Newton's laws and forces

What the exam asks

Expect a described scenario and a diagram, and a question about which forces act, what the net force is, or how the acceleration changes when one thing is altered. The commonest items are: pick the correct free body diagram from four, find the acceleration of a block on an incline or of two connected masses, decide whether a body slips, and read apparent weight in a lift. The trap that catches most candidates is an invented force: a forward force on a block that is coasting, a force of motion, or centrifugal force. Test every arrow against the rule that a force is gravity or a contact, and the wrong options usually eliminate themselves. The second trap is the incline angle: the perpendicular component carries the cosine and the along-slope component carries the sine, and swapping them is the single commonest arithmetic error in Section III physics.

This topic covers what forces do to motion, and it is examined almost entirely through one skill: drawing a correct free body diagram and resolving it. F = ma and F = mg are the whole toolkit. Everything else is bookkeeping.

The free body rule is worth stating as a rule, because it settles most questions before any arithmetic starts. A force on a body is either gravity or something touching it. That is the complete list. A push that has ended is not a force, motion is not a force, and there is no force carrying the body along. Most wrong answers on inclined planes are an invented force, and the candidate who can refuse to draw one has already done the hard part.

The rest is technique. On an incline, tilt your axes to match the slope so that the acceleration lies along one of them, and resolve the weight rather than everything else: mg sin θ down the slope, mg cos θ into it. For connected masses, treat the whole assembly as one body to get the acceleration, then isolate a single body to get the tension. Equilibrium means the net force is zero, which includes constant velocity as well as rest.

What to hold

• Every force on a free body diagram is either gravity or something in contact with the body. If you cannot name what is touching it, the force does not exist.
• Newton's third law pairs act on two different bodies, so they can never cancel each other. Forces only cancel when they act on the same body.
• The normal force is not always mg. It is whatever the surface has to push to stop the body sinking into it, and on an incline or in an accelerating lift that is not the weight.
• On an incline of angle θ the weight resolves into mg sin θ down the slope and mg cos θ perpendicular to it, so the normal force is mg cos θ.
• A frictionless block on an incline accelerates at g sin θ, which does not contain the mass, so a heavy block and a light one slide identically.
• Static friction is not μN. It takes whatever value is needed to prevent sliding, up to a maximum of μs N, and only then does the body break away.
• Kinetic friction is μk N and points against the direction of sliding, not against the applied force.
• For connected masses, the acceleration comes fastest from treating the whole system as one body, because tension is internal and cancels out.
• Tension is found by isolating one body after the acceleration is known, and in an ideal light string over a frictionless pulley it is the same throughout.
• Equilibrium means zero net force, which covers a body at constant velocity just as much as a body at rest. Terminal velocity is an equilibrium.
• Apparent weight is the normal force, so it rises when the lift accelerates upwards and falls when it accelerates downwards, whichever way the lift happens to be travelling.
• Choose axes to suit the problem: along and perpendicular to the slope on an incline, so the acceleration has only one component and the perpendicular direction is a clean equilibrium.