<p> The Accelerating Cart Microcomputer-Based Lab</p><p>In this experiment you will investigate the connection between the net force applied to a cart on an inclined track and the acceleration of the cart. PROCEDURE</p><p>For this experiment you can use the software from the “Position, Velocity, and Acceleration” experiment. The only sensor used in this experiment is the ultrasonic motion sensor, which should be mounted on one end of the track.</p><p>1. Incline the track by placing a black bar under one pair of the track’s supporting legs. It is best if the motion sensor is at the highest point. Use the height of the black bar, which you can measure with vernier calipers, to help you find the angle at which the track is inclined.</p><p>Question 1: Describe how you will determine the angle at which the track is inclined. What else do you need to measure? Show how you combine your measurements to find the angle.</p><p>2. Release the cart from rest and record the cart’s motion as it accelerates down the track.</p><p>3. On the velocity graph, click and drag with the mouse to select a region in which the cart has an approximately constant acceleration down the track. Press the Regression button, , to do a straight-line fit to determine the cart’s acceleration (this is the slope of the straight-line fit). It is a good idea to repeat this measurement a few times to get an average value of the cart’s acceleration down the slope, as well as to get a feel for the uncertainty in your measurement.</p><p>4. Draw a free-body diagram showing the forces acting on the cart as it accelerates.</p><p>5. It is often convenient to choose a coordinate system so the acceleration is parallel to one of the coordinate axes, giving no acceleration along the other axis. Aligning your coordinate system with the direction of the cart’s acceleration, break the forces on your free-body diagram into components that are parallel to your coordinate axes.</p><p>6. Determine an expression for the net force acting on the cart. This should depend on one or more of the following: m, the mass of the cart; g, the acceleration due to gravity; and θ, the angle at which the track is inclined.</p><p>7. Use Newton’s Second Law to determine a predicted value for the cart’s acceleration.</p><p>Question 2: How does the value you measured for the acceleration in step 3 compare to the value you predicted the acceleration should be based on your free-body diagram? Do your two values show reasonable agreement? If you observe a discrepancy see if you can come up with one or more possible explanations for it.</p><p>8. Change the angle of the track (stacking up additional black bars is a convenient way to do this) and repeat the experiment. Do this as many times as you have time for.</p><p>1 The Accelerating Cart</p>