University Physics (Mechanics) Lab reports (Constant Acceleration Motion) using a virtual physics labs (KET Simulation) as guided in the attached assignment instructions files. Below are detailed log in information for the KET Simulation for expert's access and installation link;
https://virtualphysicslabs.ket.org/my-account/view-order/31303/
Log in username: olowoyos
Log in password: D@rksail0rd
Go to order# 31303 (First Semester Bundle)
Click on VPL-firstsemester.zip, download and install on expert's computer system for lab simulation.
Follow instructions for lab report criteria and assignment submission rubic on the lab manual and template attached.
Please "do not submit solution in zip format", vet for plagiarism and submission deadline is today (18 Hours window) to be strictly adhered to as required (2100 US TimeZone -5 Central Time).
Microsoft Word - Constant Acceleration Motion in OneDimension.doc Page 1 of 7 Constant Acceleration Motion in One Dimension (along a straight line). Introduction and Theory: In a wide range of motions, the velocity can change from moment to moment. To provide a measure of how much the velocity changes in time, the concept of acceleration is introduced. Average acceleration = or aave = . The average acceleration is a vector that points in the same direction as the change in the velocity. The unit of acceleration is m/s2. By analogy to velocity, when the time interval for measuring the acceleration becomes extremely small, the average acceleration becomes equal to the instantaneous acceleration: a = = For most people, acceleration means speeding up. And when an object is slowing down, we sometimes say it is decelerating. But deceleration does not mean that the acceleration is necessarily negative. The sign of acceleration indicates the direction of the acceleration but doesn’t directly show whether the speed is increasing or decreasing. For a motion along a straight line, if velocity, v, and acceleration, a, have the same sign, the object is speeding up. If they have the opposite signs, it is slowing down (decelerates). If we produce a plot of velocity vs. time, the slope of the line tangent to this plot at some instant t represents the acceleration at time t. In case of uniformly accelerated motion (acceleration is constant) the velocity vs. time graph is a straight line. Derived from the definitions of velocity and acceleration, there are four basic kinematic equations governing the motion with constant acceleration. To simplify our notation, we assume that the initial time t0 = 0. The position at any given instant of time, t, of an object moving with constant acceleration a, having initial position and initial velocity v0, can be found as: x = x0 + v0t + at2 (1) The velocity (instantaneous) of an object after time t can be determined as: v = v0 + at (2) or, if we know the position x at time t, the velocity can be calculated from the following: v2 = v02 + 2a(x – x0). (3) Note that x represents position, not distance, and x – x0 is the displacement. Because in case of constant acceleration the velocity increases at a uniform rate, the average velocity, vave, will be always midway between the initial and final velocities: vave = (v0 + v). Page 2 of 7 x Fig. 1 Graphs of position (a), velocity (b) and acceleration (c) vs. time for a body moving with constant acceleration. Objects that move vertically near the surface of the Earth, either falling or having been projected vertically up or down, move with the constant downward acceleration due to gravity with magnitude of about g = 9.80 m/s2, if the air resistance can be ignored. Consider an object, initially at rest, v0 = 0, that at time t0 =0 is released from a height y above the ground. It falls down and after time t it reaches the ground. After inputting x0 =y and v0 =0 in equation (1) and rearranging it, we can find the gravitational acceleration (an unknown a) as: a = g = - . (5) Therefore, by measuring the distance an object travels for a specific amount of time under the influence of Earth’s gravitational acceleration, we can determine the value of g. Objectives: Ø To gain understanding of relationships between position vs. time and velocity vs. time in uniformly accelerated motion. Ø To determine the experimental value of the gravitational acceleration g on Earth using kinematic equations and video analysis. Equipment: VirtualPhysicsLabs environment - frictionless cart and track with ultrasonic motion sensor; pre- recorded video of freefalling objects; Graphical Analysis or Logger Pro software. Procedure: Open KET simulation "Dynamics". Run the "Dynamics" lab. Familiarize yourself with the set- up. Page 3 of 7 PART 1. Uniformly accelerated motion along the dynamic track. Run 1. Car speeds up while moving away from motion sensor. A. Turn on brakes to hold the cart in place. Set the “Recoil” feature to 0. Tilt the track to an angle of - 2° (negative 2 degrees). Keep the time “Tmax” setting at 10 s. Drag the cart close to the left end of track. Turn on the motion sensor and release the brakes. Stop the recording when the cart reaches the other end of the track. Turn on the brakes. Fig. 2. Screenshot of sample recording for run 1A. How can you tell that the cart was not moving with constant velocity? In what way is this plot different from the position time graph for constant velocity motion? Turn on the position and time grids (right click on the graph window) and try to estimate distances traveled by the moving cart in two consecutive time intervals (for example between 3.0 – 4.0 s and 4.0 – 5.0 s). Does your estimate prove the change in velocity? Be sure to answer this question in discussion section. Copy the data to the clipboard and paste it to Logger Pro. Label the columns adequately (Time and Position) and enter correct units for each quantity. Double click on the graph and uncheck the option Connect Points. On the graph highlight the curved part corresponding to the cart moving along the track and fit the selected part of data to a quadratic equation of the same kind as equation (1) in the Introduction. Hint: Click the first from right icon on the tool bar or pull down the Analyze menu and choose the Curve Fit feature. In the Curve Fit window select Quadratic, make sure that the Fit Type is automatic and press Try Fit. If the fitting line matches your original data points (in the selected region) click OK. Page 4 of 7 Interpret the numerical values of the fit parameters – name the physics quantities they present. Calculate the acceleration using one of the parameters from curve fit. Calculate velocity as derivative of position data with respect to time. To accomplish this first select 3 points for derivative calculations in the Settings for startup (in the pull down File menu). Next, create new calculated column in the data table for velocity (Data → New Calculated Column è Functions è calculus è derivative (variable“Position”)). Insert a new graph showing velocity vs. time. Based on this graph, how can you tell that the acceleration was constant? Apply linear fit to the portion of constant acceleration motion. What does the slope of this line mean? Does it agree with the value of acceleration from the position vs. time fit? B. Tilt the track to a smaller negative angle of your choice and make a new run. Copy/paste the data to Graphical Analysis as a new data set. Add this new data to the existing position vs. time display and velocity vs. time graph window. Hint: Add the new data points to the existing displays by clicking the vertical axis label on the graphs, opening the Data Set 2 option and check-marking the columns of interest. Compare the curvature of the parabolas of both runs 1A and 1B. How did the curvature change as the acceleration of the cart changed? Apply the quadratic and linear fits as you did in part A. What coefficient of velocity vs. time equation tells us the magnitude of acceleration? What attribute of graphical representation of motion characterizes the direction of acceleration? Save the GA file for future reference. Organize your GA graph windows so they fit on one page, capture the screen and paste it into a Word file – you will have to attach it to your lab report. Run 2. Car speeds up while moving towards motion sensor. Tilt the track to an angle of + 2°. Make sure the brakes are on. Drag the cart close to the right end of track. Turn on the motion sensor and release the brakes.