Newton's Laws of Motion: Quick Revision

A brief note on Newton's Laws of Motion. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• First law. A body keeps its velocity unless a net force acts. This is inertia, and mass measures it. A force changes motion; it is not needed to keep motion going.
• Second law. $F_{\text{net}} = ma$, or more generally $F = \dfrac{\Delta p}{\Delta t}$, with momentum $p = mv$.
• Impulse. $J = F\,\Delta t = \Delta p$. A longer stopping time means a smaller force for the same change of momentum.
• Third law. Forces come in pairs: equal, opposite, the same kind, and acting on different bodies.
• Conservation of momentum. With no outside force, the total momentum of a system stays the same.

The facts at a glance

A worked example

A garden hose sprays $0.75\ \text{kg}$ of water every second at $12\ \text{m/s}$ straight at a wall. The water stops at the wall. What force does the water exert on the wall?

1. Momentum each second. The wall stops $0.75\ \text{kg} \times 12\ \text{m/s} = 9.0\ \text{kg m/s}$ of momentum every second.
2. Force. Force is momentum changed per second: the wall pushes the water with $9.0\ \text{N}$.
3. Third law. So the water pushes the wall with $9.0\ \text{N}$.

Practice with new numbers

A program to try

The program works out a head-on crash: the common velocity and the impulse on each car.

Mistakes to avoid

• A force to keep things moving. A body at a steady velocity needs no net force.
• Forgetting signs. Momentum and velocity are vectors. A bounce or a head-on collision needs a minus sign.
• Third-law pairs on one body. The weight of a book and the table's push on it are not a pair.
• Conserving kinetic energy when bodies stick. Only momentum is conserved there.
• Grams in the formulas. Change grams to kilograms first.

Check yourself

1. A $1350\ \text{kg}$ car speeds up steadily from $8.0\ \text{m/s}$ to $20\ \text{m/s}$ in $4.8\ \text{s}$. What net force acts on it?

2. A steady force of $36\ \text{N}$ acts for $0.25\ \text{s}$ on a $1.5\ \text{kg}$ trolley at rest. What is its speed afterwards?

3. Two skaters, of $54\ \text{kg}$ and $72\ \text{kg}$, stand together on ice and push apart. The lighter one moves off at $2.0\ \text{m/s}$. How fast does the other move?

4. A horse pulls a cart, and the cart pulls the horse back just as hard. How can they move at all?

5. Why does a cricketer draw the hands back when catching a fast ball?