Chapter 16: Forces, Newton's laws and moments

The chapter problem: can the crate be loaded onto the lorry?

A delivery firm is loading a crate onto a lorry. The crate has a mass of $45$ kg. Take the acceleration due to gravity as $g = 9.8$ m s$^{-2}$.

The loading bay holds every situation in this chapter. The crate sits on the warehouse floor. Two workers push it along the floor. A ramp leads up to the lorry, and a rope runs over a pulley at the top of the ramp. The crate can be held on the ramp, or let go on a rough ramp. Finally, a uniform plank rests on two trestles and takes the crate's weight.

By the end of the chapter you will answer all of this. You will find the acceleration when the workers push the crate. You will find the weight of the crate and separate it from its mass. You will find the tension in a rope and the force the ramp pushes back with. You will decide whether the crate slides on a rough ramp. You will find the force each trestle carries.

First contact — no working needed yet. Look at a heavy box on a flat floor. Draw the box and add an arrow for every push or pull you think acts on it. Then push the box gently with one hand and keep it moving at a steady speed. Predict what happens to the arrows when the box moves at a steady speed. Write one sentence to say whether the pushes still balance.

By the end of this chapter you will be able to

• explain what a force is, and list the forces that act in common situations;
• draw a clear force diagram for a body, and use Newton's first law;
• use Newton's second law, $F = ma$, to find a force, a mass or an acceleration;
• explain the difference between mass and weight, and use $W = mg$;
• describe motion under gravity, including terminal velocity and apparent weight;
• state Newton's third law and use it to explain action–reaction pairs;
• solve connected-particles problems, where two bodies are joined by a string over a pulley;
• resolve a force into two perpendicular components and use them for equilibrium;
• find a resultant force and use it for motion in a plane;
• use the model $F \leq \mu R$ for friction, and decide whether a body slides;
• take moments about a point and use the principle of moments for a body in equilibrium.

Where it is used

Forces explain why things speed up, slow down, turn or stay still. Engineers use them to size a crane, a bridge or a lift. Designers use moments to place a load so a shelf does not tip. The same ideas return in the study of projectiles and circular motion, and they sit behind every machine that carries a load.

Your turn to connect it

Think of a time you pushed, pulled, carried or balanced something heavy. It could be a wheelbarrow, a door, a shopping trolley or a friend on a seesaw. Write down the forces you felt and which way each one pointed. Say which force you had to overcome to start the movement, and which one kept it going at a steady speed. Keep your answer for the Review.

Roadmap

1. 16.1 Force and Newton's first law
2. 16.2 Newton's second law and F = ma
3. 16.3 Weight and motion under gravity
4. 16.4 Newton's third law, equilibrium and connected particles
5. 16.5 Resolving forces and coplanar equilibrium
6. 16.6 Resultant forces and dynamics in a plane
7. 16.7 Friction and the model F <= mu R
8. 16.8 Moments in static contexts
9. Review