Dynamics

• Resultant force = rate of change of momentum. Third-law forces act on different bodies. Momentum is always conserved in an interaction with no resultant external force; kinetic energy only in an elastic one.
• Resultant force = rate of change of momentum. Third-law pairs: different bodies, same type. Momentum always conserved with no resultant external force; kinetic energy only if elastic.

• 3.1.1 I can understand — understand that mass is the property of an object that resists change in motion
• 3.1.2 I can recall — recall F = ma and solve problems using it, understanding that acceleration and resultant force are always in the same direction
• 3.1.3 I can define — define and use linear momentum as the product of mass and velocity
• 3.1.4 I can define — define and use force as rate of change of momentum
• 3.1.5 I can state — state and apply each of Newton's laws of motion
• 3.1.6 I can describe — describe and use the concept of weight as the effect of a gravitational field on a mass and recall that the weight of an object is equal to the product of its mass and the acceleration of free fall
• 3.2.1 I can — show a qualitative understanding of frictional forces and viscous/drag forces including air resistance (no treatment of the coefficients of friction and viscosity is required, and a simple model of drag force increasing as speed increases is sufficient)
• 3.2.2 I can describe — describe and explain qualitatively the motion of objects in a uniform gravitational field with air resistance
• 3.2.3 I can understand — understand that objects moving against a resistive force may reach a terminal (constant) velocity
• 3.3.1 I can state — state the principle of conservation of momentum
• 3.3.2 I can — apply the principle of conservation of momentum to solve simple problems, including elastic and inelastic interactions between objects in both one and two dimensions (knowledge of the concept of coefficient of restitution is not required)
• 3.3.3 I can recall — recall that, for an elastic collision, total kinetic energy is conserved and the relative speed of approach is equal to the relative speed of separation
• 3.3.4 I can understand — understand that, while momentum of a system is always conserved in interactions between objects, some change in kinetic energy may take place

Units, significant figures and working are part of the physics. Give a calculated answer to the same number of significant figures as the least precise data, or one more; keep full precision in the working and round only at the end; write the unit with every final answer. A fifth of the qualification is experimental: Papers 3 and 5 test AO3 only, and their questions may be set in contexts outside the syllabus content, so the practical work in this chapter is set out as method, recording, graphs and uncertainties rather than as theory.

• “The weight of a book on a table and the normal contact force on it are a third-law pair.” Correct They are equal and opposite only because the book is in equilibrium (first law). Both act on the book, and one is gravitational while the other is a contact force. A third-law pair acts on two different bodies and is the same type of force: the weight’s partner is the book’s pull on the Earth. (Card E.)
• “I put the driving force into F = ma.” Correct F is the resultant of all the forces on the body, added with signs. A 3000 N driving force against 1200 N of resistance gives a resultant of 1800 N. (Card B.)
• “The acceleration is in the direction the object is moving.” Correct The acceleration is always in the direction of the resultant force. A braking car moves forwards with a backward acceleration; a skydiver whose parachute has just opened moves down with an upward acceleration. (Cards B and H.)
• “The ball hit the wall at 20 m s−1 and bounced back at 15 m s−1, so its momentum changed by m(20 − 15).” Correct Momentum is a vector. With one direction positive, the velocities are −20 and +15, and Δp = m(15 − (−20)) = m × 35. (Card C.)
• “At terminal velocity there are no forces on the skydiver.” Correct The weight and the drag are both still acting; they are balanced, so the resultant is zero and the velocity is constant. (Card I.)
• “In an inelastic collision, momentum is lost.” Correct Momentum is conserved in every interaction with no resultant external force. What an inelastic collision does not conserve is kinetic energy; the total energy is still conserved. (Cards J and M.)
• “In two dimensions, the momentum before equals the sum of the momenta after, so I add the magnitudes.” Correct Momentum is conserved in each of two perpendicular directions separately. Resolve, write one equation per direction, then recombine. (Card K.)
• “I put the driving force into F = ma.” Repair F is the resultant of all the forces on the body, added with signs along the line of motion.
• “The acceleration is in the direction of motion.” Repair It is in the direction of the resultant force, which may oppose the velocity (a braking car; a skydiver as the parachute opens).
• “Weight and the normal contact force on a book are a third-law pair.” Repair Both act on the book and they are different types of force; they balance by the first law. The weight’s partner is the book’s pull on the Earth.
• “Third-law forces cancel, so nothing can ever accelerate.” Repair They act on different bodies, so they never cancel on one body. Whether a body accelerates depends only on the forces on it.
• “My weight is 70 kg.” Repair 70 kg is a mass. The weight is 70 × 9.81 = 687 N.
• “For a rebound, Δp = m(20.0 − 15.0).” Repair Velocities are signed. With away from the wall positive, Δp = m(15.0 − (−20.0)) = 35.0m.
• “The scales in the lift read my weight.” Repair They read the normal contact force, which equals the weight only when the vertical acceleration is zero.
• “At terminal velocity no forces act.” Repair The weight and the drag are both acting and are balanced; the resultant is zero.
• “When the parachute opens the skydiver goes up.” Repair The acceleration is upwards; the velocity is still downwards and decreasing.
• “Friction always opposes the motion of the object.” Repair It opposes the relative motion of the surfaces. On a walking foot or a driven tyre it points forwards.
• Asked to state the principle of conservation of momentum: “Momentum is always conserved.” Repair As a statement of the principle this is incomplete: the total momentum of a system of interacting bodies remains constant provided no resultant external force acts on the system. The syllabus’s phrase in 3.3.4, momentum “always conserved in interactions between objects”, is true of the interacting system; when you state the principle, write the condition that makes it so.
• “In an inelastic collision momentum is lost.” Repair Momentum is conserved in every collision with no resultant external force; kinetic energy is what is not conserved.
• “In two dimensions I add the magnitudes of the momenta.” Repair Momentum is a vector. Conserve each perpendicular component separately, or draw a closed vector triangle.
• “For an elastic collision, approach speed = u1 + u2.” Repair With signed velocities, u1 − u2 = v2 − v1. The signs turn the subtraction into a sum only when the bodies move towards each other.

• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.
• Three conditions to write every time. \(F = ma\) uses the resultant force and a constant mass. Conservation of momentum needs no resultant external force. The relative-speed equality holds only for an elastic collision.
• Largest source of uncertainty, and an improvement. The after-collision velocity: the joined trolleys travel some distance to gate 2, and friction acts on them all the way, while the runway was compensated for trolley A alone. Improvements that address it: move gate 2 as close to the collision point as the card allows; re-compensate the runway with both trolleys joined; or use a motion sensor and data logger in place of the gates so that the velocity is found immediately after the impact. (Name the physical cause: an answer that blames the experimenter in general identifies nothing that an improvement could address.)
• Interleave with the chapters that use this one. Topic 4 adds upthrust to the falling-ball force diagram and makes equilibrium a zero resultant force and torque: re-answer the terminal-velocity studio with upthrust included. Topic 5 turns the kinetic-energy checks here into work done: re-answer worked example 4 in terms of work done. Topic 12 applies F = ma to motion in a circle, and Topic 13 treats g as a field strength: re-answer the lift question when you reach each. Recalling a topic inside a new context is worth more than another pass over this chapter on its own; at A Level, Paper 4 assumes the whole of the AS content, so nothing here is ever finished with.

• Cambridge International AS & A Level Physics 9702 has five components. Topic 3 is AS Level content, so it is examined in Papers 1, 2 and 3. AS Level content: examined in Paper 1 (multiple choice), Paper 2 (AS structured) and, as practical context, Paper 3. Assumed knowledge for Papers 4 and 5. AS Level candidates take Papers 1, 2 and 3; A Level candidates take all five, either staged over two years (Papers 1–3 in year one, Papers 4 and 5 in year two) or together in one series. Examinations are available in the June and November series, and in March in India.
• Across both the AS Level and the A Level the assessment objectives are weighted AO1 40% (knowledge and understanding), AO2 40% (handling, applying and evaluating information) and AO3 20% (experimental skills and investigations). AS candidates are graded a–e; A Level candidates A*–E. The Data and formulas sheet is printed as page 2 of Papers 1 and 2 and as pages 2 and 3 of Paper 4: it gives the constants and a short list of formulas. Every other equation in this chapter is one the syllabus says you must recall, and this chapter says which is which.
• A multiple-choice item on dynamics can turn on a single discrimination: which force is the resultant, which pair of forces is a third-law pair, which way the acceleration points, or whether kinetic energy is conserved. Structured questions ask you to define momentum or force in terms of momentum, state Newton’s laws or the principle of conservation of momentum with its condition, explain the motion of a falling object with air resistance, and sketch its velocity–time graph.
• The calculations are F = ma with a resultant force (including lifts and connected bodies), F = Δp/Δt for a rebound or a jet, and conservation of momentum in one and two dimensions with a kinetic-energy check. No Topic 3 equation is on the Data and formulas sheet: F = ma, p = mv, F = Δp/Δt, W = mg and EK = ½mv2 must all be recalled. Only the value g = 9.81 m s−2 is given.
• The laboratory context is a collision between trolleys on a friction-compensated runway, timed with light gates: the card length and the gate times give the velocities, and the momentum before and after are compared against their combined percentage uncertainty. A falling object is the other: the terminal velocity of a ball in a liquid, timed between markers, with a check that the speed really has become constant. In both, a short time measurement tends to carry the largest percentage uncertainty.
• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.