Force, Mass, and Acceleration Worksheet

Introduction

In this worksheet, you'll design and conduct experiments to investigate Newton's Second Law of Motion, which states that $$F = ma$$ where F is the force applied to an object, m is its mass, and a is the resulting acceleration.

Part 1: Designing Your Experiments

Experiment A: Relationship between Force and Acceleration (Constant Mass)

Design an experiment to test how changing the applied force affects the acceleration of an object with constant mass.

  1. What materials will you need for this experiment?

  1. What will be your independent variable? _____________________________

  2. What will be your dependent variable? ______________________________

  3. What variables will you keep constant? ______________________________

  4. Describe your experimental procedure in steps: a. _________________________________________________________________ b. _________________________________________________________________ c. _________________________________________________________________ d. _________________________________________________________________ e. _________________________________________________________________

Experiment B: Relationship between Mass and Acceleration (Constant Force)

Design an experiment to test how changing the mass affects the acceleration of an object with constant force.

  1. What materials will you need for this experiment?

  1. What will be your independent variable? _____________________________

  2. What will be your dependent variable? ______________________________

  3. What variables will you keep constant? ______________________________

  4. Describe your experimental procedure in steps: a. _________________________________________________________________ b. _________________________________________________________________ c. _________________________________________________________________ d. _________________________________________________________________ e. _________________________________________________________________

Part 2: Data Collection

Experiment A: Force and Acceleration Data

Trial Force (N) Time (s) Distance (m) Acceleration (m/s²)
1
2
3
4
5
  1. Calculate acceleration for each trial using the formula: $$a = \frac{2d}{t^2}$$ (for constant acceleration from rest) where $$d$$ is distance and $$t$$ is time.

Experiment B: Mass and Acceleration Data

Trial Mass (kg) Time (s) Distance (m) Acceleration (m/s²)
1
2
3
4
5
  1. Calculate acceleration for each trial using the same formula.

Part 3: Creating Graphs

Force vs. Acceleration Graph (Constant Mass)

  1. Create a graph with force on the x-axis and acceleration on the y-axis.
    • Label your axes with units
    • Plot each data point from Experiment A
    • Draw a line of best fit

![Graph paper for Force vs. Acceleration]

  1. Describe the relationship shown in your graph:

  2. What is the mathematical relationship between force and acceleration based on your data?

Mass vs. Acceleration Graph (Constant Force)

  1. Create a graph with mass on the x-axis and acceleration on the y-axis.
    • Label your axes with units
    • Plot each data point from Experiment B
    • Draw a line of best fit

![Graph paper for Mass vs. Acceleration]

  1. Describe the relationship shown in your graph:

  2. What is the mathematical relationship between mass and acceleration based on your data?

Part 4: Data Analysis

  1. According to Newton's Second Law, what should be the relationship between:

    a. Force and acceleration (when mass is constant)?

    b. Mass and acceleration (when force is constant)?

  2. Calculate the following values from your experimental data:

    a. Using data from Experiment A: If $$F = ma$$, then $$m = \frac{F}{a}$$ Calculate the mass for each trial: ________________________________

    Average calculated mass: _______________________________________

    Actual mass used: ____________________________________________

    Percent error: ________________________________________________

    b. Using data from Experiment B: If $$F = ma$$, then $$F = m \times a$$ Calculate the force for each trial: _______________________________

    Average calculated force: ______________________________________

    Actual force applied: __________________________________________

    Percent error: ________________________________________________

  3. Do your experimental results support Newton's Second Law? Explain using specific evidence from your data.

  4. What were possible sources of error in your experiments?

  5. How could you improve these experiments in the future?

Challenge Question

  1. If you double the force applied to an object while keeping the mass constant, how would the acceleration change? Use mathematical reasoning to explain your answer, then check if your experimental data supports this prediction. _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________
Last modified: Tuesday, 25 February 2025, 3:41 PM