Motion, Velocity, Acceleration

Transcription

1 And thus, since God is the First Mover, simply, it is by His motion that everything seeks to be likened to God in its own way. Summa Theologica, IIa:Q109,A6 Introduction Objects in motion are moving at a certain speed at a given moment in time. Speed, in physics, can be defined as change in distance with respect to time, with no reference to direction. Velocity is change in distance over time in a given direction. Velocity is a vector quantity. The direction of the velocity vector is the direction the object is moving, regardless of whether the object is maintaining a certain speed, speeding up, or slowing down. v avg = d t = d f d 0 t f t 0 Where: vavg is the average velocity; Δd is the change in position or distance; df and d0 are the final and beginning positions at time tf and t0, respectively. Over a defined distance, the motion of the object could be uniform, increasing or decreasing. In this lab, you will perform two quick motion experiments and evaluate the speed, velocity, distance traveled, time changes and acceleration. You will determine the type of motion displayed. Graphing data on a Distance vs. Time graph, we can visualize the movements. On these graphs, the slope (rise/run) between any two points is the velocity (Δd/Δt) of the object between the two positions. In uniform motion the same distance is traveled in each time interval and a graph of distance covered vs. time would resemble that of Figure 1. Note how the slope (rise/run) between two positions on the graph gives the average velocity from the first position to the second. However, the velocity (slope) could have been obtained between any two points on the curve. For an object traveling at increasing speeds, its velocity changes by a certain number of meters each second and is accelerating. Acceleration is a vector quantity and is the rate an object changes its velocity. If an object changes its velocity, the object is accelerating. A change in velocity may be visualized by again observing a Distance vs. Time graph. On the graph in Figure 2, compare the velocity (slope) between the first set of points at A with that between the set of points at B. Clearly, there is a different slope and a different velocity as the object moves position over time. Now, compare the Distance vs. Time graph of Fig 1 with that of Fig 2. The difference between uniform motion and acceleration readily can be observed Catholic Initiatives in Math and Science, LLC All Rights Reserved 1

2 Differences between uniform and increasing motion can be even more dramatically portrayed when observing Velocity vs. Time graphs (Figure 3). In uniform motion, it is evident that the velocity of the object is constant (Fig 3A). Whereas, in accelerating motion (Fig 3B), the velocity is changing over time. In Velocity vs. Time graphs, the slope (rise/run) between any two points will yield the value of the average acceleration (Δv/Δt). The uniform motion of the object in Fig 3A reveals a line with a slope of zero. The object in Fig 3B is accelerating, so we observe a changing slope that is a changing velocity over time. The formula for average acceleration is: a avg = v t. The second thing noticed in Fig 3B is that the velocity is changing by a constant amount each second. This is referred to as Constant Acceleration. Since velocity is a vector quantity, acceleration is also a vector quantity. The direction of acceleration depends upon two things: whether the object is slowing down or speeding up; whether the object is going in the + or direction. Without discussing all permutations of +/ acceleration, we can say in general that when an object is speeding up in the same direction as the velocity, it is undergoing Positive Acceleration. Positive Acceleration is observed in Figure 3B. When an object is slowing down (not shown) while traveling in the + direction, the object is undergoing Negative Acceleration. Learning Objectives: Experimentally distinguish between uniform motion and accelerating motion Construct and interpret motion graphs Materials Required: From Physics Kit Student Supplied Masking tape Ruler Timer marking seconds Safety Perform this lab in an open area where it is permissible to place masking tape on the walking surface. Experiment MOTION Notes for Motion Experiment portion: If there are two persons, one can call out 1-second time intervals and the other can move from block to block. If there is only one person, movement should be made while watching the timer. If available, a metronome may be used to show the 1-second time intervals Catholic Initiatives in Math and Science, LLC All Rights Reserved 2

3 1. Prepare Walking Surface Find an area such as in hall or on a sidewalk giving about 10-feet of open access Using the masking tape and ruler: Place a piece of masking tape and mark on it 0 Foot Measure 12-in., place a second piece of masking tape, and mark it 1 Foot Continue in this fashion until you have a clearly defined area marked between 0 Foot and 10 Foot 2. Motion A for 10 feet For 10 feet and using a timer: Walk in a straight line, using the marked lines/blocks as guide Walk at a rate of one block for every second (1 foot/sec) Stop when the 10-foot block has been completed Keep in mind how this rate feels Chart and Graph before moving to the next part: Record in Table 1 the total distance covered at each second 0 ft at 0 sec; 1 ft at 1-sec; 2 ft at 2-sec; 3 ft at 3-sec, and etc. Calculate the average speed (s avg) and place it in Table 1 Show your calculations Remember to record BOTH a number and a unit Appropriately number the axes in Graph 1 Graph Motion A in the Graph 1: Distance vs Time graph Use the data from Table 1 to graph Use closed circles for the data set as the key instructs Draw a best-fit curve between the points 3. Motion B for 10 feet For 10 feet and using a timer: Walk in a straight line, increasing the rate by one block each second At 1 sec, walk 1 block In the next second, walk 2 blocks In the next second, walk 3 blocks Stop when the 10-foot block has been completed Mentally compare this rate with the rate in the previous step Chart and Graph before moving to the next part: Record in Table 1 the total distance covered at each second Example: 3 ft at 2-sec; 6 ft at 3-sec; and etc. Note that the 10-foot distance has been covered prior to completing the 10 seconds shown in the table Simply place a dash (--) where no data has been collected Calculate the average speed (s avg) and place it in Table 1 Show your calculations Remember to record BOTH a number and a unit Graph Motion B in the Graph 1: Distance vs Time graph Use the data from Table 1 to graph Use open circles for the data set as the key instructs Draw a best-fit curve between the points 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 3

4 CALCULATIONS 4. Velocity Calculations and Graph The average velocity can be obtained between any two points in the data. The first data set appears linear, and we could calculate velocity between t=0 and t=10. But, we wish to obtain an idea of the velocity in 1-sec intervals. Do not worry, it is not as burdensome as it may seem at first. For Motion A At 1-sec intervals, determine the distance traveled (Δd = d f d 0) Record in Table 2 Comparison of Velocities Calculate the average velocity and Record in Table 2 Show your calculations for one representative set of data points Label the axes of Graph 2 Velocity vs. Time Graph Motion A in Graph 2 using the symbols indicated in the key Draw a best-fit curve between the points For Motion B As above, determine the distance traveled at 1-sec intervals and record in Table 2 Calculate the velocity, record in Table 2 Show your calculations for one representative set of data points Graph Motion B in Graph 2 using the symbols indicated in the key Draw a best-fit curve between the points 5. Acceleration Calculations By now, it should be apparent that the velocity in one experiment is changing but not in the other. As discussed in the Introduction, the slope of a Velocity vs Time graph is the acceleration. We could perform a regression of the curves to find acceleration. But here, we will calculate the average acceleration between 0-sec and 10 sec. For Motion A From the data in Table 2, calculate difference in velocities between 0-sec and 10-sec (Δv = v f v 0) Record this difference in Table 3 Comparison of Acceleration Remember to record the units as well Calculate acceleration of Motion A over the 10 sec: a = Δv/t Record acceleration in Table 3 Show your calculations For Motion B As above, determine the difference in velocities between 0-sec and 10-sec Calculate the acceleration and record in Table 3 Show your calculations 6. Perform the rest of the Data Analysis and Conclusions 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 4

5 Lab Report for: NAME: Time (sec) Table 1 Motion Total Distance Covered (feet) Motion A Motion B savg (ft/sec) *Show calculations in Table distance traveled s avg = time traveled Graph 1 Distance vs. Time 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 5

6 Time Interval 0-1 sec 1-2 sec 2-3 sec 3-4 sec 4-5 sec 5-6 sec 6-7 sec 7-8 sec 8-9 sec 9-10 sec Table 2 Comparison of Velocities Motion A Motion B Distance traveled Avg. Vel (ft/sec) v avg = d t = d f d 0 t f t 0 Distance traveled Avg. Vel (ft/sec) Graph 2 Velocity vs. Time Time Interval 0 10 sec. Table 3 Comparison of Acceleration Motion A Motion B Difference in Velocities (ft/sec) Acceleration (ft/sec 2 ) a = v t Difference in Velocities (ft/sec) Acceleration (ft/sec 2 ) 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 6

7 Data Analysis and Conclusions Show your calculations throughout this exercise. 1. Average Speed: a. Compare your average speed in Motion A with that in Motion B b. Describe this new speed in the second experiment. Were you simply walking faster at a uniform pace? Explain c. Does a value for average speed give any information on the direction of motion? d. Does a value for average speed give any information on the type of motion that is whether the motion is uniform or accelerating? 2. Distance vs. Time Graph: a. Compare and contrast your curve for Motion A with that of Motion B in a few brief sentences. b. Is it clear from the curve whether the person in Motion B is simply going about twice or fast, or whether the person is accelerating? 3. Comparison of Velocities: a. Review data in Table 2 as well as the Velocity vs. Time graph. Compare the trend in velocities between Motion A and Motion B. b. Is Motion A uniform motion or acceleration? Explain. c. Is Motion B uniform motion or acceleration? Explain. 4. Acceleration: a. Compare the acceleration calculated for Motion A with that calculated for Motion B. b. Which graph best demonstrates acceleration? c. You calculated acceleration from Data Table 2: Comparison of Velocities. Explain how you could also calculate acceleration from a graph? Which graph would you use to calculate acceleration? d. In Motion B you calculated a certain acceleration. For every second that elapsed, by how much did your velocity change? 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 7

8 5. A student performed a similar experiment. His data and Distance vs. Time graph are shown to the right. Answer the questions regarding this experiment. Assume the student is moving in the + direction. a. Calculate the velocities. Then, construct a Velocity vs Time graph. Label graph and include units in table A data table and a graph are provided for your use Time Increment 1 sec 2 sec 3 sec 4 sec Δd (change in distance) Velocity vs. Time Graph Velocity (per 1 sec increment) b. What type of motion is this? c. Did the student accelerate? If so, which type of acceleration? d. In the experiment, you calculated an acceleration value for Motions A and B. Calculate the acceleration for this student s movement. Show your calculations and make sure your answer has both numerical value and units Catholic Initiatives in Math and Science, LLC All Rights Reserved 8