Newton's Second Law Guide

PhysicsIntermediateReading time: 4 min

Overview

Investigate the quantitative relationship between acceleration, net force, and mass using the control variable method and a ticker tape timer to verify Newton's Second Law $F = ma$ .

Background

In 1687, Isaac Newton first systematically detailed the three laws of motion in his seminal work 'Philosophiæ Naturalis Principia Mathematica'. The second law reveals the quantitative relationship between force, mass, and acceleration, laying the foundation for classical mechanics. Newton summarized this universal law applicable to macroscopic low-speed objects by observing phenomena such as apples falling and the moon orbiting the earth, combined with mathematical derivation. This experiment will use the classic ticker tape timer to precisely measure acceleration using the method of successive differences and personally verify this great law.

Key Concepts

Acceleration ( $a$ )

a \ (\text{m/s}^2)

A physical quantity describing how fast velocity changes. The greater the acceleration, the faster the velocity changes. In uniform acceleration linear motion, $a = \Delta v / \Delta t$ .

Force ( $F$ )

F \ (\text{N})

The interaction between objects, which is the cause of changes in an object's state of motion. Force is a vector with magnitude and direction.

Mass ( $m$ )

m \ (\text{kg})

A measure of an object's inertia. The greater the mass, the harder it is to change its state of motion (accelerate or decelerate).

Control Variable Method

When studying multi-variable problems, keep other variables constant and change only one variable to explore the influence of that variable on the result.

Formulas & Derivation

Newton's Second Law

F = ma

The acceleration of an object is directly proportional to the net external force acting on it and inversely proportional to its mass. The unit of force 'Newton' is defined from this: the force required to accelerate a

1\text{kg}

object by

1\text{m/s}^2

1\text{N}

acceleration by successive difference

a = \frac{(x_4+x_5+x_6)-(x_1+x_2+x_3)}{9T^2}

Calculate acceleration using the successive difference method with the displacement between 6 adjacent counting points on the ticker tape.

T

is the time interval between adjacent counting points (in this experiment

T = 0.1\text{s}

). This method makes full use of data to reduce accidental errors.

Experiment Steps

1
Investigate the relationship between acceleration and force
Keep the cart mass $M = 0.5\text{kg}$ constant. Set the pulling force $F$ to $1.0\text{N}$ , $1.5\text{N}$ , $2.0\text{N}$ , and $2.5\text{N}$ in turn, perform the experiment respectively, and record the acceleration. Observe: specific mass being constant, how does acceleration change with pulling force? (Hint: Try to draw an $a\text{-}F$ graph)
2
Investigate the relationship between acceleration and mass
Keep the pulling force $F = 1.0\text{N}$ constant. Set the cart mass $M$ to $0.5\text{kg}$ , $1.0\text{kg}$ , and $1.5\text{kg}$ in turn, perform the experiment respectively, and record the acceleration. Observe: specific force being constant, how does acceleration change with mass? (Hint: Try to draw an $a\text{-}1/M$ graph)
3
Analyze ticker tape
Observe the distribution of counting points on the ticker tape. Take 1 counting point every 5 dots, and the time interval between adjacent counting points is $T = 0.1\text{s}$ . Measure the distance between adjacent counting points $x_1, x_2, ..., x_6$ . Think: Why does the distance between adjacent counting points become larger and larger? What kind of motion does this indicate the cart is doing?
4
Introduce friction
Adjust the friction coefficient from $0$ to $0.1$ or higher. Repeat the experiment in Step 1 and observe the deviation of the measured acceleration from the theoretical value. Think: What is the difference between the experimentally measured acceleration and the theoretical value? How to explain this difference? How to 'balance friction' in actual experiments?

Learning Outcomes

Accurately describe the content and physical significance of Newton's Second Law
Master the application of the control variable method in physics experiments
Proficiently use the successive difference method to process ticker tape data and calculate acceleration
Understand the experimental conclusions of $a \propto F$ (constant mass) and $a \propto 1/m$ (constant force)
Analyze sources of experimental error and propose improvement measures

Real-world Applications

Car acceleration performance: Providing greater thrust from the engine or reducing the body mass can improve acceleration performance. F1 racing cars use carbon fiber bodies precisely to reduce mass.
Rocket launch: Rocket fuel combustion provides thrust. As fuel is consumed and mass decreases, acceleration continues to increase with constant thrust.
Elevator startup: When an elevator accelerates upwards from rest, the 'overweight' feeling people experience is a manifestation of the net external force.
Airbag: Reducing impact force by extending collision time is essentially using the deformation of $F = ma$ , $F = m \cdot \Delta v / \Delta t$ .
Sports training: The starting acceleration of a sprinter is directly related to the ground kick force and body weight, which is also the scientific basis for weight control.

Common Misconceptions

Misconception

Force is the cause of maintaining object motion

Correct

Force is the cause of changing an object's state of motion, not maintaining it. When an object is not subject to force, it will maintain uniform linear motion or remain stationary (Newton's First Law).

Misconception

Acceleration is directly proportional to velocity; the greater the velocity, the greater the acceleration

Correct

There is no direct relationship between acceleration and velocity. An object can have a high velocity but zero acceleration (uniform motion), or zero velocity but high acceleration (moment of starting).

Misconception

Heavier objects fall faster

Correct

In a vacuum (ignoring air resistance), objects of different masses fall with the same acceleration. Although gravity

F = mg

is proportional to mass, sine

a = F/m = g

, acceleration is independent of mass.

Ready to start?

Now that you understand the basics, start the interactive experiment!

Start Experiment Start Quiz

Overview

Background

Key Concepts

Acceleration (aaa)

Force (FFF)

Mass (mmm)

Control Variable Method

Formulas & Derivation

Newton's Second Law

acceleration by successive difference

Experiment Steps

Investigate the relationship between acceleration and force

Investigate the relationship between acceleration and mass

Analyze ticker tape

Introduce friction

Learning Outcomes

Real-world Applications

Common Misconceptions

Further Reading

Ready to start?

Acceleration ( $a$ )

Force ( $F$ )

Mass ( $m$ )