Newton’s Second Law — Simulations

Objectives

Newton’s Second Law, \(\vec{F} = m \vec{a}\), is a cornerstone of classical mechanics. It relates the interactions of a system with its environment — forces — to its motion — kinematics. In this lab, we will measure the motion of accelerating systems and compare these measurements with the predictions of Newton’s Second Law.

For this lab, you carry out all three of the following experiments.

  1. Investigate force and acceleration for a cart on a ramp.
  2. Investigate force and acceleration for a cart and pulley system.
  3. Investigate force and acceleration for a pulley system.

Keep detailed notes. Record your procedure, data, and observations in your lab notes. Data will include tables and plots. In your memo, summarize your findings and observations and describe any conclusions you draw.

Measuring Force and Acceleration

You will need to analyze forces in this lab. The simplest approach is to use the weight of a known mass. If you hang a 100 \(\unit{g}\) mass from a pulley, the applied force will be equal to the weight: \(F = mg = \Quantity{0.980}{N}\). However, pulley systems also involve tension forces. If the system is accelerating, then the tension is not equal to the weight. Keep this in mind when you are comparing your measurements to your theoretical predictions.

You will have to use different methods for measuring acceleration. One involves a ruler and a stopwatch. If an object starts from rest and travels distance \(D\) in time \(T\) under the action of a constant force, then the average acceleration will be \(a = 2D/T^2\). The other uses data from a motion detector. The most reliable method for determining the acceleration with the motion detector is to fit a line to your velocity data and find its slope.

Experimental Systems

You will investigate three different systems today. After you take your data, work out the predictions of Newton’s Second Law for each system. In your memo, compare your data with these theoretical predictions.

Cart on a Ramp

A cart on a ramp will roll downhill due to gravity, but its acceleration is not \(\Variable{g}{9.80}{m/s^2}\). With this system, we can vary the mass of the cart and the angle of the ramp.

Before you take any data, consider the following questions. Try to make quantitative predictions.

  • What will happen to the acceleration of the cart as you increase its mass?
  • What will happen to the acceleration of the cart as you increase the angle of the ramp?

Now collect data. Open the Inclined Plane Lab from Physics Aviary. Play with the simulation to see how it works. When you are ready carry out two sets of measurements.

  • Keep the angle of the ramp constant. Measure the acceleration of the cart for at least three different masses. Record your data in a table and plot acceleration vs. mass.
  • Keep the mass of the cart constant. Measure the acceleration of the cart for at least three different angles. Record your data in a table and plot acceleration vs. angle.

Summarize any trends or patterns you observe in your memo. Compare your measurements with the predictions of Newton’s Second Law.

Cart and Pulley

A mass hanging over a pulley will accelerate a cart on a horizontal track. With this system, we can vary the mass of the cart and the hanging mass.

Before you take any data, consider the following questions. Try to make quantitative predictions.

  • What will happen to the acceleration of the cart as you increase its mass?
  • What will happen to the acceleration of the cart as you increase the hanging mass?

Now collect data. Open the Newton's Law Lab from Physics Aviary. Play with the simulation to see how it works. When you are ready carry out two sets of measurements.

  • Keep the hanging mass constant. Measure the acceleration of the cart for at least three different cart masses. Record your data in a table and plot acceleration vs. cart mass.
  • Keep the cart mass constant. Measure the acceleration of the cart for at least three different hanging masses. Record your data in a table and plot acceleration vs. hanging mass.

Summarize any trends or patterns you observe in your memo. Compare your measurements with the predictions of Newton’s Second Law.

Atwood’s Machine

Atwood’s “machine” is simply two masses hanging over a pulley. With this system, we can vary each of the two masses, \(m_1\) and \(m_2\) independently. However, in this portion of the lab we will vary the difference and the sum of the two masses separately: \(|m_1 - m_2|\) and \((m_1 + m_2)\).

Before you take any data, consider the following questions. Try to make quantitative predictions.

  • If you keep the total mass constant, what will happen to the acceleration of the system as you increase the difference of the masses?
  • If you keep the difference of the masses constant, what will happen to the acceleration of the system as you increase the total mass?

Now collect data. Open the Atwood Machine Lab from Physics Aviary. Play with the simulation to see how it works. When you are ready carry out two sets of measurements.

  • Keep the total mass constant. Measure the acceleration of the system for at least three separate mass differences. Record your data in a table and plot acceleration vs. mass difference.
  • Keep the mass difference constant. Measure the acceleration of the system for at least three separate total masses. Record your data in a table and plot acceleration vs. total mass.

Summarize any trends or patterns you observe in your memo. Compare your measurements with the predictions of Newton’s Second Law.

Further Exploration

The following activities are not required. If you have the time and the inclination, you may carry out these investigations for extra credit. You are also free to use any of the materials available in the lab to carry out your own investigations. You need to keep a record of your work (setup, procedure, data, analysis) to get credit for your efforts.

  • Complex System: The Atwood's Machine & Inclined Plane with Friction simulation from oPhysics gives you many adjustable parameters: ramp angle, cart mass, hanging mass, and coefficient of friction. Make a series of measurements to investigate how the acceleration depends on some or all of these parameters. Try to work out the theoretical prediction from Newton’s Second Law, and compare with your measurements.