Physical Science Honors - Physical Science

11.1 Distance and Displacement frame of reference – system of objects that are not moving with respect to one another. A frame of reference is needed to describe motion accurately and completely. Relative motion – movement in relation to a frame of reference. Distance – length of a path between 2 points. Typically measured in meters (m) unless measuring large distances, which are typically measured in kilometers (km), or particularly small distances, which are measured in centimeters (cm). Displacement - the direction from the starting point and the length of a straight line from the stating point to its ending point. Sometimes used when giving directions (includes starting point and direction). After one trip around roller coaster track, the roller coaster’s car displacement will be zero. Vector – qty. that has both magnitude and direction. Magnitude can be size, length or amount. Arrows on graph or map are used to represent vectors. Length of arrow is the magnitude. Vector addition is combining of vector magnitudes and directions. ● Add displacements using vector addition. ● Displacement along straight line: simply add their magnitudes. If displacements are in opposite direction, subtract one from the other. ● Displacement that isn’t along a straight path: Combine vectors by graphing. Add the magnitude (length) of each segment to get total distance traveled. For example, if you walk 1 block East, then 1 block North, then 2 blocks East, then 3 blocks North to your ending point, you have walked a total of 1 + 1 + 2 + 3 = 7 blocks. ● The resultant vector is the vector sum of two or more vectors, which in above example shows the displacement. The resultant vector points directly from the starting point to the ending point In the above example, if you took sheet of paper and measured the vector from start point to end point, you would see that the displacement from start to end point was 5 blocks, whereas the distance walked was 7 blocks. If you drew a right triangle with horizontal edge = total blocks walked East (3) and perpendicular edge = total blocks walked North (4), the hypotenuse of the right triangle is the resultant vector and the displacement (magnitude of resultant vector) is 5 blocks. 11.2 Speed and Velocity speed – the ratio of the distance an object moves to the amt. of time the object moves. The SI unit of speed is meters/second (m/s). However, for faster objects, like a car, you might choose km/hr. Speed can be expressed in two ways: ● Average speed – computed for the entire duration of a trip ● Instantaneous speed – measured at a particular instant. For example, glancing at your car’s speedometer will tell you your instantaneous speed in mph. Average speed = Total distance/Total time, or v = d/t Graphing Motion – a distance-time graph is a good way to describe motion. The slope of a line on a distance-time graph is speed. Recall that slope is the change in the vertical (y) axis divided by the change in the horizontal (x) axis. The change in distance divided by the change in time represents speed. Measuring Distance and Speed Odometer – measures distance vehicle has traveled Speedometer – measures instantaneous speed Velocity – description of both speed and direction of motion Combining Velocities - Two or more velocities are combined by vector addition. Vector addition is used when motion involves more than one velocity. For example, the velocity of a boat (A) in the reference frame of a riverbank (17 km/h) is a combination of the relative velocities of the boat and the river. You can determine the resultant velocity of the boat relative to the riverbank (13 km/h) by measuring from the tail of one vector to the head of the other. Concepts in Action: Navigation at Sea Magnetic compass – contains a magnetized needle, which due to Earth’s magnetic field, points roughly toward the North Pole. Sextant – instrument once essential in navigation. Observer looks through telescope and move’s sextant’s arm until image of the sun or a star lines up with horizon. Angle is then read from the scale. Latitude – how far North or South one is from the equator. Longitude – how far East or West you are from Greenwich, England Modern navigation use satellite networks, GPS, radar, and master control. 11.3 Acceleration Acceleration can be described as changes in speed, changes in direction, or changes in both. ● Acceleration is a vector. ● Acceleration applies to any change in speed (increasing or decreasing). ● · Unit for acceleration is m/s2.. Deceleration - Negative acceleration or acceleration that slows an object’s speed. Free fall – movement of object toward Earth solely due to Earth’s gravity. Example of acceleration caused by change in speed. Objects falling near Earth’s surface fall at rate of 9.8 m/s2. Changes in Direction – Acceleration may be due to change of direction, if speed is constant. Changes in Speed and Direction – Sometimes motion is characterized by changes in both speed and direction at the same time (i.e., think of roller coaster ride). Constant acceleration - steady change in velocity. That is, the velocity changes by the same amt. each second. An object moving in a straight line changes at a constant rate with the object is experiencing constant acceleration. Calculating Acceleration: Acceleration = Change in Velocity/Total Time = (vf - vi)/t. ● Note that velocity is in the numerator and time is in the denominator. If velocity increases, numerator is positive and acceleration is positive. ● If velocity decreases, numerator will be negative and acceleration will be negative. ● Acceleration and velocity are both vector quantities. ● To determine a change in velocity, subtract one velocity vector from another. ● If motion is in a straight line, however, the velocity can be treated as speed. You can then find acceleration from the change in speed divided by the time. Graphs of Accelerated Motion ● The slope of a speed-time graph is acceleration (change in speed/change in time). ● Constant acceleration is graphically represented by a straight line. (linear). The slope of the line shows the acceleration. Positive acceleration will be in direction of / ● Constant negative acceleration decreases speed. Graphically, slope of line will be negative \ ● Accelerated motion is represented by a curved line on a distance-time graph (non-linear). The curve connects the data points plotted. Instantaneous Acceleration – how fast a velocity is changing at a specific instant. First, a set is simply a collection of objects; the objects are referred to as elements of the set. The statement that x is an element of set S is written x∈S , and the negation that x is not an element of S is written as x∉S . By definition, a set is completely determined by its elements; thus sets A and B are equal if they have the same elements: