Group member names: -Won-Yong Shin -Samantha Osborne - Laboratory Activity 3: Acceleration Graphs Objectives Explore how motions are related to acceleration-time graphs Relate acceleration-time graphs to velocity-time graphs and position-time graphs Learn to use vectors to represent motion Equipment Computer Ultrasonic motion sensor USB Link Dynamics cart Track for cart Fan attachment Activity One: Speeding up Velocity Acceleration Prediction 1: Using the line tool on the drawing toolbar of Word, draw a line on both the velocity and acceleration graphs below predicting the shape of a curve for a cart starting at rest and moving away, speeding up at a constant rate. Time Time Set up the equipment: Obtain a USB Link and a motion detector as in the previous lab. Open the experiment file called SpeedingUp.ds to display acceleration and velocity graphs. You can find it by going to the networked disk “PLAB” (usually disk G:), in that opening the folder “Plab”, then finding the folder for Physics 201, and then looking in the folder for Lab 3. Set the detector up as in the previous lab, except make sure the switch on top is set to the ‘cart’ instead of ‘person’ setting. Lay the track on the table and set the motion detector on the table at the end of the track that does not have the post. Check that the track is reasonably level by setting the cart in the middle and seeing if it has a tendency to roll to one end. If so, level the track by adjusting the base screw at one end. Look under the fan and check that it has two batteries installed along with two aluminum cylinders that are taking the place of batteries. Attach the fan to the cart and put a rubber band on to make sure it doesn’t fall off. Experiment: Place the cart on the track with the fan pointing away from the motion detector about 30 cm (1 foot) away from the detector and turn it on, with one person holding it in position. Have another team member start taking data. Let go of the cart as soon as the clicking sound is heard, careful to not get any hands between the detector and the cart, and let the cart speed away. Catch it just before it crashes into the other end of the track. When you have a nice graph, copy the graph and paste it in the section below. -paste graph here- Question 1: How did the result compare to your prediction? What feature of the velocity graph shows that the cart is speeding up at a constant rate? What feature of the acceleration graph shows that the cart is speeding up at a constant rate? What does it mean that both the velocity and acceleration graphs are positive (above the axis) the whole time? Our only discrepancy came from the fact that our graph showed a velocity much higher than what actually was. We are able to tell that cart is speeding up at a constant rate on the velocity graph because the graph produces a straight line, thus the slope is rather constant. Since the acceleration graph is of a straight line, it is obvious that the graph is speeding up at a constant rate. If it were not, the line would have a slope. Since both the graphs are positive, it is obvious that the fan is moving away from the motion detector. Velocity Acceleration Prediction 2: How will the graphs look if you start the cart at the far end of the track and let it speed up towards the detector? Time Time Experiment: Set the cart on the far end with the fan pointing toward the detector and let it speed up toward the detector while taking data. Catch the cart when it gets about 30 cm from the detector, so it doesn’t crash. Past your graph below. -paste graph here- Question 2: How did the result compare to your prediction? What feature of the velocity graph shows that the cart is speeding toward the detector up at a constant rate? What feature of the acceleration graph shows that the cart is speeding up towards the detector at a constant rate? What does it mean that both the velocity and acceleration graphs are negative (below the axis) the whole time? Our predictions were basically correct. The velocity graph showed in the negative, and the acceleration was basically in the negative because the cart was traveling towards the detector instead of away. We can tell that it is going at a constant rate because of the slope is constant. It is obvious that the acceleration is constant because the horizontal line is constant slope of zero it never changes. Velocity Acceleration Prediction 3: Now imagine that you return the cart to the far end of the track, only this time with the fan pointing away from the detector. You give it a quick push toward the detector, with the fan blowing to slow it down, and you then catch the cart when it comes to a momentary stop. Draw velocity and acceleration graphs for this motion. Time Time Experiment: Set the cart on the far end with the fan pointing away the detector and push it toward the detector so that it slows down while taking data. Catch the cart when it is about stopped. Past your graph below . -paste graph here- Question 3a: First identify what part of the velocity and acceleration graphs corresponds to when you pushed on the cart, and which part correspond to when the cart was moving freely. Focus on the second part in the following questions. How did the result compare to your prediction? What feature of the velocity graph shows that the cart is moving toward the detector? What feature shows that the cart is slowing down at a constant rate? Our prediction showed a much more extreme change in velocity. Our prediction also was erring as it showed a negative acceleration. It is obvious that the object is moving toward the detector as the velocity is negative. It is slowing down at a constant rate because the slope of the velocity line is constant. Also, the slope of the acceleration line is nearly perfectly horizontal. Question 3b: Do the acceleration and velocity graphs have the same sign during the whole time? The acceleration graph has the same sign as what feature of the velocity graph? What do the relative signs of the velocity and the acceleration graphs tell you about the motion? No, the two graphs do not have the same sign the whole time. The acceleration has the same sign as the slope of the velocity graph. Thus, even if the velocity