# Lab 3 Acceleration. What You Need To Know: Physics 211 Lab

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1 b Lab 3 Acceleration Physics 211 Lab What You Need To Know: The Physics In the previous lab you learned that the velocity of an object can be determined by finding the slope of the object s position vs. time graph. Δx v ave. = Δ t v ave. is the average velocity (in meters per sec., m/s) Δx is the change in position [rise] (in meters, m) Δt is the change in time [run] (in seconds, s) The next concept in motion, acceleration, can be found in a similar fashion. An object is accelerating when it is changing its velocity. The equation for average acceleration is v Δv a ave. = Δ t a ave. is the average acceleration (in, m/s 2 ) Δv is the change in velocity [rise] (in, m/s) Δt is the change in time [run] (in seconds, s) This equation tells you that in looking at a velocity vs. time graph you will be able to determine the acceleration of an object. Therefore, in this lab, you can use all of the concepts you learned in the previous lab on determining slopes. However, in this case, you will be using a v vs. t graph instead of an x vs. t graph. FIGURE 1 Positive slope t Let s review some of those ideas. The first thing you learned in last week s lab was that in moving away from the sensor you are moving in the positive direction thus you have a positive velocity. The opposite is also true. In moving towards the sensor you have a negative velocity. v You learned that if your vertical value on the graph is increasing while moving to the right along the horizontal axis, then you have a positive slope. See Figure 1. The opposite is also true. If your vertical value decreases while moving to the right along the horizontal axis then you have a negative slope. See Figure 2. You also learned that if your plotted line is straight then you will have a constant slope and therefore a constant velocity. You will still be using these ideas for this lab. FIGURE 2 Negative slope t Common Acceleration Misconceptions One misconception is that when an object s velocity at a particular time is zero then the acceleration of the object is also zero. This is not always the case. Acceleration is the CHANGE in velocity over a period of time (a = Δv/Δt) not just velocity over time (not a = v/t). For example, when you throw a ball up in the air it stops briefly at the peak before it comes back down. We would say that v = 0. However the acceleration is not zero because the velocity is still changing as the ball stops for an instant of time. You will be doing an experiment in this lab to show this idea.

2 What You Need To Do: The Equipment For this lab you will be using a track, a cart with an acceleration fan, and a motion sensor. See Figure 3. Attach the fan to the cart using two rubber bands as shown below. Place the cart with the fan on the track and make sure it is in working order. Since the batteries drain quickly, only turn on the fan when performing an experiment. FAN RUBBER BAND + CART MOTION SENSOR TRACK FIGURE 3 - Equipment Set-up (NOT DRAWN TO SCALE) ADJUSTABLE FEET There are colored arrow stickers on both sides of the fan that point in the direction of the acceleration caused by the fan. If the arrow is pointing away from the sensor then the acceleration of the cart is positive. If the arrow is pointing towards the sensor then the acceleration is negative. See Figure 4 for a chart of all sign conventions. Description Vel. Cart moving away from sensor + Cart moving towards sensor Description Accel. Arrow pointing away from sensor + Arrow pointing towards sensor FIGURE 4 - Sign Conventions v Before you begin, you should level the track. With the fan off, place the cart on the track and let it go from rest. If the track is level the cart will not move. If the cart moves then adjust the feet underneath the track (See Figure 3) to level the track. t FIGURE 5 - v vs. t graph Part 1 Constant Velocity You should already know, based on last week s lab, what a graph of constant velocity looks like in a v vs. t graph. Begin your lab report by making two v vs. t graphs: one of a positive constant velocity and one of a negative constant velocity.

