KINEMATICS LAB 2: VELOCITY AND ACCELERATION

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1 Physics 8/ICP Kinematics Lab 2 (v.1.0) p. 1 NAME PARTNER DATE TA Lab Day/Time KINEMATICS LAB 2: VELOCITY AND ACCELERATION Introduction In this lab, you will continue to explore motion graphs, this time focusing on velocity and acceleration. The main idea is for you to become comfortable at translating back and forth between graphs and real-life motion, and to understand acceleration at a deep, intuitive level. Even if you found the last lab easy, parts of this lab will challenge you. Particularly hard questions are marked with a star or a double star. As you know, acceleration is the rate of change of velocity with time. Whenever the velocity changes, there is an acceleration. Equipment You will find the relevant computer files in the Kinematics Lab 2 folder. Once inside that folder, double click on the file Kinematics Lab 2A. Position and velocity graphs should open. The motion detector has an easier time tracking the cart s motion if there is part of an index card attached to the cart s back side, providing a large flat surface. Use tape to attach a card to the cart if there isn t already one on it. The detector should be pointing roughly down the track. If you find that you re not getting good data, try angling the detector slightly upward. I. Warm-up activity Let s start with a simple case of accelerated motion: a cart rolling down a ramp. Use the screws on the feet of the track to make a ramp angled down away from the detector. The ramp angle should be very small, so that the cart takes a few seconds to roll down the track. Hit the Collect button in the top right of the toolbar. When the detector starts clicking, release the cart from rest. Record data only until the cart reaches the bottom of the ramp: these first questions are only about the speeding-up motion as it rolls away from the detector. Repeat the experiment, if necessary, until you get nice graphs. Sketch the results on the axes at the top of the next page. In your sketches, smooth out any small bumps.

2 Physics 8/ICP Kinematics Lab 2 (v.1.0) p. 2 GRAPHS OF SPEEDING-UP MOTION 1. In last week s lab, most position vs. time graphs consisted of straight line segments. Here, by contrast, the position graph is curved. Using everyday, common sense language, explain why the position graph is curved as it is (concave up or concave down?), and how that relates to the velocity graph. 2. Imagine instead that the cart traveled along a flat, straight track at constant speed. Sketch what the position and velocity curves would be in that case. 3. Prediction: Using the axes to the right, sketch the cart s acceleration when it rolled down the ramp. To check your answer, use the file Kinematics Lab 2B. If the result disagrees with your prediction, make your correction using a dashed line. (Ignore the little up-and-down fluctuations, and focus instead on the general shape of the result.)

3 Physics 8/ICP Kinematics Lab 2 (v.1.0) p Prediction: Suppose you repeat the previous experiment, but with a somewhat steeper ramp. How do you think the velocity and acceleration graphs will be different from before? Will the acceleration still be constant? What will be different? First answer in words here: Also sketch your predictions here. Now do the experiment, using the black stand to raise the detector-end of the track. If necessary, double click on the vertical axis and choose Axis Options to change the range of values shown so you can clearly see the result. Also ignore any data that gets collected after the cart hits the end of the track. If the results differ from your predictions, sketch them on these same axes, using dashed lines. 5. How is the magnitude (size) of the acceleration represented on a velocity vs. time graph? II. Slowing down In this experiment, you ll attach a brake to the cart, and roll it along a flat track (not a ramp). The cart slows down after you release it, due to friction. Lay the track flat on your lab bench. Place the cart on the track to check if the track is level. If not, find a way to level it: it s probably easier to raise or lower the right end than the left end. Lower the position of the index card so that it scrapes some along the track. This will act as our brake.

4 Physics 8/ICP Kinematics Lab 2 (v.1.0) p Predictions. You re going to give the cart a brief push away from the detector. Sketch your predictions for the velocity vs. time and acceleration vs. time graphs of the cart after it has left your hand, and while it is slowing due to friction. Do the experiment a few times, until you get a good run. Start collecting when you begin pushing the cart. If the acceleration is too large or too small to see easily on the graph, double click the vertical scale and choose Axis Options to choose a different scale. Record your results here. Label these RESULT graphs with A at the spot where you started pushing. B at the spot where you stopped pushing. C at the spot where the cart hit the end of the track or got caught, or where it came to rest on its own. 7. Consider only the period between when you stopped pushing and the cart hit the end (or came to rest). Do the shapes of the velocity and acceleration graphs agree with your predictions? How is the sign of the acceleration represented on a velocity vs. time graph?