is negative, as long as the line it creates has a positive slope, the acceleration graph will be positive. Likewise, visa versa. Prediction 4: In this final case, you will start with the cart about 30 cm from the detector, with the fan pointing towards the detector, and give it a push away from the detector. Let the cart slow down and come back, catching it before it hits the detector. Draw a prediction of the velocity and acceleration graphs. Acceleration Velocity Time Time Experiment: Set the cart about 30 cm from the detector with the fan blowing the cart towards the detector. Give the cart a quick push, being careful to not let your hand get in front of the detector. (You may find it easier to grab the sides of the cart or the end away from the detector.) -paste graph here- Question 4: First identify what part of the velocity and acceleration graphs corresponds to when you pushed on the cart, and which part correspond to when the cart was moving freely. Focus on the second part in the following questions. What does it mean that the velocity graph changes signs? What does the point that it is zero correspond to in the motion of the cart? Does the acceleration graph change signs, or is it ever zero? When you push the cart it is time zero, akk thee other times the cart is moving freely. Means that the object is moving at a different direction from the detector. The point that it is zero correspond to in the motion of the cart is where the cart is changing direction. No it never change signs because the slope of the velocity is negative. The acceleration is never zero unless the object has no constant velocity. Activity Two: Vector representations Vectors (arrows) are an alternative way to indicate the motion of an object. A velocity vector can be drawn at the location of the object at a particular time with the length of the arrow representing the relative velocity of the object. Question 6a: On the picture below, use the arrow drawing tool to draw a velocity vector underneath each carat in the figure below. (from RealTime Physics (Electronic Version) by David Sokolof, et al., John Wiley and Sons, NY, 1999) Question 6b: Compare the method of representing velocity with a graph and that of using vectors. What aspects indicate the relative time? What aspects indicate the velocity at a given time? What tells us how the velocity is changing? Fill the chart out below Graph Vectors Time Velocity Direction Change in velocity Question 6c: How would you draw a vector to represent the acceleration of the cart at each point? Draw vectors on the above diagram below the velocity vectors to represent the acceleration. Question 7: Draw velocity and acceleration vectors for the cart speeding up toward the detector. (from RealTime Physics (Electronic Version) by David Sokolof, et al., John Wiley and Sons, NY, 1999) Question 8: Draw velocity and acceleration vectors for the cart slowing down as it moves toward the detector. (from RealTime Physics (Electronic Version) by David Sokolof, et al., John Wiley and Sons, NY, 1999) Summary The following questions will help you get the main ideas out of this lab. You should find these straightforward questions, but take the time to talk it over with your team and write complete answers to these questions. You may find your answers here to be the most useful part of this lab down the road. Summary 1: In an acceleration graph, what does the vertical distance from the axis mean? What does it mean if the line is above the axis, on the axis, or below the axis? The vertical distance from the axis is the magnitude of the acceleration. The slope of the velocity is positive. If it is on the axis there is no acceleration, if it is below the axis means the velocity is negative slope Summary 2: How are velocity and acceleration graphs related? What aspect of an acceleration graph and what aspect of a velocity graph tell us how something is changing its motion? Acceleration is drived by the slope of velocity, We can tell by the graphs of how something is moving by the slopes of the line that they create. Summary 3: How do you know your above statements are true? What experimental observations and/or logical reasoning can you give to justify what you said in summary questions 1&2? We know it is true because we have tested it. Velocity graph will have a line if the acceleration is constant, if the velocity is constant there will be no acceleration. Summary 4: Look over your graphs. How can you tell if an object is speeding up or slowing down from velocity and acceleration graphs? If both acceleration and velocity are positive, how is it moving? Both negative? One positive and one negative? Explain your reasoning. It is obvious if an object is speeding up on a velocity graph above the axis if the object has a positive slope. Likewise, the velocity is decreasing if the slope is negative. However, if the velocity graph lies below the origin, the object is actually losing speed when the slope is positive and gaining speed when the slope is negative. To determine if something is speeding up or slowing down on an acceleration graph, one must look at the velocity graph since the acceleration is derived from the slope of the velocity graph. For example, if an object is decelerating with negative velocity, the slope of the line will be positive, thus the acceleration will have a positive value. If both acceleration and velocity are positive, the object is speeding up and moving away from the detector. If both are negative, the object is going to be accelerating towards the detector. If one is positive, and one is negative, more than one situation can be. If an object is decelerating and moving towards the origin, the velocity is negative, but the acceleration is positive. Like wise, if and object is decelerating and moving away from the origin, there is positive velocity and negative acceleration. This is obvious because the sign of the slope of the velocity line determines whether the acceleration is negative or not. Summary 5: Describe how to use vectors to represent velocity and acceleration of an object. How can you tell from the directions of the velocity and acceleration vectors if the object is speeding up or slowing down?