Kinematics - Velocity and Acceleration

Lab #4: Kinematics - Velocity and Acceleration

Introduction:

The purpose of this lab is to discover and understand the relationships between position, velocity, and acceleration. Additionally, constant/uniform acceleration due to the force of gravity will be examined to find possible mathematical relationships to position and velocity. Velocity and acceleration are changes in position and velocity, respectively, with regards to time. This change can be shown mathematically in calculus derivatives:

EQ 1.

EQ 2.

As dt decreases in value, the instantaneous velocity and acceleration can also be found. Furthermore, if constant acceleration is established, two basic relations between distance, velocity, and the constant acceleration can be found:

EQ 3. EQ 4.

In any environment near Earth, the acceleration in the vertical direction is constant at a value of g=9.8m/s2 towards the center of Earth or often written as g=-9.8m/s2. In such an environment there is no natural acceleration in the horizontal direction, thus the horizontal motion is analyzed independently of the vertical motion. Thus it can be established that the general form of a position curve for a projectile would follow an inverse parabola shape and the maximum height occurs when vertical velocity is zero. By calculus derivation, it can also be found that the velocity graph would display a linear line with a negative slope.

Procedure:

This lab consists of two separate but related experiments, first one involving the study of the motion of a tossed ball and the second focusing on the precise measurement of the value of g with the use of a photo-gate detector.

Materials

* DataStudio software

* Ball

* Motion Detector

* Photo-gate Detector

* Picket Fence

Motion of a Tossed Ball

In the first part of the experiment, a motion detector was used to collect data on distance, velocity, and acceleration for a ball thrown upward. After opening the file for 'Ball...