5 Physics 8/ICP Kinematics Lab 2 (v.1.0) p Prediction: Consider again the braking experiment, but now with a small twist: You start the cart near the far end of the track, and give it a push toward the detector. (a) After the cart leaves your hand, will the acceleration be positive or negative? Explain. (b) Sketch your predictions for the velocity vs. time and acceleration vs. time graphs. Now test your predictions, and sketch the results below. Label these RESULT graphs with A at the spot where you started pushing. B at the spot where you stopped pushing. C at the spot where the cart hit the end of the track or got caught, or came to rest on its own.

6 Physics 8/ICP Kinematics Lab 2 (v.1.0) p In question 8, why is the acceleration positive even though the cart is slowing down? Explain it in terms that... (a)...a mathematician would find acceptable. Hint: Look at your v vs. t graph. (b)**...a younger sibling would find understandable and convincing. III. Up and down a ramp In this activity, you will give the cart a brief push up a ramp, and you ll let it slide up and then back down. This is similar to throwing a ball straight up in the air, but the motion is slower and easier to study. So, your graphs and explanations in this experiment apply equally well to a ball going up and down. Because we usually consider up to be the positive direction, for this experiment we are going to place the detector at the bottom of the ramp by raising the opposite side of the track. That way as the cart travels up the ramp, the detector will record the its position as increasing in the positive direction. 10. Predictions. Suppose you throw a ball straight up in the air, or give a cart a brief push up a ramp and then release it. (a) What is the velocity at the moment the ball or cart reaches its highest point (and is about to start back down)? Explain. (b) At this same moment, is the acceleration positive, negative or zero? (Assume that the positive direction is upward for the ball, and up-the-ramp for the cart.) Why?

7 Physics 8/ICP Kinematics Lab 2 (v.1.0) p Sketch your predictions for the velocity vs. time and acceleration vs. time graphs of the cart. Your predictions should indicate the point at which your hand lets go of the cart, and should also indicate the point at which the cart reaches its highest point. Move the index card so that it no longer brakes the cart, but still acts as a large flat surface for the detector to see. Place the right hand end of the cart on the black stand. When you push the cart away from the detector, don t push so hard that the cart bumps the top of the track. We want the cart s motion to be slowed by gravity, not a collision. Try the experiment. Start the motion just when hear the detector clicking. Give the cart a push up the ramp, but release it quickly. After getting a good run, sketch your results. Again, if you need to change the vertical axis, double click on it and choose Axis Options. Label both graphs with A where the cart started being pushed. B where the push ended (i.e., where your hand left the cart). C where the cart reached its highest point (and is about to start down). D where the cart got caught.

8 Physics 8/ICP Kinematics Lab 2 (v.1.0) p (a) Explain, in both mathematical and non-mathematical terms, why the acceleration is not zero at the top of the cart s motion, even though it isn t moving there. (b) Why is the acceleration negative even when the cart is speeding up (on its way down)? Measuring g Move the stand so that the detector-end of the ramp is once again raised. For the following, you will release the cart from rest at that end, and read off the resulting acceleration from the acceleration vs. time graph. We will see later in the semester that the acceleration due to gravity in this case is given by a = g sinθ, where θ is the angle that the track makes with the horizontal. (We hope this makes some intuitive sense: When the track is horizontal (so θ = 0 and sinθ = 0), there is no acceleration due to gravity (a = 0). If the track is vertical, θ = 90, the object is in free fall, and a = g.) Take measurements of a for 4-5 different values of θ. (Be sure to measure θ too.) Record your data below. Then plot a vs. sinθ on the graph paper.

9 Physics 8/ICP Kinematics Lab 2 (v.1.0) p. 9

10 Physics 8/ICP Kinematics Lab 2 (v.1.0) p Use your data to estimate a value for g. Explain your method. 14. How certain are you of your answer? (To within 0.1%? 1%? 10%? 50%?) Don t judge based on how close you come to 9.8 m/s 2 ; instead estimate the possible spread given by your data. *15. How would your data and results be affected if you began each run by giving the cart a push up the ramp instead of releasing it from rest? Explain.