Newton's laws, force and momentum
Why soft hands catch an egg
- Catch a thrown egg with stiff hands and it breaks; with soft, giving hands it survives.
- Both stop the same egg — but soft hands take more time, so the force is smaller.
- That link between force, momentum and time is the heart of dynamics.
Momentum
- Momentum $p = mv$ — mass times velocity. It is a vector (same direction as $v$).
- Unit: $\dfrac{\text{kg}\cdot\text{m}}{\text{s}}$, the same as $\text{N}\cdot\text{s}$.
A $2.0\ \text{kg}$ ball moves at $3.0\ \dfrac{\text{m}}{\text{s}}$. What is its momentum?
$p = mv = 2.0 \times 3.0 = 6.0\ \dfrac{\text{kg}\cdot\text{m}}{\text{s}}$.
Momentum is a vector.
Yes — $p = mv$ points the same way as the velocity, so it has a direction.
Force = rate of change of momentum
- Newton's second law, in full: $F = \dfrac{\Delta p}{\Delta t}$.
- When the mass is constant this becomes the familiar $F = ma$.
In its general form, Newton's second law says the resultant force equals the:
$F = \dfrac{\Delta p}{\Delta t}$ — the rate of change of momentum. For constant mass this is $F = ma$.
Impulse and collisions
- The average force in a hit is $F = \dfrac{\Delta p}{\Delta t}$ — change in momentum over contact time.
- A longer contact time means a smaller force (the egg, a crumple zone, a bent knee on landing).
- Energy link: $E_{\text{k}} = \dfrac{p^{2}}{2m}$.
Catching an egg with soft hands makes the contact time longer, which makes the average force ____.
Same change in momentum over a longer time means a smaller force: $F = \dfrac{\Delta p}{\Delta t}$.
Newton's first law
- With zero resultant force, an object stays at rest or moves at constant velocity.
- You lurch forward when a bus brakes because your body "wants" to keep moving — inertia.
Newton's second law
- A resultant force gives an acceleration: $F = ma$.
- The acceleration always points the same way as the resultant force.
Newton's third law
- If A pushes B, then B pushes A back — equal in size, opposite in direction.
- The two forces act on different objects and are the same type of force.
A book's weight and the table's upward push are not a third-law pair — they act on the same object (the book) and are different types of force.
Which pair are genuine Newton's third-law partners?
The contact forces "book on table" and "table on book" are equal, opposite, same type, and act on different objects. The book's weight and the table's push act on the same object, so they are not a pair.
Select all the true statements about a Newton's third-law pair of forces.
A third-law pair is equal, opposite, the same type, and acts on two different objects — never on the same one.
Weight
- Weight is the gravitational force on a mass: $W = mg$.
- Mass is the same everywhere; weight changes with $g$ (less on the Moon).
What is the weight of a $5.0\ \text{kg}$ bag near Earth's surface? (Use $g = 9.81\ \dfrac{\text{m}}{\text{s}^2}$.)
$W = mg = 5.0 \times 9.81 \approx 49\ \text{N}$.
You've got it
- momentum $p = mv$ (a vector); force $F = \dfrac{\Delta p}{\Delta t} = ma$
- a longer contact time gives a smaller force (impulse)
- third-law pairs are equal, opposite, same type, different objects; $W = mg$