4 Question 4 Based on the linear fit line, do you have a positive or negative acceleration? How can you tell from the graph? Question 5 Based on the linear fit line, do you have an increasing, decreasing, or constant acceleration? How can you tell from the graph? From the information in the little window, record the acceleration of the cart. Do two more trial runs and record those accelerations. Question 6 What do you conclude about the acceleration offered by the fan? Is it changing or roughly constant? Make a chart like Figure 6. (You will fill in the chart as you progress through the lab. Do not fill out the entire chart now.) The first row is for the motion you are currently doing (i.e. Part 2) in which your cart started close to the sensor and moved away. Put in a + or a in the v and a columns for the first row. In the fourth column, write down the motion of the cart; was it speeding up or slowing down? Keep in mind the sign conventions that were given to you in Figure 4 on the previous page. Fill in the first row now. Part v a Motion of cart FIGURE 6 Motion Chart v Part 3 Changing Velocity Towards The Sensor Take your cart and place it about 140 cm from the motion sensor. Make sure the arrow on the fan is pointing towards the sensor. Make a v vs. t graph like the one in Figure 5. Turn on the fan and release the cart WITHOUT THE COMPUTER SOFTWARE RUNNING. NOTE: Make sure someone is always ready to catch the cart at the end of the t

5 track before it hits the motion sensor. Examine the motion of the cart and fill in your v vs. t graph based on your observations on the motion of the cart. Repeat the above procedure with the computer tracking the cart. Sketch the graph on the computer screen next to the one that you just made. Compare the two graphs. Are the graphs the same? If not, then what error did you make in your reasoning? Question 7 In examining the graph on the computer, is the velocity of the cart positive or negative? How can you tell from the graph? Question 8 In examining the graph on the computer, do you have an increasing, decreasing, or constant velocity? How can you tell from the graph? On the computer screen, highlight the area of your graph that matches the motion from when you released the cart until just before you stopped it. Click on R= for your linear fit. Question 9 Based on the linear fit line, do you have a positive or negative acceleration? How can you tell from the graph? Question 10 Based on the linear fit line, do you have an increasing, decreasing, or constant acceleration? How can you tell from the graph? Go back to your motion chart that you made like Figure 6. For the row Part 3, fill in the columns for v, a, and Motion. It is often believed that when an object has a negative acceleration that the object will slow down. Is this the case for Part 3?

6 Part 4 Opposite Velocity And Acceleration NOTE: You do not need the computer software for this part. Take the cart and place it at 50 cm away from the sensor with the arrow pointing towards the sensor. Turn on the fan. Give the cart a push away from the sensor and catch the cart when it stops at its peak. Based on what you observed, fill in the row corresponding to Part 4 in your motion chart. (Do not take into account the acceleration of the cart due to your hand pushing on the cart. Only take into account the acceleration due to the fan.) Was the cart s velocity +/? How can you tell? Was the cart s acceleration +/? How can you tell? What kind of motion did the cart have? Part 5 Opposite Velocity And Acceleration Again Take the cart and place it 140 cm away from the sensor with the arrow pointing away from the sensor. Turn on the fan. Give the cart a push towards the sensor and catch the cart when it stops at its peak. Based on what you observed, fill in the final row in your motion chart. Before answering the next question, ask your TA to come over and check to make sure that your motion chart is correct. Question 11 Upon examining your completed motion chart, write down an overall statement that you can make about the relationship between velocity of an object, acceleration of an object, and its motion.

8 Using a spreadsheet provided, make a plot v vs. t. Format the graph with large axis labels (including units) so it is easy to read. Compare the graph you plotted and the one you sketched in Question 12. Were the graphs the same? If not, then what error did you make in your reasoning? Using your plotted graph, calculate the acceleration of the object. Again, make sure you use all that you learned from the Graphical Analysis lab. Using a percent error, compare your calculated value for the acceleration and its true value. Question 13 What were the signs (+ or ) for your velocity and acceleration of the object according to our defined system? Question 14 What kind of motion did the object have ( speeding up or slowing down )? Does this agree with what you learned from the Figure 6 Motion Chart? Part 7 Back And Forth Motion Re-open the ACCELERATION file. Take the cart and place it 170 cm away from the sensor with the arrow pointing away from the sensor. Turn on the fan, push COLLECT on the computer, and give the cart a push towards the sensor. Let the cart move towards the sensor and then back to its starting point. Repeat this until the cart turns around at just about 50 cm from the sensor AND you have a smooth graph while the cart is freely moving. Make a sketch of this graph in your lab report.

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