbols are indicated with arrows Example, g, K facing the right on top of the symbols. Example, g,K⃗ . NOTE: It is key to know the difference between scaler and vector quantities because it is possible to have scaler and vector quantities in the same question. Vector arrows over the symbols should always be pointed to the right never towards the left. ´ ´ or K is NOT allowed. Displacement. Displacement is used to demonstrate a change of position of a physical body. For example, we have two dots representing the motion diagram of a car, the displacement of that car is the arrow drawn in between the two dots, showing the change in the car’s position. The symbol for displacement is ∆⃗r . Motion Position Vector Displacement. change of a physical body an arrow that is drawn from change of position of a with time the origin to a position on the physical body motion diagram r ∆ r I put this table above for you to differentiate because definitions and symbols sometimes can be confusing. Addition and Subtraction of Vectors. Adding vector quantities differs from adding numbers. Subtracting vector quantities involves ⃗ ⃗ ⃗ ⃗ adding negative vectors. Example M N = M+(−N) . ⃗ ⃗ ⃗ ⃗ ⃗ Zero vector: occurs when a vector has zero length. Example, M−M=M+ (−M =0 . The difference between a positive and negative vector of a position is the negative faces opposite direction. Initial position: r i Final position: ⃗ f ⃗ ⃗ ∆ r ∆ r r ⃗ f i OR = f i When using a graph, the displacement vector is a vector arrow drawn from the initial position to the final position. NOTE: A vector can be moved around as long as its length and the direction it points doesn’t change. Motion Diagrams with Displacement Vectors. Important information: A physical body that starts and ends with resting position usually has little space in between its initial and final dots. You should always put the displacement vector arrows in between the dots. If the displacement vector of a physical body is increasing in length then the object is speeding up. If the displacement vector of a physical body is decreasing in length then the object is speeding down. Time Interval Time interval, also known as change in time, ∆ t = tf ti used to measure the elapsed time as a body moves from an initial position ⃗ i initial time i to a final position ⃗ f , at final time tf The change in time is the same no matter what time instrument is used. Velocity Average Speed is a quantity used to measure how fast or slow a physical body moves. distancetraveled d Average speed = change∈time = ∆t . Average velocity is the quantity that measures not only the distance traveled by a physical body but also the direction of motion during a time interval. OR (a better definition) Average velocity is the quantity that measures a body’s displacement during time interval ∆ t. ∆r⃗ displacement = = avg ∆t change∈time NOTE: Displacement is very important when studying motion because it not only tells you the distance traveled by an object, but also the direction the object is moving. It is very essential when studying physics that you should be able to differentiate between speed and velocity. Speed measures how fast (18mph) while velocity measures how fast and what direction (18mph, south). v Important information: From now on average velocity avg,ould be referred to as symbol v . Motion Diagram with Velocity Vectors. The velocity v, and displacement ∆⃗r , vector arrows both point in the same direction. The velocity v, and displacement ∆⃗r , vector arrows both have the same length. So this tells us that we can use velocity vectors and displacement vectors interchangeably when drawing motion diagrams. Also, the length of the velocity ⃗vector and average speed that a body moves is the same. The above information might be confusing but look at it this way. Velocity and displacement are very similar, except that velocity involves change in time. Its distance travelled and direction is still the same with that of displacement. Linear Acceleration. ∆⃗v=v⃗ ⃗ Change in velocity f i occurs in two ways: Change in speed during motion Change in direction during motion Initial velocity: ⃗ i Final velocity: ⃗ f change∈velocity ∆⃗v Rate of change of velocity = change∈time = ∆t = average acceleration. a ∆⃗v avg ∆t . NOTE: Both the change in velocity vector and acceleration vector point in the same direction, but they do not necessarily have the same magnitude. Just like that of displacement vector and velocity vector. We would also from now on refer to average acceleration symbol a as ⃗ . avg Relationship between Acceleration and Velocity in Motion Diagram. 1. Whenever a body’s ⃗ and a are facing the same direction, its speeding up. 2. Whenever a body’s v and a are facing the opposite direction, its slowing down. 3. Whenever a body’s acceleration ⃗ =0, its velocity is unchanging (constant). Note: In Physics acceleration means change in velocity not just speeding up.
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