Group member names: Laboratory Activity 6: Force, Motion and Mass Objectives Explore how force is related to acceleration and velocity. Develop a quantitative understanding of the force relationship. Learn about proportional and inversely proportional graphs. Equipment Computer Track for cart Ultrasonic motion sensor 2 cart masses Force sensor 2 USB Links Pulley to mount on end of track USB hub String and cup for weight Dynamics cart Masses for hanging. Activity One: Force and motion Velocity Acceleration Prediction 1: Using the line tool on the drawing toolbar of Word, draw a line on both the velocity, acceleration and force graphs below predicting the shape of a curve for a cart starting at rest and being pulled with a constant force. Time Force Time Time Set up the equipment: Obtain 2 USB Links, a force sensor and a motion detector. Plug the USB links into the USB hub and that into the computer. Download from the website and then open in DataStudio the experiment file called MotionAndForce.ds to display force, acceleration and velocity graphs. Set the track on the table so one end is hanging off, place the motion detector at the other end. Attach the pulley so that it is on the end off the table. Attach the force sensor the cart on the magnet side by using the screw. Make sure the screw goes through the hole labeled “cart” and not “IDL bracket.” Hook the length of fishing line on the hook of the force sensor, run it over the pulley, with the cup over the end. Place both of the black cart masses on the cart. See diagram below. Experiment: Place the cart on the track about 30 cm (1 foot) away from the motion detector and turn it on, with one person holding it in position. Just before taking data, zero the force sensor without the string pulling on it. 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. Make sure that cord connecting the force sensor to the USB link is not inadvertently messing up your data. Do this by picking up the cord a couple feet from the sensor so that the cord is slack between your hand and the sensor and is not rubbing on the table or anything else. As the cart moves towards the end of the track, move your hand with it so that the cord remains slack the whole time it is in motion. This is especially important for the first few runs. Catch the cart just before it crashes into the other end of the track. Question 1: How did the result compare to your prediction? Explain how the velocity, acceleration graphs are related. Experiment 2: Measure the average force and average acceleration of the cart during the time it is moving freely. Do this by click-dragging a rectangle around the data points with the mouse, and then selecting “mean” from the “Statistics” button at the top of the window. Record the force and acceleration in the chart below. Keep your data in Data Studio and label the acceleration graph as to the mass of the cup and masses. Add masses to the cup hanging at the other end of the string and repeat, remembering to zero the force sensor with the string slack before each run. Fill out the chart below with the data from each run. Acceleration (m/s2) Force (N) Cup alone Cup + 10 g Cup +20 g Cup +30 g Cup + 40 g After labeling each run (at least on the acceleration graph) as to the weight involved, copy and paste your graph below. (Paste graph here.) Pull up the ForceVsAcceleration Data chart and enter the force and acceleration data in the table in DataStudio. The data chart is in a window hidden behind the original graph you have used. You may be able to find it by clicking on the name in the lower panel on the left-hand side. A graph of Force Vs. Acceleration will be automatically created for you in a different window, also hidden behind the first. If your graph is far from being a nearly straight line, pick out the most suspicious data points and re-do that run to check your data. The most common causes of error are forgetting to re-zero the force sensor while the string is slack before each run, not keeping the force sensor cord slack during the entire run, or failing to select data while the cart is freely moving. When you have a good graph, add a linear fit from the fit menu and paste the graph in the space below. -paste graph here- Question 2: Record below the slope of the fit on your graph, then measure the mass of the cart, force sensor and cart masses that you used Slope of graph Mass of cart (kg) Question 3: How does the acceleration relate to force? Can you write down a mathematical expression? Activity Two: Mass and motion Set up the equipment: Use the same equipment set up as in the first activity, except this time you will keep the mass in the cup the same at 20g, and you will vary the number of black cart masses on the cart. For the first run, remove all the cart masses so you have just the cart and the force sensor. If you still have data from the previous part, clear it. Experiment: As before, place the cart on the track about 30 cm (1 foot) away from the motion detector, zero the force sensor without the string pulling on it, start taking data just before releasing the cart, and hold the USB cable so that it doesn’t pull one way or another on the cart. Measure the average force and average acceleration of the cart during the time it is moving freely by selecting a box with the mouse. Record the acceleration in the chart below. (You have already determined the mass a cart with two masses; determine the mass of the masses and enter it for the mass in the first case.) Mass (kg) Acceleration (m/s2) Cart and force sensor Cart, sensor & 1 mass Cart, sensor & 2 mass Cart, sensor & 3 mass Cart, sensor & 4 mass Next, add one cart mass and repeat the experiment, recording the acceleration in the appropriate line. Repeat for 2, 3 & 4 car masses. (You will need to share cart masses with other groups at your table.) Then enter the mass and acceleration data in the second data chart DataStudio. A graph of Acceleration vs. Mass will be automatically created for you. If your data does not seem to approximate a smooth curve, re-do any suspicious data points. Add an ‘inverse fit’ from the fit menu. Paste the graph in the space below. -paste graph here- Question 4: Record below the “Scale Factor” of the fit on your graph, then the average applied force during the runs. (The inverse graph takes the form of y=A/x.) Scale Factor (A) Average force (N) Question 5: How does the mass relate to acceleration? Can you write down a mathematical expression that involves acceleration, force and mass? Activity Three: Force of gravity Question 6: In a previous laboratory activity, you observed the acceleration of several objects falling due to gravity. What did you observe to be the acceleration due to gravity? How did it change (or not change) due to different masses of dropped objects? Question 7: Now combine with what you have found out about the acceleration of objects due to gravity with what you have figured out about the relationship between force, acceleration and mass. Objects experience a constant acceleration due to gravity independent of how they are moving. Given what you have discovered about force and acceleration, what must be true about objects being accelerated due to gravity? Question 8: Previously, you observed that the acceleration of an object is the same independent of the mass of the object. Given what you have discovered about force, mass and acceleration, how must the force on an object due to gravity depend on its mass? Can you use your knowledge to come up with an equation to describe the force of gravity on an object? 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: Force is directly related to which of the motion quantities? How does changing the force change its motion? Summary 2: How does mass of the object affect motion and force? Can you write down an expression that relates force, mass and acceleration? Summary 3: Given the above information and that all objects experience a constant acceleration due to gravity, the force due to gravity must be what? Summary 4: 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?