How Do Forces Influence Motion?
Force
A force is a mechanical interaction between two objects or bodies.
- Early explanations of motion were based largely on observation and reasoning rather than experimentation.
- Philosophers in ancient times attempted to explain why objects move and fall, but they lacked precise scientific concepts such as velocity, acceleration, and force as we define them today.
Aristotle’s View of Motion
- Aristotle was a Greek philosopher who lived in the 4th century BCE.
- He believed that:
- Heavier objects fall faster than lighter objects
- A force is required to keep an object moving
- These ideas appeared reasonable at the time because:
- There were no clear definitions of velocity or acceleration
- No controlled experiments were carried out
Aristotle’s ideas were based mainly on observation and reasoning, not experimentation.
Galileo’s Contribution
- In the late 16th century, Galileo Galilei tested Aristotle’s ideas using experiments.
- Galileo found that:
- Objects fall at the same rate regardless of mass (if air resistance is negligible)
- An object with no resultant force acting on it:
- Continues moving at a constant speed in a straight line
- Or remains at rest if it was initially stationary
Why We Need Laws to Describe Motion
- Objects around us move in many different ways, such as falling, sliding, turning, or stopping.
- Simply observing motion is not enough.
- Scientists need rules that apply to all situations.
- Newton developed laws that explain how forces are linked to changes in motion.
- These laws allow predictions to be made before motion occurs.
Newton's First Law: Constant Velocity Requires No Resultant Force
Newton's First Law of Motion
Newton's first law states, "An object remains at rest or continues to move at constant velocity unless acted on by an external resultant force."
- Objects do not naturally slow down or stop on their own.
- If an object is not speeding up, slowing down, or changing direction, then the overall effect of forces on it must be zero.
- Forces are only needed to change motion, not to maintain motion.
- When objects appear to slow down naturally, this is usually because of friction or air resistance acting as forces.
- This law helps explain why objects behave differently in low-friction environments, such as ice or space.
A puck sliding on smooth ice keeps moving for a long time because very little force is acting to stop it.
What "Constant Velocity" Really Means
- Because velocity is a vector, it changes if either:
- the speed changes, or
- the direction changes.
- So an object moving at constant speed in a circle is not at constant velocity, it is accelerating (because its direction is changing).
As Earth orbits the Sun, it changes direction continuously, so its velocity changes and therefore it must experience a force (gravity).
- "Constant speed" does not guarantee "constant velocity."
- Many exam mistakes come from forgetting that direction matters.
Inertia
Inertia
Inertia is the tendency of an object to resist changes in its motion.
- Heavier objects resist changes more strongly than lighter objects.
- This resistance explains why it is harder to stop or turn heavy objects.
Newton's Second Law: Resultant Force Determines Acceleration
Newton’s Second Law
Newton’s Second Law of Motion states that the resultant force on an object is equal to the mass of the object multiplied by its acceleration.
- This law explains what happens when forces are not balanced.
- A larger force causes a larger change in motion.
- Objects with greater mass require larger forces to change their motion.
- Acceleration shows how quickly velocity changes.
- The acceleration occurs in the same direction as the resultant force.
- Newton's second law links force and acceleration:
$$F_{\text{resultant}} = m a$$
where:
- $F_{\text{resultant}}$ is the net force on the object (in newtons, N)
- $m$ is the mass (in kilograms, kg)
- $a$ is the acceleration (in m s$^{-2}$)
A football accelerates more than a heavy suitcase when pushed with the same force.
Direction Matters
- Acceleration is in the same direction as the resultant force.
- If the forces balance (resultant force is zero), then $a=0$ and the object stays at rest, or continues at constant velocity.
A box of mass $5\,\text{kg}$ is pulled with a horizontal force of $20\,\text{N}$. Friction is $8\,\text{N}$ opposite the motion.
Resultant force: $F_{\text{res}} = 20 - 8 = 12\,\text{N}$ (to the right)
Acceleration:
$$a = \frac{F_{\text{res}}}{m} = \frac{12}{5} = 2.4\,\text{m s}^{-2}$$
So the box accelerates to the right at $2.4\,\text{m s}^{-2}$.
- Always compute the resultant force first (including signs/directions), then apply $F=ma$.
- Many errors come from using the applied force instead of the net force.
Newton's Third Law: Forces Come In Equal And Opposite Pairs
Newton’s Third Law
When object A exerts a force on object B, object B exerts an equal-magnitude force on object A in the opposite direction.
- According to Newton's third law, when object A exerts a force on object B, object B exerts a force of equal magnitude on object A in the opposite direction.
- These are called a Newton's third-law pair.
- When one object pushes or pulls, the other responds immediately.
- The forces are equal in size and opposite in direction.
- Each force acts on a different object.
- Because the forces act on different objects, they do not cancel.
When a racket hits a tennis ball, the racket pushes the ball forward, and the ball pushes the racket backward.
- In the MYP eAssessment of M23, Question 6a required explaining the motion of a balloon using Newton’s laws.
- When air is released, the balloon pushes air backwards, and the air exerts an equal and opposite force on the balloon, causing it to accelerate forwards (Newton’s third law).
- This unbalanced force results in acceleration in the opposite direction to the expelled air (Newton’s second law).
- For questions like this, explanations must clearly link force, direction, and acceleration, not just state that the balloon moves forward.
Key Properties Of Third-Law Pairs
- It is the same type of force (both normal, both gravitational, both tension, etc.)
- It has equal size and opposite direction
- It acts on different objects
- Balanced forces on the same object are not a Newton's third-law pair.
- Third-law pairs act on two different objects.
- For example, for a book resting on a table:
- Forces on the book: weight $W$ downward and normal reaction $N$ upward. These can balance, so the book is in equilibrium.
- But $W$ and $N$ are not a third-law pair because they are different types and act on the same object.
- The correct third-law pairs are:
- The table's normal force on the book (up) pairs with the book's normal force on the table (down).
- The Earth's gravitational pull on the book (down on the book) pairs with the book's gravitational pull on the Earth (up on the Earth).
- The forces are equal, but Earth's acceleration is too small to notice.
Weight, Mass, And Falling Objects
In everyday language, "weight" and "mass" are often mixed up, but in physics they are different:
Weight
The gravitational force acting on an object due to a gravitational field.
Mass
The amount of material in a body or object.
Near Earth's surface:
$$W = mg$$
where $g \approx 9.8\,\text{m s}^{-2}$.
Why Earth Does Not Move Noticeably
- The force an object exerts on Earth is equal to the force Earth exerts on the object.
- Earth has a very large mass.
- Because of its large mass, Earth’s motion change is extremely small and not noticeable.
- Why does an object remain at rest unless a force acts on it?
- Explain how force and mass together affect acceleration.
- Describe an action–reaction force pair when a person walks.
- Why do action–reaction forces not cancel each other out?
- Identify the Newton’s third-law force pair when a runner starts a race.
