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Worksheet 2

In this lab, we will explore fundamental measurement techniques in mechanics, focusing on motion analysis. Precise data collection and interpretation are essential in experimental physics, and this lab will provide hands-on experience with uncertainty propagation, numerical differentiation, and theoretical comparisons.

Motion of a Smart Cart on an Inclined Plane

We will analyze the motion of a smart cart rolling down an inclined plane. The cart is equipped with position and acceleration sensors and will wirelessly transmit real-time data to a computer using Capstone.

Figure 1: Smart cart on inclined track with ruler to measure height of track.
  • We will raise one end of the track to different heights (5 cm, 10 cm, and 20 cm) and record position, velocity, and acceleration data simultaneously.
  • The cart will be released without pushing to ensure that only gravity influences its motion.
  • The collected data will be used to generate plots for position, velocity, and acceleration as functions of time, allowing us to analyze how each variable changes.

Understanding Displacement, Velocity, and Acceleration

  • Displacement tells us where the cart is at any given moment relative to a starting point. It is measured directly using the cart’s position sensor.
  • Velocity is the rate of change of displacement, representing how fast the cart is moving and in which direction. Since the sensor does not directly measure velocity, we will compute it using finite difference approximations.
  • Acceleration is the rate of change of velocity and describes how the velocity evolves over time. The cart’s built-in accelerometer provides direct acceleration data, but we will also calculate it numerically for comparison.