Pre Laboratory Work-MTSU.

Pre-Laboratory Work (estimated time 45 mins) Part I: Problem 1. Consider a cart moving along an incline of angle  with respect to the horizontal plane. a. Suppose you give an initial push to the cart that starts at the bottom of the incline. Your push is in the upward direction along the track. Assume that the incline and the cart are frictionless. Describe the motion of the cart right after the push. b. Is the velocity of the cart constant? Is the acceleration constant? c. The diagram below shows the cart (represented by a box) at initial time (t0) and final time (t3) (the cart is moving from the bottom to the top of the incline). Draw the position of the cart at times t1 and t2, such that the time intervals (t1-t0), (t1-t2) and (t3-t2) are all equal. Also, indicate the velocity and acceleration vectors at each of the four time instants (t0, t1, t2, and t3) in the figure below. d. Suppose that the distance between the initial and the final positions drawn on the previous figure is 0.8 𝑚, the initial velocity of the cart is 0.5 𝑚/𝑠, and (𝑡3 − 𝑡0 ) = 1.3 𝑠. Find the value of 𝑎. Show your work explicitly. e. Find the velocity of the cart when it reaches the final position (at 𝑡3 ). f. Does the acceleration depend on the angle of inclination of the track? If so, how? Date Modified: 04/18/19 Project I Lab 1 – Kinematics Page 1 g. What do you think are the initial experimental conditions that affect the motion of the cart? List them below. Part II: Discretization of the kinematic equations: a. Watch the video “Project 1 video 1” that you can find in E-learning. b. Write down the equation for the numerical evaluation of the derivative of the velocity with respect to time as explained in the video. End of Pre-Laboratory Work Date Modified: 04/18/19 Project I Lab 1 – Kinematics Page 2 Auto Run #1 Run #1 Run #1 Run #1 Position Angle of Incline Time (s) Speed (m/s) Speed (m/s) Speed (m/s) Speed (m/s) (m) 3 degrees 2,477 0,66 0 2,922 0,54 0,3 3,428 0,47 0,6 4,186 0,29 Time (s) Speed (m/s) Acceleration 2,477 0,66 0,26 2,922 0,54 0,28 3,428 0,47 0,13 4,186 0,29 0,06