Group member names: -Jennifer Russell Laboratory Activity 3: Acceleration Graphs -Jeff Evans -Holly Pelt 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. 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? The velocity graph turned out similar to our prediction, but the acceleration was more constant than we had predicted. The line being straight and increasing on the velocity graph shows that it is speeding up at a constant rate. The line being horizontal and above the axis on the acceleration graph shows that it was constantly accelerating. Both graphs being positive the whole time means that the car was moving away from the detector and increased speed until we stopped it. 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. - 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? The result was just as we predicted. The negative constant slope of the velocity graph shows that the car is moving toward the detector at a constant rate. The horizontal line below the horizontal axis on the acceleration graph shows the same thing. Both graphs being negative means that the car was moving toward the detector the whole time. 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. 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? The result was similar to our prediction. The velocity line is below the axis, so it is moving toward the detector. The line is increasing with a constant slope, so it is slowing down at a constant rate. 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? The signs are not the same. The acceleration graph has the same sign as the slope of the velocity graph. The negative velocity and positive acceleration tells us that the cart was moving toward the detector, but constantly decreasing velocity. Velocity Acceleration 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. 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.) 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 the velocity graph changes signs, it means that the cart stopped moving away from the detector and began to move toward it. When the velocity is zero, the car is instantly not moving as it makes the transition from moving away to moving toward the detector. The acceleration never changes signs, because after the initial push, the fan is the only force acting on the cart. The fan consistently pushes the cart toward the detector, giving it a constant negative acceleration. 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) b 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 rate of acceleration. The rate is increasing when the line is above the axis, the velocity is constant on the axis, and decreasing below the axis. 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? The graph of acceleration is the graph of the slope of the velocity graph. The distance of the acceleration graph from the horizontal axis tells us the rate at which the velocity of the object is increasing or decreasing. The distance of the velocity graph from the horizontal axis tells us how fast the object is moving at any given time. (In both cases, the line above the axis means positive acceleration or velocity, and below the axis means negative acceleration or velocity.) 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 observed that when the car is accelerating quickly, the slope of the velocity graph is high, and when the car is accelerating slowly, the slope of the velocity graph is not as high. The faster our cart moved, the higher the graph of velocity was. 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. An object is speeding up if the velocity line has a positive slope or if the acceleration graph is above the axis. An object is slowing down if the velocity graph has a negative slope or if the acceleration graph is below the axis. If both graphs are positive, the object is moving away from the point of reference and increasing velocity. If both graphs are negative, the object is moving toward the point of reference and the object is moving faster as time passes (the velocity is negative). If velocity is positive and acceleration is negative, the object is moving away from the point of reference and it is slowing down. If the velocity is negative and acceleration is positive, the object is moving toward the point of reference and slowing down. 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?